6th Grade Math Workbook

Chapter Chapter X1 Resource Resource Masters Masters

Course 11 Course

Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Study Guide and Intervention Workbook Study Guide and Intervention Workbook (Spanish) Practice: Skills Workbook Practice: Skills Workbook (Spanish) Practice: Word Problems Workbook Practice: Word Problems Workbook (Spanish) Reading to Learn Mathematics Workbook

0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5

Answers for Workbooks The answers for Chapter 1 of these workbooks can be found in the back of this Chapter Resource Masters booklet.

Spanish Assessment Masters Spanish versions of forms 2A and 2C of the Chapter 1 Test are available in the Glencoe Mathematics: Applications and Concepts Spanish Assessment Masters, Course 1 (0-07-860095-2).

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge; and be used solely in conjunction with Glencoe Mathematics: Applications and Concepts, Course 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240 Mathematics: Applications and Concepts, Course 1 Chapter 1 Resource Masters

ISBN: 0-07-846545-1 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03

CONTENTS Vocabulary Builder .............................vii Family Letter ............................................ix Family Activity ........................................x Lesson 1-1 Study Guide and Intervention ............................1 Practice: Skills ....................................................2 Practice: Word Problems....................................3 Reading to Learn Mathematics..........................4 Enrichment .........................................................5

Lesson 1-2 Study Guide and Intervention ............................6 Practice: Skills ....................................................7 Practice: Word Problems....................................8 Reading to Learn Mathematics..........................9 Enrichment .......................................................10

Lesson 1-3 Study Guide and Intervention ..........................11 Practice: Skills ..................................................12 Practice: Word Problems..................................13 Reading to Learn Mathematics........................14 Enrichment .......................................................15




Chapter 1 Assessment

Lesson 1-5

Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter

Study Guide and Intervention ..........................21 Practice: Skills ..................................................22 Practice: Word Problems..................................23 Reading to Learn Mathematics........................24 Enrichment .......................................................25

Standardized Test Practice Student Recording Sheet ..........................................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A32


iii

1 Test, Form 1 ..............................41–42 1 Test, Form 2A ............................43–44 1 Test, Form 2B ............................45–46 1 Test, Form 2C............................47–48 1 Test, Form 2D............................49–50 1 Test, Form 3 ..............................51–52 1 Extended Response Assessment ...53 1 Vocabulary Test/Review...................54 1 Quizzes 1 & 2..................................55 1 Quizzes 3 & 4..................................56 1 Mid-Chapter Test .............................57 1 Cumulative Review..........................58 1 Standardized Test Practice........59–60

Teacher’s Guide to Using the Chapter 1 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 1 Resource Masters includes the core materials needed for Chapter 1. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the Glencoe Mathematics: Applications and Concepts, Course 1, TeacherWorks CD-ROM.

Vocabulary Builder Pages vii-viii include a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. When to Use Give these pages to students before beginning Lesson 1-1. Encourage them to add these pages to their mathematics study notebook. Remind them to add definitions and examples as they complete each lesson.

Family Letter and Family Activity Page ix is a letter to inform your students’ families of the requirements of the chapter. The family activity on page x helps them understand how the mathematics students are learning is applicable to real life. When to Use Give these pages to students to take home before beginning the chapter.

Study Guide and Intervention There is one Study Guide and Intervention master for each lesson in Chapter 1. When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.

Practice: Skills

There is one master for each lesson. These provide practice that more closely follows the structure of the Practice and Applications section of the Student Edition exercises. When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson.

Practice: Word Problems

There is one master for each lesson. These provide practice in solving word problems that apply the concepts of the lesson. When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson.

Reading to Learn Mathematics

One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques. When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students.

iv

There is one extension master for each lesson. These activities may extend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. These are not written exclusively for honors students, but are accessible for use with all levels of students.

• A Vocabulary Test, suitable for all students, includes a list of the vocabulary words in the chapter and ten questions assessing students’ knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet.

When to Use These may be used as extra credit, short-term projects, or as activities for days when class periods are shortened.

• Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter.

Enrichment

Intermediate Assessment

• A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and freeresponse questions.

Assessment Options The assessment masters in the Chapter 1 Resources Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use.

Continuing Assessment • The Cumulative Review provides students an opportunity to reinforce and retain skills as they proceed through their study of Glencoe Mathematics: Applications and Concepts, Course 1. It can also be used as a test. This master includes free-response questions.

Chapter Assessment Chapter Tests • Form 1 contains multiple-choice questions and is intended for use with basic level students.

• The Standardized Test Practice offers continuing review of pre-algebra concepts in various formats, which may appear on the standardized tests that they may encounter. This practice includes multiplechoice, short response, grid-in, and extended response questions. Bubble-in and grid-in answer sections are provided on the master.

• Forms 2A and 2B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. • Forms 2C and 2D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with axes are provided for questions assessing graphing skills.

Answers • Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 46-47. This improves students’ familiarity with the answer formats they may encounter in test taking.

• Form 3 is an advanced level test with free-response questions. Grids without axes are provided for questions assessing graphing skills. All of the above tests include a free-response Bonus question.

• Detailed rubrics for assessing the extended response questions on page 47 are provided on page A2.

• The Extended-Response Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment.

• The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. • Full-size answer keys are provided for the assessment masters in this booklet.

v

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics This is an alphabetical list of new vocabulary terms you will learn in Chapter 1. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add this page to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term

Found on Page

Definition/Description/Example

algebra [AL-juh-bruh]

algebraic [AL-juh-BRAY-ihk] expression area

base

composite [com-PAH-zit] number cubed

divisible

equals sign

equation [ih-KWAY-zhuhn] evaluate

even

© Glencoe/McGraw-Hill

vii

Mathematics: Applications and Concepts, Course 1

Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Vocabulary Builder Vocabulary Term

Found on Page

(continued) Definition/Description/Example

exponent [ex-SPOH-nuhnt] factor

formula [FOR-myuh-luh] numerical expression

odd

order of operations

power

prime factorization

prime number

solution

solve

squared

variable [VAIR-ee-uh-buhl]


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: classes because they do Students are often frustrated in math ial in the real world. In our not see how they can use the mater mathematics beyond the math class, however, we try to take realize and appreciate its classroom to a point where students importance in their daily lives. Algebra, your child will In Chapter 1, Number Patterns and patterns, prime factors, the be learning about problem solving, ressions, and powers and order of operations, variables and exp equations and find the area exponents. Your child will also solve pter, your child will of rectangles. In the study of this cha assignments and activities complete a variety of daily classroom . and possibly produce a chapter project it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 1 to the real world. You math we will be learning in Chapter line Study Tools for selfmay also wish to log on to the On dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any other study help at www.msmath1.n contact me at school. questions or comments, feel free to Sincerely,

Signature of Parent or Guardian ______________________________________ Date ________


ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Using Patterns Draw the next three figures in each pattern. You can take turns with a family member. 1.

2.

Find a pattern in your home or neighborhood. Sketch at least the first three figures in the pattern. Have a family member draw the next three figures in the pattern.

Have a family member find a pattern in your home or neighborhood. Have him or her sketch at least the first three figures. Draw the next three figures in the pattern.

2. Sample answer:

x

1. Sample answer:



NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention A Plan for Problem Solving When solving problems, it is helpful to have an organized plan to solve the problem. The following four steps can be used to solve any math problem. 1 Explore – Read and get a general understanding of the problem. 2 Plan – Make a plan to solve the problem and estimate the solution. 3 Solve – Use your plan to solve the problem. 4 Examine – Check the reasonableness of your solution. SPORTS The table shows the number of field goals made by Henry

Name

3-Point Field Goals

Brad

216

Chris

201

Denny

195

Explore

You know the number of field goals made. You need to find how many more field goals Brad made than Denny.

Plan

Use only the needed information, the goals made by Brad and Denny. To find the difference, subtract 195 from 216.

Solve

216 2 195 5 21; Brad made 21 more field goals than Denny.

Examine Check the answer by adding. Since 195 1 21 5 216, the answer is correct.

1. During which step do you check your work to make sure your answer is correct?

2. Explain what you do during the first step of the problem-solving plan.

SPORTS For Exercises 3 and 4, use the field goal table above and the

four-step plan. 3. How many more field goals did Chris make than Denny?

4. How many field goals did the three boys make all together?


1


Lesson 1–1

High School’s top three basketball team members during last year’s season. How many more field goals did Brad make than Denny?

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills A Plan for Problem Solving Use the four-step plan to solve each problem. 1. GEOGRAPHY The president is going on a campaign trip to California, first flying about 2,840 miles from Washington D.C. to San Francisco and then another 390 to Los Angeles before returning the 2,650 miles back to the capital. How many miles will the president have flown?

2. POPULATION In 1990, the total population of Sacramento, CA was 369,365. In 2000, its population was 407,018. How much did the population increase? 3. MONEY The Palmer family wants to purchase a DVD player in four equal installments of $64. What is the cost of the DVD player?

4. COMMERCIALS The highest average cost of a 30-second commercial in October, 2002 is $455,700. How much is this commercial worth per second? 5. A tennis tournament starts with 16 people. The number in each round is shown in the table. How many players will be in the 4th round?

1st Round 2nd Round 3rd Round 4th Round

16 8 4 ?

Complete the pattern. 6. 2, 4, 8, 16, 32, …

7. 16, 19, 22, 25, 28, 31, …

8. 81, 72, 63, 54, …

9. 5, 15, 20, 30, 35, 45, 50, …

10. 50, 40, 45, 35, 40, 30, 35, ___, ___, ___, ___

11. 6, 12, 18, ___, ___, ___, ___


2


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems A Plan for Problem Solving Use the four-step plan to solve each problem. GEOGRAPHY For Exercises 1 and 2, use the poster information about Crater Lake National Park in Oregon.

Visit Crater Lake National Park 90 miles of trails 26 miles of shoreline Boat tours available Open 24 hours

1. How many more miles of trails are there than miles of shoreline in Crater Lake National Park?

2. How many miles is it from Klamath Falls to Crater Lake National Park?

3. SPORTS Jasmine swims 12 laps every afternoon, Monday through Friday. How many laps does she swim in one week?

4. SPORTS Samantha can run one mile in 8 minutes. At this rate, how long will it take for her to run 5 miles?

5. SPORTS On a certain day, 525 people signed up to play softball. If 15 players are assigned to each team, how many teams can be formed?

6. PATTERNS Complete the pattern: 5, 7, 10, 14, ___, ___, ___

7. SHOPPING Josita received $50 as a gift. She plans to buy two cassette tapes that cost $9 each and a headphone set that costs $25. How much money will she have left?

8. BUS SCHEDULE A bus stops at the corner of Elm Street and Oak Street every half hour between 9 A.M. and 3 P.M. and every 15 minutes between 3 P.M. and 6 P.M. How many times will a bus stop at the corner between 9 A.M. and 6 P.M.?


3


Lesson 1–1

Directions from Klamath Falls: Take U.S. Highway 97 north 21 miles, then go west on S.R. 62 for 29 miles.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics A Plan for Problem Solving Pre-Activity Read the introduction at the top of page 6 in your textbook. Write your answers below. 1. How many pennies are in a row that is one mile long? (Hint: There are 5,280 feet in one mile.)

2. Explain how to find the value of the pennies in dollars. Then find the value.

3. Explain how you could use the answer to Exercise 1 to estimate the number of quarters in a row one mile long.

Reading the Lesson 4. Think of how you use the word explore. When was the last time you did some exploring of your own? Write a definition of the word explore that matches what you did during your exploration. Or maybe you would like to consider someone from history who was an explorer. Write a definition of the word explore that matches what that person did.

5. If you were doing an exploratory, when do you think this would happen? Before or after the thing you were exploring?

6. In the four-step plan for problem solving, think about the term examine. Does examine come before or after the solution? (Hint: What are you examining?)

Helping You Remember 7. Think about the four steps in the problem-solving plan: Explore, Plan, Solve, Examine. Write a sentence about something you like to help you remember the four words. For example, “I like to explore caves.”


4


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Using a Reference Point There are many times when you need to make an estimate in relation to a reference point. For example, at the right there are prices listed for some school supplies. You might wonder if $5 is enough money to buy a small spiral notebook and a pen. This is how you might estimate, using $5 as the reference point. • The notebook costs $1.59 and the pen costs $3.69. • $1 1 $3 5 $4. I have $5 2 $4, or $1, left. • $0.59 and $0.69 are each more than $0.50, so $0.59 1 $0.69 is more than $1. So $5 will not be enough money.

Spira l No Large tebook Smal $2.29 l $1.5 9

Three -Ri Binde ng r $4.75

1. Jamaal has $5. Will that be enough money to buy a large spiral notebook and a pack of pencils?

2. Andreas wants to buy a three-ring binder and two packs of filler paper. Will $7 be enough money?

3. Rosita has $10. Can she buy a large spiral notebook and a pen and still have $5 left?

Filler P Pack aper of 10 $1.29 0

Ball-P oint Pen $3.69

4. Kevin has $10 and has to buy a pen and two small spiral notebooks. Will he have $2.50 left to buy lunch?

5. What is the greatest number of erasers you can buy with $2?

Penc Pack ils of 1 $2.39 0

6. What is the greatest amount of filler paper that you can buy with $5?

7. Lee bought three items and spent exactly $8.99. What were the items?

Erase r $0.55

8. Select five items whose total cost is as close as possible to $10, but not more than $10. © Glencoe/McGraw-Hill

5


Lesson 1–1

Use the prices at the right to answer each question.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Divisibility Patterns A whole number is divisible by another number if the remainder is 0 when the first is divided by the second. A whole number is even if it is divisible by 2. A whole number is odd if it is not divisible by 2. Rule

Examples

A whole number is divisible by: • 2 if the ones digit is divisible by 2. • 3 if the sum of the digits is divisible by 3. • 4 if the number formed by the last two digits is divisible by 4. • 5 if the ones digit is 0 or 5. • 6 if the number is divisible by both 2 and 3. • 9 if the sum of the digits is divisible by 9. • 10 if the ones digit is 0.

2, 4, 6, 8, 10, 12, 14, 16, … 3, 6, 9, 12, 15, 18, 21, 24, … 4, 8, 12, …, 104, 108, 112, … 5, 10, 15, 20, 25, 30, … 6, 12, 18, 24, 30, 36, … 9, 18, 27, 36, 45, … 10, 20, 30, 40, 50, …

Tell whether 112 is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd. 2: Yes; the ones digit is divisible by 2. 3: No; the sum of the digits, 4, is not divisible by 3. 4: Yes; the number formed by the last two digits, 12, is divisible by 4. 5: No; the ones digit is not a 0 or a 5. 6: No; the number is not divisible by 2 and 3. 9: No; the sum of the digits, 4, is not divisible by 9. 10: No; the ones digit, 2, is not 0. The number 112 is even because it is divisible by 2.

Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd. 1. 80

2. 93

3. 324

4. 81

5. 650

6. 23,512

7. 48

8. 268

9. 665

10. 3,579

11. 7,000

12. 24,681

Tell whether each sentence is sometimes, always, or never true. 13. A number that is divisible by both 2 and 3 is also divisible by 6.

14. Any number that is divisible by 10 is also divisible by 2 and 5.


6


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Divisibility Patterns Tell whether the first number is divisible by the second number. 1. 527; 3

2. 1,048; 6

3. 693; 9

4. 1,974; 2

5. 305; 10

6. 860; 5

7. 4,672; 9

8. 2,310; 6

9. 816; 3

10. 13,509; 5

11. 2,847; 2

12. 192; 6

13. 24

14. 27

15. 90

16. 81

17. 104

18. 205

19. 1,000

20. 6,598

21. 399

22. 27,453

23. 33,324

24. 16,335

Use divisibility rules to find each missing digit. List all possible answers. 25. 1__2 is divisible by 9

26. 1,__24 is divisible by 4

27. 1,25__ is divisible by 3

28. 5,__32 is divisible by 6

29. 31,45__ is divisible by 5

30. 1,679,83__ is divisible by 2


7


Lesson 1–2

Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Divisibility Patterns MONTHS OF THE YEAR For Exercises 1–3, use the table that shows how many days are in each month, excluding leap years. (Every four years, the calendar is adjusted by adding one day to February.)

JAN. FEB. MAR. APR. MAY JUN. JUL. AUG. SEP. OCT. NOV. DEC. 31

28

31

30

31

30

31

31

30

31

30

31

1. Which month has a number of days that is divisible by 4? During a leap year, is this still true?

2. Which months have a number of days that is divisible by both 5 and 10? During a leap year, is this still true?

3. The total number of months in a year are divisible by which numbers?

4. FOOD Jermaine and his father are in charge of grilling for a family reunion picnic. There will be 40 people attending. Ground beef patties come 5 to a package. How many packages of patties should they buy to provide 1 hamburger for each person? Will there by any patties left over? If so, how many?

5. RETAIL Li is stacking bottles of apple juice on the shelf at her parent’s grocery store. She has space to fit 4 bottles across and 6 bottles from front to back. She has 25 bottles to stack. Will all of the bottles fit on the shelf? Explain.

6. FARMING Sally is helping her mother put eggs into egg cartons to sell at the local farmer’s market. Their chickens have produced a total of 108 eggs for market. Can Sally package the eggs in groups of 12 so that each carton has the same number of eggs? Explain.


8


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Divisibility Patterns Pre-Activity Complete the Mini Lab at the top of page 10 in your textbook. Write your answers below. Describe a pattern in each group of numbers listed. 1. the numbers that can be evenly divided by 2 2. the numbers that can be evenly divided by 5 3. the numbers that can be evenly divided by 10 4. the numbers that can be evenly divided by 3 (Hint: Look at both digits.)

Reading the Lesson 5. Complete the following table. is divisible by

because

12

2

the ones digit is divisible by 2

12

3

the sum of the digits is divisible by 3

12

4

the number formed by the last two digits is divisible by 4

12

6

the number is divisible by both 2 and 3

20

5

the ones digit is 0 or 5

20

10

the ones digit is 0

6. The Pledge of Allegiance uses the term indivisible. How do the meanings of divisible and indivisible compare to each other?

Helping You Remember 7. Several commonplace items come in amounts that are divisible by smaller units. For example, a deck of playing cards has 4 suits of 13 cards, so 52 is divisible by 4 and 13. Name other everyday items that illustrate divisibility patterns. © Glencoe/McGraw-Hill

9


Lesson 1–2

The number

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Leap Years You probably know that a leap year has 366 days, with the extra day being February 29. Did you know that divisibility can help you recognize a leap year? That is because the number of a leap year is always divisible by 4. A number is divisible by 4 if the number formed by its tens and ones digits is divisible by 4. 1936 is divisible by 4 because 36 is divisible by 4. 1938 is not divisible by 4 because 38 is not divisible by 4. So 1936 was a leap year, and 1938 was not. Be careful when you decide if a year is a leap year. A century year—like 1800, 1900, or 2000—is a leap year only if its number is divisible by 400. Decide whether each year is a leap year. Write yes or no. 1. 1928

2. 1930

3. 1960

4. 1902

5. 1492

6. 1776

7. 1812

8. 1900

9. 1994

10. 2000

11. 2001

12. 2100

13. How many leap years are there between 1901 and 2001? 14. How many leap years were there from the Declaration of Independence in 1776 to the bicentennial celebration in 1976? (Include 1776 and 1976 in your count.) 15. In 1896, the first modern Olympic games were held in Athens, Greece. After that, the officially recognized games were held every four years except for 1916, 1940, and 1944, when the world was at war. How many times were the games held from 1896 to 1992? 16. George Washington was first elected president in 1789. Since 1792, United States presidential elections have been held every four years. How many presidential elections will there have been up to and including the election in the year 2000? 17. CHALLENGE If a person lives to be exactly 100 years old, how many leap years or parts of leap years will that person see?


10


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Prime Factors Factors are the numbers that are multiplied to get a product. A product is the answer to a multiplication problem. A prime number is a whole number that has only 2 factors, 1 and the number itself. A composite number is a number greater than 1 with more than two factors.

Tell whether each number is prime, composite, or neither. Number

Factors

Prime or Composite?

15

1 3 15 335

Composite

17

1 3 17

Prime

1

1

Neither

Find the prime factorization of 18. Write the number that is being factored at the top.

18 2

3

9

2 3 3 3 3

Choose any pair of whole number factors of 18. Except for the order, the prime factors are the same.

18 is divisible by 2, because the ones digit is divisible by 2. Circle the prime number, 2. 3 3 6 9 is divisible by 3, because the sum of the digits is divisible by 3. 3 3 2 3 3 Circle the prime numbers, 3 and 3. The prime factorization of 18 is 2 3 3 3 3. 18

1. 7

2. 12

3. 29

4. 81

5. 18

6. 23

7. 54

8. 28

9. 120

10. 243

11. 61

12. 114

Find the prime factorization of each number. 13. 125

14. 44

15. 11

16. 56


11


Lesson 1–3

Tell whether each number is prime, composite, or neither.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Prime Factors Tell whether each number is prime, composite, or neither. 1. 0

2. 1

3. 2

4. 3

5. 4

6. 5

7. 6

8. 7

9. 8

10. 9

11. 10

12. 11

Find the prime factorization of each number. 13. 9

14. 25

15. 28

16. 54

17. 34

18. 72

19. 55

20. 63

SCHOOL For Exercises 21–24, use the table below.

Marisa’s History Test Scores Date

Test Score

January 28

67

February 15

81

March 5

97

March 29

100

21. Which test scores are prime numbers?

22. Which prime number is the least prime number?

23. Find the prime factorization of 100.

24. Find the prime factorization of 81.


12


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Prime Factors ANIMALS For Exercises 1–3, use the table that shows the height and

weight of caribou. Height at the Shoulder

Weight

inches

centimeters

pounds

kilograms

Cows (females)

43

107

220

99

Bulls (males)

50

125

400

180

1. Which animal heights and weights are prime numbers?

2. Write the weight of caribou cows in kilograms as a prime factorization.

3. ANIMALS Caribou calves weigh about 13 pounds at birth. Tell whether this weight is a prime or a composite number.

4. SPEED A wildlife biologist once found a caribou traveling at 37 miles per hour. Tell whether this speed is a prime or composite number. Explain.

5. GEOMETRY To find the area of a floor, you can multiply its length times its width. The measure of the area of a floor is 49. Find the most likely length and width of the room.

6. GEOMETRY To find the volume of a box, you can multiply its height, width, and length. The measure of the volume of a box is 70. Find its possible dimensions.


13


Lesson 1–3

CARIBOU

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Prime Factors Pre-Activity Complete the Mini Lab at the top of page 14 in your textbook. Write your answers below. 1. For what numbers can more than one rectangle be formed?

2. For what numbers can only one rectangle be formed?

3. For the numbers in which only one rectangle is formed, what do you notice about the dimensions of the rectangle?

Reading the Lesson 4. The word factorization is made up of factor 1 a verb ending 1 a noun ending. Write a definition for each of the following mathematical terms: a. factor

b. to factorize, or to factor

c. factorization

5. Is 9 a prime number or a composite number? Explain.

Helping You Remember 6. Pick a number that has two or three digits. Explain to someone else how to use a factor tree to find the prime factors of the number. In your explanation, show how the rules of divisibility help you to do the factoring.


14


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Making Models for Numbers Have you wondered why we read the number 32 as three squared? The reason is that a common model for 32 is a square with sides of length 3 units. As you see, the figure that results is made up of 9 square units.

3 units

3 units

32 5 9 square units

Make a model for each expression. 1. 22

2. 42

3. 12

4. 52

Since we read the expression 23 as two cubed, you probably have guessed that there is also a model for this number. The model, shown at the right, is a cube with sides of length 2 units. The figure that results is made up of 8 cubic units.

2 units 2 units 2 units

23

5 8 cubic units

Exercises 5 and 6 refer to the figure at the right. 5. What expression is being modeled?

a. How many small cubes are there in all? b. How many small cubes have red paint on exactly three of their faces? c. How many small cubes have red paint on exactly two of their faces? d. How many small cubes have red paint on exactly one face? e. How many small cubes have no red paint at all? 7. CHALLENGE In the space at the right, draw a model for the expression 43. © Glencoe/McGraw-Hill

15


Lesson 1–3

6. Suppose that the entire cube is painted red. Then the cube is cut into small cubes along the lines shown.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Powers and Exponents A product of prime factors can be written using exponents and a base. Numbers expressed using exponents are called powers. Powers 56

Words 4 to the second power or 4 squared 5 to the sixth power

434 5 35 3 5 3 5 3 5 3 5

74 93

7 to the fourth power 9 to the third power or 9 cubed

7373737 93939

42

Expression

Value 16 15,625 2,401 729

Write 6 · 6 · 6 using an exponent. Then find the value of the power. The base is 6. Since 6 is a factor 3 times, the exponent is 3. 6 · 6 · 6 5 63 or 216 Write 24 as a product. Then find the value of the product. The base is 2. The exponent is 4. So, 2 is a factor 4 times. 24 5 2 · 2 · 2 · 2 or 16 Write the prime factorization of 225 using exponents. The prime factorization of 225 can be written as 3 3 3 3 5 3 5, or 32 3 52.

Write each product using an exponent. Then find the value of the power. 1. 2 · 2 · 2 · 2 · 2

2. 9 · 9

3. 3 · 3 · 3

4. 5 · 5 · 5

5. 3 · 3 · 3 · 3 · 3

6. 10 · 10

Write each power as a product. Then find the value of the product. 7. 72

8. 43

9. 84

10. 55

11. 28

12. 73

Write the prime factorization of each number using exponents. 13. 40

14. 75

15. 100

16. 147


16


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Powers and Exponents Write each expression in words. 1. 72 2. 83 3. 44 4. 56 Write each product using an exponent. Then find the value of the power. 5. 4 · 4 · 4 · 4

6. 3 · 3 · 3 · 3

7. 5 · 5 · 5 · 5

8. 7 · 7

9. 3 · 3 · 3 · 3 · 3 11. 6 · 6 · 6

10. 2 · 2 · 2 · 2 · 2 · 2 12. 6 · 6 · 6 · 6

Write each power as a product. Then find the value of the product. 13. 38

14. 25

15. 83

16. 105

17. 62

18. 74

19. 23

20. 35

21. 65

22. 27

23. 54

24. 36

25. 63

26. 245


17


Lesson 1–4

Write the prime factorization of each number using exponents.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Powers and Exponents 1. SPACE The Sun is about 10 · 10 million miles away from Earth. Write 10 · 10 using an exponent. Then find the value of the power. How many miles away is the Sun?

2. WEIGHT A 100-pound person on Earth would weigh about 4 · 4 · 4 · 4 pounds on Jupiter. Write 4 · 4 · 4 · 4 using an exponent. Then find the value of the power. How much would a 100-pound person weigh on Jupiter?

3. ELECTIONS In the year 2000, the governor of Washington, Gary Locke, received about 106 votes to win the election. Write this as a product. How many votes did Gary Locke receive?

4. SPACE The diameter of Mars is about 94 kilometers. Write 94 as a product. Then find the value of the product.

5. SPACE The length of one day on Venus is 35 Earth days. Express this exponent as a product. Then find the value of the product:

6. GEOGRAPHY The area of San Bernardino County, California, the largest county in the U.S., is about 39 square miles. Write this as a product. What is the area of San Bernardino County?

7. GEOMETRY The volume of the block shown can be found by multiplying the width, length, and height. Write the volume using an exponent. Find the volume.

8. SPACE A day on Jupiter lasts about 10 hours. Write a product and an exponent to show how many hours are in 10 Jupiter days. Then find the value of the power.


2 in.

2 in.

2 in.

18


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Powers and Exponents Pre-Activity Complete the Mini Lab at the top of page 18 in your textbook. Write your answers below. 1. What prime factors did you record?

2. How does the number of folds relate to the number of factors in the prime factorization of the number of holes?

3. Write the prime factorization of the number of holes made if you folded it eight times.

Reading the Lesson 4. Describe the expression 25. In your description, use the terms power, base, and exponent.

5. In the power 35, what does the exponent 5 indicate?

6. Complete the following table. Expression 72 96 8383838 333333333

4 7 9 8 3

to to to to to

the the the the the

third power or 4 cubed second power or 7 squared sixth power fourth power fifth power

Lesson 1–4

43

Words

Helping You Remember 7. Explain how to find the value of 54.


19


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment The Sieve of Erathosthenes Erathosthenes was a Greek mathematician who lived from about 276 B.C. to 194 B.C. He devised the Sieve of Erathosthenes as a method of identifying all the prime numbers up to a certain number. Using the chart below, you can use his method to find all the prime numbers up to 120. Just follow these numbered steps. 1. The number 1 is not prime. Cross it out. 2. The number 2 is prime. Circle it. Then cross out every second number—4, 6, 8, 10, and so on. 3. The number 3 is prime. Circle it. Then cross out every third number—6, 9, 12, and so on. 4. The number 4 is crossed out. Go to the next number that is not crossed out. 5. The number 5 is prime. Circle it. Then cross out every fifth number—10, 15, 20, 25, and so on. 6. Continue crossing out numbers as described in Steps 2–5. The numbers that remain at the end of this process are prime numbers. 7. CHALLENGE Look at the prime numbers that are circled in the chart. Do you see a pattern among the prime numbers that are greater than 3? What do you think the pattern is?


20

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Lesson 1–5

Order of Operations Order of Operations 1. Simplify the expressions inside grouping symbols, like parentheses. 2. Find the value of all powers. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.

Find the value of 48 4 (3 1 3) 2 22. 48 4 (3 1 3) 2 22 5 5 5 5

48 4 6 2 22 48 4 6 2 4 824 4

Simplify the expression inside the parentheses. Find 22. Divide 48 by 6. Subtract 4 from 8.

Write and solve an expression to find the total cost of planting flowers in the garden. Item

Cost Per Item Number of Items Needed

pack of flowers bag of dirt bottle of fertilizer Words cost of 5 flower packs Expression 5 3 $4

$4 $3 $4 plus 1

5 1 1 cost of dirt $3

plus 1

cost of fertilizer $4

5 3 $4 1 $3 1 $4 5 $20 1 $3 1 $4 5 $23 1 $4 5 $27 The total cost of planting flowers in the garden is $27.

Find the value of each expression. 1. 7 1 2 3 3

2. 12 4 3 1 5

3. 16 – (4 1 5)

4. 8 3 8 4 4

5. 10 1 14 4 2

6. 3 3 3 1 2 3 4

7. 80 – 8 3 32

8. 11 3 (9 – 22)

9. 25 4 5 1 6 3 (12 – 4)

10. GARDENING Refer to Example 2. Suppose that the gardener did not buy enough flowers and goes back to the store to purchase four more packs. She also purchases a hoe for $16. Write an expression that shows the total amount she spent to plant flowers in her garden.


21


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Order of Operations Find the value of each expression. 1. 7 – 6 1 5

2. 31 1 19 – 8

3. 64 – 8 1 21

4. 17 1 34 – 2

5. 28 1 (89 – 67)

6. (8 1 1) 3 12 – 13

7. 63 4 9 1 8

8. 5 3 6 – (9 – 4)

9. 13 3 4 – 72 4 8

10. 16 4 2 1 8 3 3

11. 30 4 (21 – 6) 3 4

12. 6 3 7 4 (6 1 8)

13. 88 – 16 3 5 1 2 – 3

14. (2 1 6) 4 2 1 4 3 3

15. 43 – 24 4 8

16. 100 4 52 3 43

17. 48 4 23 1 25 3 (9 – 7)

18. 45 4 9 1 8 – 7 1 2 3 3

19. 18 1 72 3 (8 – 2) 4 3 1 8

20. (52 1 33) 3 (81 1 9) 4 10


22


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems MONEY For Exercises 1–3, use the table that shows the price of admission to a movie theater.

Movie Theater Admission Adults: $8 Children (under 13): $5 Matinee (before 6 P.M.): $3 1. Janelle (age 12) and her cousin, Marquita (age 14), go to a 7:00 P.M. show. Write an expression for the total cost of admission. What is the total cost?

2. Jan takes her three children and two neighbor’s children to a matinee. All of the children are under age 13. Write an expression for the total cost of admission. How much in all did Jan pay for admission?

3. Connor (age 13), his sister (age 7), and Connor’s parents go to a movie on Saturday night. Write an expression for the total cost. What is the total cost?

4. SOCCER Eduardo is 16. Eduardo’s dad takes him and his younger sister to a soccer match. Tickets are $17 for adults and $13 for children (18 and under). Write an expression for the total cost of the tickets. What is the total cost of the tickets?

5. MONEY Frankie orders two hamburgers and a soda for lunch. A hamburger is $3 and a soda is $1.00. Write an expression to show how much he paid for lunch. Then find the value of the expression.

6. MONEY A store sells barrettes for $2 each and combs for $1. Shelby buys 3 barrettes and a comb. Kendra buys 2 barrettes and 4 combs. Write an expression for the amount the two girls spent all together. Find the total amount spent.


23


Lesson 1–5

Order of Operations

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Order of Operations Pre-Activity Read the introduction at the top of page 24 in your textbook. Write your answers below. 1. How many Calories would you burn by walking for 2 hours?

2. Find the number of Calories a person would burn by walking for 2 hours and bike riding for 3 hours.

3. Explain how you found the total number of Calories.

Reading the Lesson 4. The steps for finding the value of a numerical expression are listed below. Number the steps in the correct order. _____ Find the value of all powers. _____ Add and subtract in order from left to right. _____ Simplify the expressions inside grouping symbols. _____ Multiply and divide in order from left to right. 5. Using the order of operations, explain how you would find the value of (7 1 5) 4 22 1 8.

6. How would the value of (7 1 5) 4 22 1 8 differ if you added the 8 before you divided by 4?

Helping You Remember 7. Using only operation symbols and grouping symbols, write the order of operations.


24


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Lesson 1–5

Operations Puzzles Now that you have learned how to evaluate an expression using the order of operations, can you work backward? In this activity, the value of the expression will be given to you. It is your job to decide what the operations or the numbers must be in order to arrive at that value.

Fill in each

with 1, 2, 3, or 4 to make a true statement.

1. 48

3

3. 24

12

12 5 12

6

2. 30

15

356

354

4. 24

12

6

6. 45

3

8. 72

12

5. 4

16

2

8 5 24

7. 36

2

3

12

Fill in each

250

3 5 18

3

953

4

8

350

with one of the given numbers to make a true

statement. Each number may be used only once. 9. 6, 12, 24 4

10. 4, 9, 36 3

5 12

2

11. 6, 8, 12, 24 4

5 0

4

1

12. 2, 5, 10, 50 1

2

5 4

2

13. 2, 4, 6, 8, 10 4

4

5 50

14. 1, 3, 5, 7, 9 3

1

15. CHALLENGE Fill in each

2

5 0

4

1

2

4

5 1

with one of the digits from 1 through 9 to

make a true statement. Each digit may be used only once. 4

3


1

3

3

4

25

1

3

5 100


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Algebra: Variables and Expressions • A variable is a symbol, usually a letter, used to represent a number. • Multiplication in algebra can be shown as 4n or 4 3 n. • Algebraic expressions are combinations of variables, numbers, and at least one operation.

Evaluate 35 1 x if x 5 6. 35 1 x 5 35 1 6 5 41

Replace x with 6. Add 35 and 6.

Evaluate y 1 x if x 5 21 and y 5 35. y 1 x 5 35 1 21 5 56

Replace x with 21 and y with 35. Add 35 and 21.

Evaluate 4n 1 3 if n 5 2. 4n 1 3 5 4 3 2 1 3 Replace n with 2. 813 Find the product of 4 and 2. 11 Add 8 and 3. Evaluate 4n 2 2 if n 5 5. 4n 2 2 5 4 3 5 2 2 Replace n with 5. 20 2 2 Find the product of 4 and 5. 18 Subtract 2 from 20.

Evaluate each expression if y 5 4. 1. 3 1 y

2. y 1 8

3. 4 3 y

4. 9y

5. 15y

6. 300y

7. y2

8. y2 1 18

9. y2 1 3 3 7

Evaluate each expression if m 5 3 and k 5 10. 10. 16 1 m

11. 4k

12. m 3 k

13. m 1 k

14. 7m 1 k

15. 6k 1 m

16. 3k – 4m

17. 2mk

18. 5k – 6m

19. 20m 4 k

20. m3 1 2k2

21. k2 4 (2 1 m)


26


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Algebra: Variables and Expressions Complete the table. Variables

Numbers

Operations

1. 5d 1 2c

? d, c

? 5, 2

? 3, 1

2. 5w 2 4y 1 2s

? w, y, s

? 5, 4, 2

? 3, 2, 1

3. xy 4 4 1 3m 2 6

? x, y, m

? 4, 3, 6

? 3, 4, 1, 2

Evaluate each expression if a 5 3 and b 5 4. 4. 10 1 b

5. 2a 1 8

6. 4b – 5a

7. a 3 b

8. 7a 3 9b

9. 8a – 9

10. b 3 22

11. a2 1 1

12. 18 4 2a

13. a2 3 b2

14. ab 4 3

15. 15a – 4b

16. ab 1 7 3 11

17. 36 4 6a

18. 7a 1 8b 3 2

Evaluate each expression if x 5 7, y 5 15, and z 5 8. 19. x 1 y 1 z

20. x 1 2z

21. xz 1 3y

22. 4x – 3z

23. z2 4 4

24. 6z – 5z

25. 9y 4 (2x 1 1)

26. 15y 1 x2

27. y2 1 4 3 6

28. y2 – 2x2

29. x2 1 30 – 18

30. 13y – zx 4 4

31. xz – 2y 1 8

32. z2 1 5y – 20

33. 3y 3 40x – 1,000


27


Lesson 1–6

Algebraic Expressions

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Algebra: Variables and Expressions TRAVEL For Exercises 1 and 2, use the table that shows the distance between cities in Arizona.

Arizona Mileage Chart Flagstaff

Phoenix

Phoenix

136 miles

Tucson

253 miles

117 miles

Nogales

317 miles

181 miles

Tucson

Nogales

117 miles

181 miles 64 miles

64 miles

1. To find the speed of a car, use the expression d 4 t where d represents the distance and t represents time. Find the speed of a car that travels from Phoenix to Flagstaff in 2 hours.

2. To find the time it will take for a bicyclist to travel from Nogales to Tucson, use the expression d/s where d represents distance and s represents speed. Find the time if the bicyclist travels at a speed of 16 miles per hour.

3. PERIMETER The , perimeter of a rectangle can be w found using the formula 2, 1 2w, where , represents the length and w represents the width. Find the perimeter if , 5 6 units and w 5 3 units.

4. PERIMETER Another formula for perimeter is 2(, 1 w). Find the perimeter of the rectangle in Exercise 3 using this formula. How do the answers compare? Explain how you used order of operations using this formula.

5. SHOPPING Write an expression using a variable that shows how much 3 pairs of jeans will cost if you do not know the price of the jeans. Assume each pair costs the same amount.

6. SHOPPING Write an expression using variables to show how much 3 plain T-shirts and 2 printed T-shirts will cost, assuming that the prices of plain and printed T-shirts are not the same.


28


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Algebra: Variables and Expressions Pre-Activity Complete the Mini Lab at the top of page 28 in your textbook. Write your answers below.

2. Find the value of the expression if the unknown value is 4.

3. Write a sentence explaining how to evaluate an expression like the sum of some number and seven when the unknown value is given.

Reading the Lesson 4. Look up the word variable in a dictionary. What definition of the word matches its use in this lesson? If classmates use different dictionaries, compare the meanings among the dictionaries.

5. Exercise 4 of the Mini Lab uses the expression unknown value, which can also be read as "value of the unknown." In the expression value of the unknown, would the expression value of the variable mean the same thing?

Helping You Remember 6. Explain the difference between a numerical expression and an algebraic expression.


29


Lesson 1–6

1. Model the sum of five and some number.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment What’s in a Word? Suppose you use the following code for the letters of the alphabet. A B C D E F G

5 5 5 5 5 5 5

1 2 3 4 5 6 7

H I J K L M N

5 8 5 9 5 10 5 11 5 12 5 13 5 14

O P Q R S T

U 5 21 V 5 22 W 5 23 X 5 24 Y 5 25 Z 5 26

5 15 5 16 5 17 5 18 5 19 5 20

To evaluate a word using this code, you replace each letter with its code number, then multiply. For instance, at the right you see how to find the value of the word MATH, which is 2,080. Use the code above to evaluate each word. 1. BOX

2. CUBE

3. TABLE

4. CATTLE

5. VARIABLE

6. ALGEBRA

13 (M) 3 1 (A) 13 3 20 (T) 260 3 8 (H) 2,080

Circle the word that has the greater value. (Hint: Do you have to evaluate the entire word, or is there a shortcut?) 7. PRINCIPAL or PRINCIPLE 9. THOUGHT or THROUGH

8. MARCH or CHARM 10. RIGHT or WRITE

Find a three-letter word that has a value as close as possible to the given number. 11. 1,000

12. 2,000

13. 3,000

14. 6,000

15. CHALLENGE What is the least possible value that you can find for a threeletter word? the greatest possible value?


30


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Algebra: Solving Equations An equation is a sentence that contains an equals sign, =. Some equations contain variables. When you replace a variable with a value that results in a true sentence, you solve the equation. The value for the variable is the solution of the equation.

Solve m 1 12 5 15 mentally. m 1 12 5 15 Think: What number plus 12 equals 15? 3 1 12 5 15 You know that 12 1 3 5 15. m53 The solution is 3. Solve 14 – p 5 6 using guess and check.

Try 7. 14 – p 0 6 14 – 7 Þ 6 no

Try 6. 14 – p 0 6 14 – 6 Þ 8 no

Try 8. 14 – p 0 6 14 – 8 5 6 yes

The solution is 8 because replacing p with 8 results in a true sentence.

Identify the solution of each equation from the list given. 1. k – 4 5 13; 16, 17, 18

2. 31 1 x 5 42; 9, 10, 11

3. 45 5 24 1 k; 21, 22, 23

4. m – 12 5 15; 27, 28, 29

5. 88 5 41 1 s; 46, 47, 48

6. 34 – b 5 17; 16, 17, 18

7. 69 – j 5 44; 25, 26, 27

8. h 1 19 5 56; 36, 37, 38

Solve each equation mentally. 9. j 1 3 5 9

10. m – 5 5 11

11. 23 1 x 5 29

12. 31 – h 5 24

13. 18 5 5 1 d

14. 35 – a 5 25

15. y – 26 5 3

16. 14 1 n 5 19

17. 100 5 75 1 w


31


Lesson 1–7

Guess the value of p, then check it out.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Algebra: Solving Equations Solve each equation mentally. 1. 9 – m 5 8

2. 4 1 k 5 11

3. 23 – x 5 10

4. 31 – h 5 21

5. 18 5 20 – b

6. 16 1 z 5 25

7. y – 25 5 3

8. 7 1 f 5 15

9. 20 1 r 5 25

10. 18 – v 5 9

11. 26 – d 5 19

12. 49 – c 5 41

13. 45 1 r 5 59

14. 64 1 n 5 70

15. 175 5 w 1 75

True or False? 16. If 31 1 h 5 50, then h 5 29. 17. If 48 5 40 1 k, then k 5 8. 18. If 17 – x 5 9, then x 5 7. 19. If 98 – g 5 87, then g 5 11. 20. If p – 8 5 45, then p 5 51. Identify the solution of each equation from the list given. 21. s 1 12 5 17; 5, 6, 7

22. 59 – x 5 42; 15, 16, 17

23. 24 – k 5 3; 21, 22, 23

24. h – 15 5 31; 44, 45, 46

25. 69 5 50 1 s; 17, 18, 19

26. 34 – b 5 13; 20, 21, 22

27. 66 – d 5 44; 21, 22, 23

28. h 1 39 5 56; 15, 16, 17

29. 54 1 f 5 70; 16, 17, 18

30. 47 5 72 – b; 25, 26, 27

31. 28 1 v 5 92; 64, 65, 66

32. 56 1 c 5 109; 52, 53, 54


32


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Algebra: Solving Equations INSECTS For Exercises 1–3, use the table that gives the average lengths

of several unusual insects in centimeters. Insect

Length (cm)

Insect

Length (cm)

Walking stick

15

Giant water bug

6

Goliath beetle

15

Katydid

5

Giant weta

10

Silkworm moth

4

Harlequin beetle

7

Flower mantis

3

2. The equation 7 1 y 5 13 gives the length of a Harlequin beetle and one other insect. If y is the other insect, which insect makes the equation a true sentence?

3. Bradley found a silkworm moth that was 2 centimeters longer than average. The equation m – 4 5 2 represents this situation. Find the length of the silkworm moth that Bradley found.

4. BUTTERFLIES A Monarch butterfly flies about 80 miles per day. So far it has flown 60 miles. In the equation 80 – m 5 60, m represents the number of miles it has yet to fly that day. Find the solution to the equation.

5. CICADAS The nymphs of some cicada can live among tree roots for 17 years before they develop into adults. One nymph developed into an adult after only 13 years. The equation 17 – x 5 13 describes the number of years less than 17 that it lived as a nymph. Find the value of x in the equation to tell how many years less than 17 years it lived as a nymph.

6. BEETLES A harlequin beetle lays eggs in trees. She can lay up to 20 eggs over 2 or 3 days. After the first day, the beetle has laid 9 eggs. If she lays 20 eggs in all, how many eggs will she lay during the second and third day?

Lesson 1–7

1. The equation 15 – x 5 12 gives the difference in length between a walking stick and one other insect. If x is the other insect, which insect is it?


33


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Algebra: Solving Equations Pre-Activity Complete the Mini Lab at the top of page 34 in your textbook. Write your answers below. 1. Suppose the variable x represents the number of cubes in the cup. What equation represents this situation? 2. Replace the cup with centimeter cubes until the scale balances. How many centimeter cubes did you need to balance the scale? Let x represent the cup. Model each sentence on a scale. Find the number of centimeter cubes needed to balance the scale. 3. x 1 1 5 4 4. x 1 3 5 5 5. x 1 7 5 8 6. x 1 2 5 2

Reading the Lesson 7. In the Mini Lab, how did you make the scale balance?

8. In this lesson, what makes a mathematical sentence true?

9. How are the words solve and solution related?

10. Look up the word equate in a dictionary. How does it relate to the word equation?

Helping You Remember 11. Suppose you are buying a soda for $0.60 and you are going to pay with a dollar bill. Write an equation that represents this situation. What does your variable represent?


34


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Equation Chains In an equation chain, you use the solution of one equation to help you find the solution of the next equation in the chain. The last equation in the chain is used to check that you have solved the entire chain correctly.

1. 5 1 a 5 12,

so a 5

.

ab 5 14,

so b 5

16 4 b 5 c,

2. 9f 5 36,

so f 5

.

.

g 5 13 2 f, so g 5

.

so c 5

.

63 4 g 5 h, so h 5

.

14 2 d 5 c,

so d 5

.

h 1 i 5 18, so i 5

.

e 4 d 5 3,

so e 5

.

j 2 i 5 9,

.

a 1 e 5 25 → Check:

3. m 4 4 5 8,

so j 5

j 4 f 5 5 → Check:

so m 5

.

m 2 n 5 12,

so n 5

.

v 4 w 5 3,

so w 5

.

np 5 100,

so p 5

.

80 5 wx,

so x 5

.

q 5 40 1 p,

so q 5

.

w 1 x 5 2y, so y 5

.

p 1 q 2 10 5 r, so r 5

4. 18 5 v 2 12,so v 5

.

xy 2 z 5 40, so z 5

r 2 m 5 8 → Check:

.

.

z 2 v 5 2 → Check:

5. CHALLENGE Create your own equation chain using these numbers for the variables: a 5 10, b 5 6, c 5 18, and d 5 3.


35


Lesson 1–7

Complete each equation chain.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Geometry: Area of Rectangles The area of a figure is the number of square units needed to cover a surface. You can use a formula to find the area of a rectangle. The formula for finding the area of a rectangle is A 5 , 3 w. In this formula, A represents area, , represents the length of the rectangle, and w represents the width of the rectangle.

Find the area of a rectangle with length 8 feet and width 7 feet. A5,3w Area of a rectangle A5837 Replace , with 8 and w with 7. A 5 56 The area is 56 square feet.

Find the area of a rectangle with width 5 inches and length 6 inches. A5,3w Area of a rectangle A5635 Replace , with 6 and w with 5. A 5 30 The area is 30 square inches.

Find the area of each rectangle. 1.

2.

3.

5 ft

7 cm

3 cm

4.

6 yd

5 yd 8 ft

5. What is the area of a rectangle with a length of 10 meters and a width of 7 meters?

6. What is the area of a rectangle with a length of 35 inches and a width of 15 inches?


36


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Geometry: Area of Rectangles Complete each problem. 1. Give the formula for finding the area of a rectangle. 2. Draw and label a rectangle that has an area of 18 square units.

3. Give the dimensions of another rectangle that has the same area as the one in Exercise 2.

4. Find the area of a rectangle with a length of 3 miles and a width of 7 miles. 5. Find the area of a rectangle with a width of 54 centimeters and a length of 12 centimeters. Find the area of each rectangle. 9 in.

7.

6 in.

14 ft

8.

10 ft

9. 2 m

10.

16 cm

Lesson 1–8

6.

32 cm

7 yd

11.

9 in.

3 yd

11 m

8 in.

12.

5 ft

12 ft


13.

15 m

24 m

14.

7 cm

7 cm

37


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Geometry: Area of Rectangles FLOOR PLANS For Exercises 1–6, use the diagram that shows the floor

plan for a house. 7 ft

Bath

2 ft

6 ft

10 ft

Closet

13 ft

2 ft Closet

9 ft

Bedroom 1

Bedroom 2

13 ft

Hall

14 ft

Kitchen

Living/Dining Room

12 ft

18 ft

14 ft

1. What is the area of the floor in the kitchen?

2. Find the area of the living/dining room.

3. What is the area of the bathroom?

4. Find the area of Bedroom 1.

5. Which two parts of the house have the same area?

6. How much larger is Bedroom 2 than Bedroom 1?


38


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Geometry: Area of Rectangles Pre-Activity Complete the activity at the top of page 39 in your textbook. Write your answers below. 1. Complete the table below. Object

Squares Along the Length

Squares Along the Width

Squares Needed to Cover the Surface

flag game board

2. What relationship exists between the length and the width, and the number of squares needed to cover the surface?

Reading the Lesson

4. In order to find the area of a surface, what two measurements do you need to know?

5. On page 39, the textbook says that the area of a figure is the number of square units needed to cover a surface. If the length and width are measured in inches, in what units will the area be expressed?

6. What unit of measure is indicated by m2? How large is one unit?

Helping You Remember 7. With a partner, measure a surface in your classroom. Explain how to find its area. Then find the area in the appropriate square units.


39


Lesson 1–8

3. Look up the word area in a dictionary. Write the meaning of the word as used in this lesson.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Tiling a Floor The figure at the right is the floor plan of a family room. The plan is drawn on grid paper, and each square of the grid represents one square foot. The floor is going to be covered completely with tiles. 1. What is the area of the floor?

2. Suppose each tile is a square with a side that measures one foot. How many tiles will be needed?

3. Suppose each tile is a square with a side that measures one inch. How many tiles will be needed?

4. Suppose each tile is a square with a side that measures six inches. How many tiles will be needed?

Use the given information to find the total cost of tiles for the floor. 5. tile: square, 1 foot by 1 foot cost of one tile: $3.50

6. tile: square, 6 inches by 6 inches cost of one tile: $0.95

7. tile: square, 4 inches by 4 inches cost of one tile: $0.50

8. tile: square, 2 feet by 2 feet cost of one tile: $12

9. tile: square, 1 foot by 1 foot cost of two tiles: $6.99

10. tile: rectangle, 1 foot by 2 feet cost of one tile: $7.99

11. Refer to your answers in Exercises 5-10. Which way of tiling the floor costs the least? the most?


40



Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860065-0 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03

CONTENTS Vocabulary Builder .............................vii Family Letter ............................................ix Family Activity ........................................x Lesson 2-1 Study Guide and Intervention ..........................61 Practice: Skills ..................................................62 Practice: Word Problems..................................63 Reading to Learn Mathematics........................64 Enrichment .......................................................65







Lesson 2-8 Study Guide and Intervention ..........................96 Practice: Skills ..................................................97 Practice: Word Problems..................................98 Reading to Learn Mathematics........................99 Enrichment .....................................................100

Chapter 2 Assessment Chapter 2 Test, Form 1 ..........................101–102 Chapter 2 Test, Form 2A ........................103–104 Chapter 2 Test, Form 2B ........................105–106 Chapter 2 Test, Form 2C........................107–108 Chapter 2 Test, Form 2D........................109–110 Chapter 2 Test, Form 3 ..........................111–112 Chapter 2 Extended Response Assessment .113 Chapter 2 Vocabulary Test/Review.................114 Chapter 2 Quizzes 1 & 2................................115 Chapter 2 Quizzes 3 & 4................................116 Chapter 2 Mid-Chapter Test ...........................117 Chapter 2 Cumulative Review........................118 Chapter 2 Standardized Test Practice....119–120 Unit 1 Test/Review..................................121–122 Standardized Test Practice Student Recording Sheet ............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A33

iii


Vocabulary Builder Pages vii-viii include a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. When to Use Give these pages to students before beginning Lesson 2-1. Encourage them to add these pages to their mathematics study notebook. Remind them to add definitions and examples as they complete each lesson.

Family Letter and Family Activity Page ix is a letter to inform your students’ families of the requirements of the chapter. The family activity on page x helps them understand how the mathematics students are learning is applicable to real life. When to Use Give these pages to students to take home before beginning the chapter.


Practice: Skills





One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques. When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students.

iv





Enrichment








Answers • Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 94–95. This improves students’ familiarity with the answer formats they may encounter in test taking.





v

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


average

bar graph

box-and-whisker plot

circle graph

data

frequency table

graph

horizontal axis

interval

key

leaves


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


line graph

mean

measure of central tendency median

mode

outlier

range

scale

statistics

stem-and-leaf plot

stems

tally mark

vertical axis


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Family Letter

routines. One of the things We use math in many of our daily ivities in the classroom to we try to do in this class is relate act this connection will help activities in the real world. Making rning math concepts. students realize the importance of lea s, your child will be learnIn Chapter 2, Statistics and Graph le graphs, stem-and-leaf ing about bar graphs, line graphs, circ dian, and mode. In the plots, frequency tables, and mean, me complete a variety of daily study of this chapter, your child will and possibly produce a classroom assignments and activities chapter project . it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get r child that also relates the an activity that you can do with you 2 to the real world. You math we will be learning in Chapter line Study Tools for selfmay also wish to log on to the On dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any quesother study help at www.msmath1.n t me at school. tions or comments, feel free to contac Sincerely,



ix


Family Letter

Dear Parent or Guardian:

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Bar Graphs and Line Graphs 1. Have a family member help you count the number of cans of food, glass jars of food, boxes of food, and bags of food you have in your pantry. Food in Pantry

Number

cans glass jars boxes bags other 2. Make a bar graph to represent the data.

3. Name the type of container of which you have the most (can, glass jar, box, or bag). 4. Do you have more cans of food or more bags of food? 5. Make a line graph of the data.

6. Do you think a line graph or a bar graph is better for answering the questions? Why?


x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Frequency Tables Statistics involves collecting, organizing, analyzing, and presenting data. Data are pieces of information and are usually numbers. You can organize data by making a frequency table. A frequency table shows the number of times each piece of data appears. The parts of a frequency table: Scale:

lets you record all of the data; includes the least and the greatest number

Interval:

separates the scale into equal parts

Tally marks:

lets you record a mark each time a piece of data appears

Frequency:

gives the sum of the tally marks for each category

SCHOOL Vinnie recorded his scores

Step 1

Choose a scale and interval. A scale that includes all the data is 0 to 10. An interval that separates the scale into equal parts is 2.

9

8

9

5

5

9

6

2

9

8

9

4

My Quiz Scores Score

Tally

Frequency

Draw a table with three columns and label the columns.

1–2

1

1

3–4

1

List the intervals, tally the data, and add the tallies.

1

5–6

3

3

Since the quiz score 9 has the greatest number in the frequency column, Vinnie scored 9 most often.

7–8

2

2

9–10

5

5

Step 2 Step 3

MUSIC Use the table that shows

the number of hours the band members practiced in a week. 1. Make a frequency table for the data. 2. Which number of hours practicing is most common?

Hours Spent Practicing 3

4

3

5

2

2

3

4

3

1

3

2

1

5

2

4

1

3

2

1

3. How many band members practiced more than 4 hours a week?


61


Lesson 2–1

My Quiz Scores

on this month’s math quizzes. Make a frequency table of the data. Which score did Vinnie get most often?

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Frequency Tables Make a frequency table for each set of data. 1. Class Quiz Scores

2.

4

10

8

6

9

9

8

7

7

7

5

8

8

8

10

9

6

8

Students’ Eye Colors R

G

R

L

H

L

L

V

G

R

R

R

L

R

R

R

H

L

R

H

H

R

R

G

R

L 5 Blue G 5 Green V 5 Violet

R 5 Brown H 5 Hazel

MOVIES Use the frequency table shown.

All-Time Top 27 Kids’ Films

3. Describe the scale.

Gross Sales Tally (millions $)

4. Describe the interval.

5. What is the most common gross sales category?

Frequency

100–149

554

14

150–199

5

5

200–249

2

2

250–299

4

4

300–349

2

2

6. How many films grossed more than $299 million?


62


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Frequency Tables ANIMALS For Exercises 1–3, use Table A. For Exercises 4–6, use Table B.

Table A

Table B

Insects Under a Rock E S S B S B

S E S E E S

B E B E B E

E B E E S E

E S E B E S

B E S E E E

B 5 beetle E 5 earwig S 5 sow bug

Weights (lb) of Dogs at the Vet Clinic Weight 1–10

Tally

Frequency

554

14

11–20

5554

19

21–30

55555

25

31–40

55

10

41–50

5

5

2. How many more earwigs did Maria find than beetles?

3. When Maria writes her report, she will list the insects in order of most common to least common. What order should she write in her report?

4. The strength of medicine given to a dog depends on the dog’s weight. There is a different strength for each weight group. For which weight group should a veterinarian order the most medicine? the least medicine?

5. Describe the scale and the interval in Table B.

6. How many more dogs are in the most frequent group than in the second most frequent group?


Lesson 2–1

1. Maria is counting three types of insects she finds under rocks in the park for an ecology survey. Make a frequency table showing her data from Table A.

63


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Frequency Tables Pre-Activity Complete the activity at the top of page 50 in your textbook. Write your answers below. 1. What is the height of the tallest tree? 2. How many trees are between 41 and 80 feet tall? 3. Tell how you might organize the heights of the trees so that the information is easier to find and read.

Reading the Lesson Refer to the frequency table in the middle of page 50. 4. What does the number 13 in the Frequency column indicate?

5. Does the number in the Frequency column tell you anything about the frequency of individual numbers within the data set? How do you know?

6. How is frequency related to interval?

7. Why do the numbers in the Height column begin at 51 and end at 140?

8. How does an interval make it easier to read the table?

Helping You Remember 9. Write the three steps used to make a frequency table. Then, using any data set you want, make a frequency table for those numbers.


64


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Histograms

Use the histogram at the right to answer each question. 1. How many scores are in the interval 81–90?

Scores on a Math Test

10 9 8 7

Frequency

Often a graph is used to picture the data in a frequency table. When frequencies are pictured in a bar graph, the graph is called a histogram. For example, at the right is a histogram that pictures the frequencies of the scores on a math test. Each bar in a histogram shows the number of pieces of data in a certain interval.

6 5 4 3 2 1 91 –1 00

81 –9 0

71 –8 0

61 –7 0

2. In which interval(s) are there exactly three scores?

51 –6 0

41 –5 0

0

Lesson 2–1

Score

3. How many scores are 70 or less?

4. Suppose that, to pass this test, a student needed a score of 61 or higher. How many students passed the test?

5. Can you tell in which interval there is the greatest number of scores? Explain. Pulse Rates of Students in a Biology Class 10 9

6. Can you tell what was the highest score on the test? Explain.

8

Frequency

7

7. Use the histogram at the right. In the space below, write two questions about the data in the histogram. Then answer each question.

6 5 4 3 2 1 91 –9 5

81 –8 5 86 –9 0

76 –8 0

71 –7 5

66 –7 0

0

Beats per Minute


65


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Bar Graphs and Line Graphs A graph is a visual way to display data. A bar graph is used to compare data. A line graph is used to show how data changes over a period of time.

Make a bar graph of the data. Compare the number of students in jazz class with the number in ballet class. Dance Class Attendance 12 10

Students

Step 1 Decide on the scale and interval. Step 2 Label the horizontal and vertical axes. Step 3 Draw bars for each style. Step 4 Label the graph with a title. About twice as many students take ballet as take jazz.

Dance Classes Style

Students

Ballet Tap Jazz Modern

11 4 5 10

8 6 4 2 0

Tap

Ballet

Jazz Modern

Style

Make a line graph of the data. Then describe the change in Gwen’s allowance from 1998 to 2002.

Gwen's Allowance

Year

1997

1998

1999

2000

2001

2002

Amount ($)

10

15

15

18

20

25

Decide on the scale and interval. 0 Label the horizontal and vertical axes. Draw and connect the points for each year. Year Label the graph with a title. allowance did not change from 1998 to 1999 and then increased from 1999 to 2002.

19 9 19 7 9 19 8 9 20 9 0 20 0 2001 02

Step 1 Step 2 Step 3 Step 4 Gwen’s

Amount ($)

Gwen’s Allowance

26 24 22 20 18 16 14 12 10

Make the graph listed for each set of data. 1. bar graph

2. line graph

Riding the Bus Student

Getting Ready for School

Time (min)

Day

Time (min)

10 40 20 15 35

Monday Tuesday Wednesday Thursday Friday

34 30 37 20 25

Paulina Omar Ulari Jacob Amita


66


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Bar Graphs and Line Graphs Make a bar graph for each set of data. 1.

Cars Made in 2000 Country

Cars (millions)

Brazil Japan Germany Spain U.S.A.

1 8 5 2 6

2.

People in America in 1630 Colony

People (hundreds)

Maine New Hampshire Massachusetts New York Virginia

4 5 9 4 25

Use the bar graph made in Exercise 1. 3. Which country made the greatest number of cars?

4. How does the number of cars made in Japan compare to the number made in Spain?

For Exercises 5 and 6, make a line graph for each set of data. Yuba County, California

6.

Year Population (thousands) 1990 1992 1994 1996 1998 2000

59 61 62 61 60 60

Everglades National Park Month

Rainfall (inches)

January February March April May June

2 2 2 2 7 10

7. POPULATION Refer to the graph made in Exercise 5. Describe the change in Yuba County’s population from 1990 to 2000.

8. WEATHER Refer to the graph made in Exercise 6. Describe the change in the amount of rainfall from January to June.


67


Lesson 2–2

5.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Bar Graphs and Line Graphs TREES For Exercises 1, 3, and 4, use Table A. For Exercises 2, 5, and 6, use Table B.

Table A

Table B

Average Heights of Pine Trees Tree Eastern White Lodgepole Longleaf Pitch Ponderosa

Lemons Produced by My Tree

Height (ft)

Year

Number of Lemons

75 48 110 55 140

1999 2000 2001 2002 2003

26 124 122 78 55

1. You and Jorge are writing a report on different kinds of pine trees. Make a bar graph for the report that shows the average heights of different kinds of pine trees. Use the data from Table A.

2. Table B shows the number of lemons your tree produced each year. Make a line graph for the data in Table B.

3. Use your graph for Exercise 1. Which tree is about half as tall as a ponderosa?

4. How does the average height of a pitch pine compare to the average height of a lodgepole pine?

5. Use the line graph you made in Exercise 2. Describe the change in fruit production for your lemon tree.

6. FRUIT Suppose you want to make a graph of the total number of lemons produced by your lemon tree and the total number of oranges produced by your orange tree in one year. Would you make a bar graph or a line graph? Explain.


68


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Bar Graphs and Line Graphs Pre-Activity Complete the activity at the top of page 56 in your textbook. Write your answers below. 1. What type of roller coaster is most common? 2. What might be an advantage of organizing data in a table? Are there any disadvantages of organizing data in this way?

Reading the Lesson Compare the frequency table at the top of page 56 with the bar graph in the middle of the same page. 3. How are they similar?

5. For purposes of comparison, which do you find easier to use to compare differences among frequencies—the frequency table or the bar graph? Explain.

Refer to the line graph at the bottom of page 56. 6. Represent the same data in a table that uses only numbers.

U.S. Wooden Roller Coasters

7. Compare the table you just created with the line graph. Which do you think presents the data in a way that is easier to compare changes over periods of time? Explain.

Helping You Remember 8. Explain how the information in a line graph differs from the information in a bar graph.


69


Lesson 2–2

4. How are they different?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Line Plots In a line plot, data are pictured on a number line. An ✕ is used to represent each item of data. For example, the figure below is a line plot that pictures data about the number of CDs owned by the students in a math class. Number of CDs Owned by Students in a Math Class

3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3

0

5

10

3 3 3 3 3 15

3

20

25

30

35

Use the line plot above to answer each question. 1. How many students own exactly eighteen CDs?

2. What number of CDs is owned by exactly three students?

3. A data item that is far apart from the rest of the data is called an outlier. Is there an outlier among these data? What is it?

4. What would you say is the number of CDs owned by the “typical” student in this class?

5. Use the data in the table to complete the line plot below. Four data points have been graphed for you. Number of Seconds for 24 Sixth-Graders to Run 200 Meters 130 125

100 105

85 100

120 70

100 125

100 85

110 95

150 130

90 105

100 90

110 105

130 100

3 3 3

3 70


70


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Circle Graphs A circle graph is used to compare parts of a whole. The pie-shaped sections show the groups. The percents add up to 100%.

Mike's Homework

SCHOOL The circle graph shows the

subjects Mike studies during homework time. Which subject does Mike spend most of his time studying?

Math 48%

The largest section of the graph is the section representing math. So, math takes up the most time. How does the time spent studying social studies compare to the spent studying science?

Social Studies 17% Science 8%

Reading 26%

Music 1%

The section representing social studies is about twice the size of the section representing science. So, twice as much time is spent on social studies as on science.

SURVEYS Use the graph that shows the results of a favorite

Favorite Colors

colors survey. 1. Which color is the least favorite?

Blue 33%

Red 25%

2. Which colors are the favorites of the same number of people? Green 19% Yellow 10% Orange Purple 10% 3%

FOOD Use the graph of Mike’s study time from

the Examples. 4. Which subject does Mike spend the least time studying? 5. On which two subjects together does Mike spend about the same time as reading? 6. How does the amount of time spent on math compare to the amount of time Mike spends on science?


71


Lesson 2–3

3. How does the number of people who say green is their favorite color compare to the number who say yellow is their favorite color?

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Circle Graphs GEOGRAPHY Use the graph that shows how much of Earth’s land that each continent represents.

Continents North America 16%

1. Which continent has the greatest area?

South America 12%

Asia 30%

2. Which two continents are the smallest? Africa 20%

Australia 6%

3. How does the size of Europe compare to the size of Africa? Antartica 9%

Europe 7%

4. How much larger is Asia than Africa?

LAKES Use the graph that shows how much of the

Great Lakes

total surface of the Great Lakes each lake takes up. 5. Which of the Great Lakes is the smallest?

Superior 34%

Huron 24% Ontario 8%

6. Which two lakes are about the same size? Michigan 24%

Erie 10%

7. How does Lake Erie compare to Lake Ontario?

8. Which two lakes together are the same size as Lake Superior?

VACATIONS Use the graph that shows how families will spend winter vacation.

Winter Vacation Beach 7%

9. How will most families spend their vacations? Shop 22%

10. Will more families go to the beach or go shopping?

Ski 11%

Visit Family 33%

Home 27%

11. Compare how many families will be skiing to how many will be visiting family.


72


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Circle Graphs SPORTS For Exercises 1–3, use Graph A. For Exercises 4–6, use Graph B.

Graph A

Graph B

Favorite Sports of Mr. Franco's Class

Attendance at the Baseball Game Age 46-60 14%

Age 61 and older 5%

Baseball 49% Hockey 10% Age 31-45 21% Basketball 20%

Age 16-30 35%

1. Kwan surveyed Mr. Franco’s class to find out the favorite sports of the class. Which sport was the favorite of the largest percent of students in the class? Which sport was the favorite of the smallest percent of students?

2. Which sports were the favorite of about the same number of students?

3. Which sport is the favorite of half as many students as basketball?

4. Mr. Jackson kept track of attendance at the baseball game for an advertising agency. The agency wants to target its advertising to the age group that has the highest percent in attendance. To which group should the agency target ads?

5. Which two age groups have about the same percent of people?

6. Mr. Jackson’s daughter is in the age group with the second highest percent. In which age group is Mr. Jackson’s daughter?


73


Lesson 2–3

Football 21%

Age 0-15 25%

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Circle Graphs Pre-Activity Complete the Mini Lab at the top of page 62 in your textbook. Write your answers below. 1. Make a bar graph of the data.

Driving Together in One Car to Spring Break

2. Which graph represents the data better, a circle graph or a bar graph? Explain.

Reading the Lesson 3. A circle graph compares parts of a whole. How is a circle well suited for this kind of representation?

4. At the bottom of page 62, the text says that the percents add up to 100%. Why is this important?

Helping You Remember 5. Find a circle graph in a newspaper or magazine. Explain to a classmate what the sections of the graph represent. © Glencoe/McGraw-Hill

74


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment A Circle Graph Mystery The circle graph below was drawn to show the leading causes of fire in the United States. However, all the labels except one have mysteriously disappeared. Use the clues below to decide what the labels should be and where they belong. Then complete the graph. (Remember: Each label must include a word or phrase and a percent.) Causes of Fires

Clue 1

Most fires are caused by heating equipment.

Clue 2

Fires caused by electrical wiring and fires caused by heating equipment together make up 46% of all fires.

Clue 3

The percent of fires caused by children playing is 12% less than the percent of fires caused by cooking.

Clue 4

The percent of fires caused by open flames is equal to the percent of fires caused by children playing.

Clue 5

The percent of the fires caused by cooking and the percent of fires caused by arson are together just 1% less than the percent of fires caused by heating equipment.

Clue 6

The percent of the fires caused by electrical wiring is 15% greater than the percent caused by children playing.

Clue 7

Fires caused by smoking and fires caused by arson together make up 17% of all fires.

Clue 8

Fires that result from other causes are listed in a category called other.


75


Lesson 2–3

cooking 16%

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Making Predictions Because they show trends over time, line graphs are often used to predict future events.

Piano Scale Practice Times 2

Hours

The graph shows the time Ruben spends each day practicing piano scales. Predict how much time he will spend practicing his scales on Friday.

1

Continue the graph with a dotted line in the same direction until you reach a vertical position for Friday. By extending the graph, you see that Ruben will probably spend half an hour practicing piano scales on Friday.

Sa t. Su n M . on Tu . e W . ed Th . ur . Fr i.

0

Day

MONEY Use the graph that shows the price of a

Football Tickets

ticket to a local high school football game over the last few years.

9 8

1. Has the price been increasing or decreasing? Explain.

7

2. Predict the price of a ticket in year 6 if the trend continues.

Price ($)

6 5 4 3 2 1 0

3. In what year do you think the price will reach $9.00 if the trend continues?

1

2

3

4

5

6

7

8

7

8

Year

BANKS Use the graph that shows the interest rate

Interest Rates

for a savings account over the last few years. 6%

4. What does the graph tell you about interest rates?

5%

Rate

4% 3% 2%

5. If the trend continues, when will the interest rate reach 1 percent?

1% 0

1

2

3

4

5

6

Year


76


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Making Predictions INTERNET Use the graph that shows Internet users

Active Internet Users

in the United States. 120

1. Describe the change in active Internet users from April 2000 to April 2001.

115 110

2. Predict how many active users there were in October 2001 if the trend continued.

Users (millions)

105 100 95 90 85 80 75 70

3. Predict when the number of active users exceeded 115 million if the trend continued.

65

Ap

ril Ju '00 ly O '00 ct Ja . '00 n. Ap '01 ril Ju '01 ly O '01 ct . Ja '01 n. '0 2

0

Date

4. Were there more active users in January 2002 or October 2001? Explain.

SPORTS Use the graph that shows the winning

10K Biathlon Winning Times

times of the 10K Biathlon rounded to the nearest minute.

33 32

5. How did the winning time change from 1980 to 2002?

31

Time (min)

30 29 28 27 26 25

6. To the nearest minute, by how much did the winning time change from 1980 to 2002?

24 0 '80 '84 '88 '92 '94 '98 '02 '06

7. Predict the winning time for 2006 if the trend continues.

8. Predict when the winning time will be less than 20 minutes if the trend continues. © Glencoe/McGraw-Hill

77


Lesson 2–4

Winter Olympic Year

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Making Predictions FITNESS For Exercises 1–3, use Graph A. For Exercises 4–6, use Graph B.

Graph A

Graph B Sit-ups

14

80

12

70

Number of Sit-ups

Number of Students

Aerobics Class

10 8 6 4 2

60 50 40 30 20 10

0

1

2

3

4

5

6

0

Week

1

2

3

4

5

6

7

8

Week

1. Refer to Graph A. Describe the change in the number of students taking the aerobics class.

2. Predict how many students will be in the aerobics class in week 6 if the trend continues.

3. Predict how many students will be in the aerobics class in week 8.

4. Describe the change in the number of sit-ups Cara can do.

5. Predict how many sit-ups Cara will be able to do in week 6 if the trend continues.

6. Predict the week in which Cara will be able to do 80 sit-ups if the trend continues.


78


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Making Predictions Pre-Activity Complete the activity at the top of page 66 in your textbook. Write your answers below. 1. Describe the trends in the winning amounts.

2. Make a prediction as to the amount of money the winner of the 2005 Daytona 500 will receive.

Reading the Lesson Refer to the sentence just below the activity at the top of page 66: “Line graphs are often used to predict future events because they show trends over time.” 3. The word predict comes from two Latin words that mean “to tell in advance.” Look up the word predict in a dictionary. What meaning is given for the word?

4. Look up the word trend in a dictionary. What meaning is given for the word as it is used in the definition of line graph?

5. Look at the line graph at the bottom of page 66. In terms of trend, what happened between 1997 and 1998? What is the difference between prediction and data or statistics?

6. Find two line graphs, one where you feel you can predict the future with confidence and one where you cannot. Explain the difference.


79


Lesson 2–4

Helping You Remember

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Graphs and Decision Making Just as important as knowing how to make a bar graph or a line graph is deciding what type of graph to use. Here are some guidelines to help you make that decision. • A bar graph compares data that fall into distinct categories. Example Use a bar graph to show how the populations of several cities compare in one year. • A line graph shows changes in data over a period of time. Example Use a line graph to show how the population of one city changed over several years. Would you use a bar graph or a line graph to show these data? 1. average temperatures in Sacramento for each month of the year 2. average temperatures in January in five California cities 3. land area of the continents 4. number of CD players purchased each year from 1981 through 1990 5. weight of a baby in each month from birth to one year of age 6. heights of the world’s five tallest trees Make an appropriate graph for each set of data. 7.

Cars in Use

8. Seating Capacity of Aircraft

Year

Number (millions)

Model

Number of Seats

1970 1980 1990 2000

80 105 124 136

B747 DC-10 L-1011 MD-80

405 288 296 142

Cars in Use

Seating Capacity of Aircraft

Model


80


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Sometimes it is hard to read data in a table. You can use a stem-and-leaf plot to display the data in a more readable way. In a stem-and-leaf plot, you order the data from least to greatest. Then you organize the data by place value.

Make a stem-and-leaf plot of the data in the table. Then write a few sentences that analyze the data. Step 1 Order the data from least to greatest. 41 51 52 53 55 60 65 65 67 68 70 72

Money Earned Mowing Lawns ($)

Step 2 Draw a vertical line and write the tens digits from least to greatest to the left of the line.

60 67 65

Step 3 Write the ones digits to the right of the line with the corresponding stems. Stem In this data set, the tens digits form the stems.

→

5

4 5 6 7

55 72 70

53 65 52

41 68 51

Leaf 1 1 2 3 5 0 5 5 7 8 0 2

6

The ones digits of the data form the leaves.

←

6|5 5 $65 Always write each leaf, even if it repeats.

Key

Step 4 Include a key that explains the stems and leaves. By looking at the plot, it is easy to see that the least amount of money earned was $41 and the greatest amount was $72. You can also see that most of the data fall between $51 and $68.

Make a stem-and-leaf plot for the set of data below. Write a few sentences that analyze the data. 34 44 51 48 55 41 47 22 55


81


Lesson 2–5

Stem-and-Leaf Plots

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Stem-and-Leaf Plots Make a stem-and-leaf plot for each set of data. 1. 18, 16, 13, 20, 33, 58, 32, 14, 61, 67, 52

2. 61, 75, 62, 63, 74, 71, 75, 82, 64, 81, 91, 65

3. $52, $49, $37, $21, $65, $23, $49, $51, $22, $21, $24, $47, $44, $53, $61

4. 82°, 91°, 80°, 55°, 63°, 54°, 83°, 90°, 84°, 91°, 59°, 62°, 50°, 92°, 85°, 92°, 92°

SPORTS For Exercises 5–8, use the stem-and-

leaf plot that shows the total number of points earned by each volleyball team at a tournament.

Stem 2 3 4 5 6

5. What was the greatest number of points earned?

Leaf 9 6 4 1 1

6 5 4 3

7 8 9 5 7 9 9 5

4|5 5 45 points 6. What was the least number of points earned?

7. How many teams earned more than 50 points?

8. Between what numbers are most of the points earned?


82


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems TRAFFIC For Exercises 1 and 2, use the table. For Exercises 3 and 4, use

the stem-and-leaf plot. Number of Birds at a Watering Hole Each Hour

Number of Trucks Passing Through the Intersection Each Hour 5 19 32 10

15 18 26 6

6 19 34 8

42 22 19 40

34 23 29 14

Stem

28 21 21 17

1 2 3 4 5

Leaf 8 4 3 2 0

9 8 4 5 0

9 4 4 5 5 5 7 8 3 3 4 6 6 7 3|4 5 34 birds

1. Mr. Chin did a traffic survey. He wrote down the number of trucks that passed through an intersection each hour. Make a stem-and-leaf plot of his data.

2. Refer to your stem-and-leaf plot from Exercise 1. Mr. Chin needs to know the range of trucks passing through the intersection in one hour into which the greatest number of hours fall.

3. What is the least number of birds at the watering hole in one hour? What is the greatest number?

4. What is the most frequent number of birds to be at the watering hole in one hour?

5. RVs Make a stem-and-leaf plot for the number of RVs Mr. Chin counted in 12 hours: 3, 4, 9, 13, 7, 9, 8, 5, 4, 6, 1, 11.

6. RVs Write a few sentences that analyze the RV data for Mr. Chin’s report in Exercise 5.


83


Lesson 2–5

Stem-and-Leaf Plots

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Stem-and-Leaf Plots Pre-Activity Complete the activity at the top of page 72 in your textbook. Write your answers below. 1. What were the least and greatest number of points scored? 2. Which number of points occurred most often?

Reading the Lesson 3. In a stem-and-leaf plot, in what order are the data?

4. In a stem-and-leaf plot of two-digit numbers, how are the data represented?

5. In the box below the stem-and-leaf plot on page 72, it says "Always write each leaf even if it repeats." Because of this rule, what do the leaves of a stem-and-leaf plot tell you that you do not know from a frequency table?

6. Look at the stem-and-leaf plot at the top of page 73. What number of butterflies per day occurs the most often in the stem-and-leaf plot? What does that number indicate?

Helping You Remember 7. Write the steps for making a stem-and-leaf plot. Show someone what a stem-and-leaf plot is, how to read one, and how to make one.


84


NAME ________________________________________ DATE ______________ PERIOD _____

A back-to-back stem-and-leaf plot is used to compare two sets of data. In this type of plot, the leaves for one set of data are on one side of the stems, and the leaves for the other set of data are on the other side of the stems. Two keys to the data are needed. ELECTIONS Use the back-to-back stem-and-leaf plot of the electoral

votes cast by each state and the District of Columbia for the Democratic and Republican candidates for U.S. president in 2000. Democrat 2 3 3 4 4 4 5 7 7 8 0 0 1 1 2 5 8 2 3 3 4 2|0 5 2 votes

Stem 0 1 2 3 4 5

Republican 3 3 3 3 3 4 4 4 5 5 5 6 6 7 8 8 8 8 8 9 9 1 1 2 3 3 4 1 5 2

0|3 5 3 votes

1. What is the greatest number of electoral votes cast by a state for the Democratic candidate? the greatest number of electoral votes cast by a state for the Republican candidate?

2. Which candidate received votes from the greater number of states?

3. Which candidate received the greater number of total votes?

4. What is the difference between the number electoral votes cast for the candidates?

5. Write a sentence or two comparing the number of electoral votes cast for the two candidates.


85


Lesson 2–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Mean The mean is the most common measure of central tendency. It is an average, so it describes all of the data in a data set.

The prices of twelve different jackets are shown. Find the mean. 25 1 34 1 39 1 … 1 27 mean 5 }}} 12

← sum of the data ← number of data items

Jacket Prices ($) 25 45 56

34 52 61

39 27 15

41 22 27

444 5} } or 37 12

The mean price of a jacket is $37. A set of data may contain very high or very low values. These values are called outliers.

Find the mean for the snowfall data with and without the outlier. Then tell how the outlier affects the mean of the data. Compared to the other values, 4 inches is low. So, it is an outlier.

Month Snowfall (in.) Nov. Dec. Jan. Feb. Mar.

mean with outlier

mean without outlier

20 1 19 1 20 1 17 1 4 mean 5 }}}

20 1 19 1 20 1 17 mean 5 }}}

5

20 19 20 17 4

4 76 5 }} or 19 4

80 5} } or 16 5

With the outlier, the mean is less than the values of most of the data. Without the outlier, the mean is close in value to the data.

Find the mean for each set of data. 1. 11, 8, 7, 12, 10, 9, 13, 26

2. 15, 10, 9, 17, 24, 27, 39, 15, 24

3. 26, 19, 29, 15, 2, 31, 56, 30

4. 108, 121, 73, 79, 56, 91

5. Find the mean for the set of data in Exercise 1 without the outlier. Then tell how the outlier affects the mean of the data.


86


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Mean 1. 6, 9, 2, 4, 3, 6, 5

2. 25, 18, 14, 27, 25, 14, 18, 25, 23

3. 13, 6, 7, 13, 6

4. 8, 2, 9, 4, 6, 8, 5

5. 13, 7, 17, 19, 7, 15, 11, 7

6. 1, 15, 9, 12, 18, 9, 5, 14, 7

7. 28, 32, 23, 43, 32, 27, 21, 34

8. 30, 16, 29, 32, 14, 21, 26

9. 42, 35, 27, 42, 38, 35, 29, 24

10. 157, 124, 157, 124, 157, 139

Identify the outlier or outliers in each set of data. 11.

Price

Tally

Frequency

$10

4

4

$20

5

5

$30

3

3

$40

1

1

12.

Stem 2 3 4 5

Leaf 0 1 4 7 0 0 1 5 6 3 6 7 2|4 5 24

WEATHER Use the data in the table that shows daily temperatures.

13. Identify the outlier.

14. What is the mean of the data with the outlier included?

Day

Temp. (°F)

Monday Tuesday Wednesday Thursday Friday

69 70 73 35 68

15. What is the mean of the data without the outlier included?

16. How does the outlier temperature affect the mean of the data?


87


Lesson 2–6

Find the mean for each set of data.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Mean ANIMALS For Exercises 1–3, use the table about bears.

Bear

Average Height (ft)

Average Weight (lb)

Alaskan Brown Black Grizzly Polar

8 6 7 7

1,500 338 588 850

1. You are writing a report on bears. You are analyzing the data on heights and weights in the table above. First look for outliers. Identify the outlier for the height data. Identify the outlier for the weight data.

2. Find the mean of the bear weight data with and without the outlier.

3. Describe how the outlier affects the mean of the bear weight data.

4. WORK Carlos earned $23, $29, $25, $16, and $17 working at an ice cream shop after school. What is the mean amount he earned?

5. CARS The cost of a tank of gas at nine different gas stations is shown below. What was the mean cost of a tank of gas?

6. SCHOOL Sally received scores on math quizzes as shown below. Find her mean score with and without both outliers. Quiz Scores: 84, 85, 91, 81, 52, 92, 99, 91, and 45

Cost of Gas: $17, $18, $22, $15, $17, $16, $25, $21, and $20


88


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Mean Pre-Activity Complete the Mini Lab at the top of page 76 in your textbook. Write your answers below. 1. How many pennies are in each cup?

3. Suppose your teacher gave you another quiz and you scored 14 points. How many pennies would be in each cup?

Reading the Lesson 4. Look up the word mean in a dictionary. Write the meaning that fits the way the word is used in this lesson.

Look at the paragraph below the activity at the top of page 76 in your textbook. A number that helps describe all of the data in a data set is an average. An average is also referred to as a measure of central tendency. 5. Is the mean a good measure of central tendency when there is no outlier? Give an example.

6. Is the mean a good measure of central tendency when there is an outlier? Give an example.

Helping You Remember 7. Explain one problem with using the mean as a measure of central tendency.


89


Lesson 2–6

2. For the five quizzes, your average score was _______ points.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Linguistic Statistics Linguistics is the study of human speech. The activity on this page shows the type of data collection and analysis that might be done by a linguist who is researching the structure of the English language. All questions refer to the Preamble to the U.S. Constitution, printed at the bottom of the page. 1. Which two consonants do you think appear most often in the Preamble? 2. Which vowel do you think appears most often in the Preamble? least often? 3. Complete this table by counting the occurrences of each letter. A few letters have been counted already, to help you get started. (Hint: Your total should be 268.) Letter

Frequency

Letter

Frequency

Letter

a

j

s

b

k

t

c

l

u

m

v

d

11

e

n

f

o

x

g

p

y

q

z

h i

9

r

17

Frequency

w

20

4. Which two consonants actually appear most often in the Preamble? 5. Find the mean frequency for the consonants. Which two consonants occur the closest number of times to this mean? 6. Which vowel actually appears most often in the Preamble? least often? 7. Find the mean frequency for the vowels. Which vowel occurs the closest number of times to this mean? 8. Which word do you think occurs most often in the Preamble? Verify your answer. Preamble to the Constitution of the United States of America We the People of the United States, in order to form a more perfect Union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America. © Glencoe/McGraw-Hill

90


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Median, Mode, and Range The median is the middle number of the data put in order, or the mean of the middle two numbers. The mode is the number or numbers that occur most often.

The table shows the costs of seven different books. Find the mean, median, and mode of the data.

Book Costs ($) 22 14

105 22 1 13 1 11 1 16 1 14 1 13 1 16 mean: }}}}} 5} } or 15 7

13 13

11 16

16

7

To find the median, write the data in order from least to greatest. median: 11, 13, 13, 14, 16, 16, 22 To find the mode, find the number or numbers that occur most often. mode: 11, 13, 13, 14, 16, 16, 22

Whereas the measures of central tendency describe the average of a set of data, the range of a set of data describes how the data vary.

Find the range of the data in the table. Then write a sentence describing how the data vary.

Temperature (°F) 40 60

32 63

55 50

The greatest value is 63. The least value is 32. So, the range is 63° 2 32° or 31°. The range is large. It tells us that the data vary greatly in value.

Find the mean, median, mode, and range of each set of data. 1. 14, 13, 14, 16, 8

2. 29, 31, 14, 21, 31, 22, 20

3.

4.

Quiz Scores 72 68

60 72


80 86

Snowfall (in.) 2 3

91

6 0

5 1

4


Lesson 2–7

The mean is $15. The median is $14. There are two modes, $13 and $16.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Median, Mode, and Range Find the mean, median, mode, and range for each set of data. 1. 6, 9, 2, 4, 3, 6, 5

2. 13, 6, 7, 13, 6

3. 1, 15, 9, 12, 18, 9, 5, 14, 7

4. 13, 7, 17, 19, 7, 15, 11, 7

5. 3, 9, 4, 3, 9, 4, 2, 3, 8

6. 25, 18, 14, 27, 25, 14, 18, 25, 23

7. 8, 3, 9, 4, 6, 7, 5

8. 28, 32, 23, 43, 32, 27, 21, 34

9. 157, 124, 157, 124, 157, 139

10. 42, 35, 27, 42, 38, 35, 29, 24

11. Write a sentence that describes how the data items in Exercise 5 vary.

12. Why is mode not the best choice to describe the data in Exercise 5? Explain.

MUSEUMS Use the table showing the number of visitors to the art museum each month.

Vistors to the Art Museum (thousands)

13. What is the mean of the data?

3 5 12

11 3 2

5 6 2

4 3 4

14. What is the median of the data?

15. What is the mode of the data?

16. Which measure of central tendency best describes the data? Explain.


92


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Median, Mode, and Range SCIENCE For Exercises 1–3, use Table A. For Exercises 4–6, use Table B.

Table A shows the number of days it took for some seeds to germinate after planting. Table B shows how tall the plants were after 60 days.

15 9

Table A

Table B

Number of Days for Seeds to Germinate

Height (in.) of Plants After 60 Days

20 21

30 21

15 15

16

17 15

19 17

13 21

17 14

20

2. Use your answer from Exercise 1. Which measure of central tendency best describes the data? Explain.

3. What is the range of the seed germination data? Describe how the data vary.

4. What are the mean, median, and mode of the plant height data?

5. Refer to your answer in Exercise 4. Which measure of central tendency best describes the data? Explain.

6. What is the range of the plant height data? Describe how the data vary.


Lesson 2–7

1. Refer to Table A. You are doing some experiments with germinating seeds. You are preparing a report on your findings to a seed company. What are the mean, median, and mode of the data?

93


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Median, Mode, and Range Pre-Activity Complete the activity at the top of page 80 in your textbook. Write your answers below. 1. Find the mean wingspan. 2. List the data in order from least to greatest. 3. Which data are in the middle of the arranged data? 4. Compare the number that is in the middle of the data set to the mean of the data.

Reading the Lesson 5. How are mean, median, and mode similar? How are they different?

Look at Example 3 at the bottom of page 81. Also, look at its opening statement, "Some averages may describe a data set better than other averages." 6. Which averages are discussed in the example? 7. What is causing the mean to be so high? 8. What if there were two 54s? How would that affect the averages?

9. Does this example illustrate its opening statement?

Helping You Remember 10. You may already know that a median strip refers to the concrete or landscaped divider that runs down the center of many roads. How does this idea of median relate to the meaning of median in this lesson?


94


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Puzzling Over Data Each puzzle on this page contains an incomplete set of data. The clues give you information about the mean, median, mode, or range of the data. Working from these clues, you can decide what the missing data items must be. For example, this is how you might solve the data puzzle at the right.

Clue: mean 5 18 Data: 12, 17, 18, 19, 19,

There are 6 items of data. The mean is 18, so the sum of the data must be 6 3 18 5 108. Add the given data: 12 1 17 1 18 1 19 1 19 5 85. Subtract from 108: 108 2 85 5 23. So the complete set of data is: 12, 17, 18, 19, 19, 23 .

1. Clue: mode 5 8 Data: 7, 7, 8,

2. Clue: median 5 54.5 ,

, 14

3. Clues: mean 5 27 mode 5 30 , 30,

Data: 110, 112,

5. Clues: mean 5 13 median 5 13 range 5 13 , 9, 12,

, 52,


, 124, 136,

6. Clues: mean 5 7 median 5 8.5 mode 5 10 , 18,

7. Clues: mean 5 60 mode 5 52 range 5 28 Data:

, 65, 84

4. Clues: median 5 120 range 5 46

Data: 10, 25, 27,

Data:

Data: 36, 40, 49,

Data:

, 4, 8,

,

,

8. Clues: median 5 24 mode 5 28 range 5 24 ,

, 72, 78

Data: 6, 15,

95

,

,

,


Lesson 2–7

Find the missing data. (Assume that the data items are listed in order from least to greatest.)

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Analyzing Graphs Graphs can lead readers to the wrong conclusion about the data when the numbers on either scale are inconsistent, the vertical or horizontal scale does not start at zero, or different scales are used.

Movie Tickets Graph B 10 9 8 7 6 5 4 3 2 1 0 19 9 20 9 0 20 0 0 20 1 0 20 2 03

Price ($)

20 18 16 14 12 10 8 6 4 2 0 19 9 20 9 0 20 0 0 20 1 0 20 2 03

Both graphs show the same data, but Graph B appears to show the cost increasing more quickly. Graph A uses a scale of 2 and Graph B uses a scale of 1.

Movie Tickets Graph A

Price ($)

The graphs at the right show how the cost of a movie increased over time. Which graph appears to show that the cost increased more quickly? Explain.

Year

Year

Using an inappropriate measure of central tendency can cause readers to make a wrong conclusion.

Refer to the table. The store says the average price of an electronic pet is $12. Explain how using this average to attract customers with low prices is misleading.

Electronic Pet Prices ($) 14 21

15 12

15 12

20 20

49 12

Order the data from least to greatest: 12, 12, 12, 14, 15, 15, 20, 20, 21, 49. mean: $19 median: $15 mode: $12 The store used the mode as the average. Because the mode price is less than the other prices, it is not the most accurate average to use.

1. In Example 1, how could you change Graph A to appear to show that the cost rose more slowly? 2. Oleta’s test scores in order from least to greatest were 19, 75, 76, 82, 83. Find the mean, median, and mode of the data. Which measure might be misleading in describing the average number of points Oleta earned.


96


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Analyzing Graphs ANIMALS For Exercises 1–3, use the graph that shows the weight of bears.

Weight of Bears Graph A 700

Weight (lb)

1. About how many times heavier does a grizzly bear appear to be than a black bear?

2. Explain how this graph is misleading.

600 500 400 300 0

3. Redraw the graph so that it is not so misleading.

Black Bear

Grizzly Bear

Weight of Bears Graph B

4. BUSINESS The graphs below show company sales. Which graph makes the sales appear to be increasing more rapidly? Explain. Company Sales Graph B

12

24

10

20

Users (millions)

8 6 4 2

12

Grizzly Bear

8 4 9 19 8 9 20 9 0 20 0 0 20 1 02

19

Year

Year

BUDGETS Use the table that shows the 2003

National Park 2003 Budget

budgets for eight national parks. 5. Find the mean, median, and mode of the data.

6. Which measure would be misleading in describing the average budget for these parks? Explain.

7. Which measure describes the data most accurately? Explain.


Lesson 2–8

0 9 19 8 9 20 9 0 20 0 0 20 1 02

0

Black Bear

16

19

Users (millions)

Company Sales Graph A

97

Park

Budget ($)

Acadia Crater Lake Denali Everglades Mammoth Cave Olympic Great Smokies Zion

6,000,000 4,000,000 11,000,000 14,000,000 6,000,000 10,000,000 15,000,000 6,000,000


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Analyzing Graphs BUSINESS For Exercises 1 and 2, use Graph A. For Exercises 3 and 4, use Graphs B and C. The graphs show the number of DVDs and videos sold by a video store.

Graph A

Graph B

March Sales

Sales

250 200 0

DVDs

Videos

Sales

6

12

5

10

Number Sold (thousands)

350

Number Sold (thousands)

Number Sold

400 300

Graph C

4 3 2 1

6 4 2

Month

Month

Ja

Ja n. Fe b M . ar Ap . r. M ay Ju ne

0 n. Fe b M . ar Ap . r. M ay Ju ne

0

8

1. About how many times fewer DVDs than videos appear to have been sold?

2. Explain how Graph A is misleading.

3. The graphs show the same data. Which graph appears to shows that the number of DVDs and videos sold increased more rapidly? Explain.

4. The store owner is trying to get a loan from the bank and wants to show that business is good. Which graph should the store owner show the bank? Explain.

5. MARKETING A store advertises that it has the lowest average price for T-shirts in town. Find the mean, median, and mode of the prices.

6. MARKETING Use your answer from Exercise 5. Which measure of central tendency describes the average T-shirt price the most accurately? Explain.

T-Shirt Prices: $14, $5, $10, $12, $5, $4, $13


98


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Analyzing Graphs Pre-Activity Complete the activity at the top of page 86 in your textbook. Write your answer below. 1. Suppose you look at the lengths of the bars that represent Dan Marino and Terry Bradshaw. You might conclude that Dan Marino threw three times as many touchdown passes as Terry Bradshaw. Why is this conclusion incorrect?

Reading the Lesson For Exercises 2–4, look at the first sentence below the activity at the top of page 86: “Graphs let readers analyze and interpret data easily.” 2. Look in a dictionary for meaning of the word analyze. Write a definition that fits the sentence just quoted. 3. Do the same for the word interpret. Write a definition that fits the sentence just quoted.

Lesson 2–8

4. Why is it important to analyze as well as interpret data in a graph?

5. Why is the graph in the activity at the top of page 86 misleading? 6. On a separate sheet of paper, redraw the graph in the activity at the top of page 86 to correct the problem. Do the lengths of the Marino and Bradshaw bars represent more closely the relationship between touchdown passes actually thrown by these players?

Helping You Remember 7. Look up the word mislead in a dictionary. Write the definition here. Then tell how it is easy for a graph to mislead.


99


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Be a Data Detective! Each of the graphs on this page has been drawn incorrectly. Can you detect the mistake? 1.

2.

Weekly Book Sales

United States Population 300 250

Population (millions)

Fiction Biography

200 150 100 50

Reference

0 1800 1900

Other

1925

1950

Year

Mistake:

3.

Mistake:

Areas of the Great Lakes

4.

Retail Sales of Automobiles

100

2002

80

2000

Year

Square Miles (thousands)

1975 2000 (projected)

60

1998

40

1996

20

1994

8, 84 6, 00 0

8, 14 2, 00 0

Lake

8, 52 6, 00 0

8, 99 0, 00 0

O nt ar io

Er ie

H ur on

M ic hi ga n

Su pe rio r

0

Number of Automobiles

Mistake:

Mistake:

5. Draw a corrected graph for Exercise 3.

6. Draw a corrected graph for Exercise 4. Retail Sales of Automobiles

Areas of the Great Lakes


100



Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860066-9 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03

CONTENTS Vocabulary Builder .............................vii Family Letter ............................................ix Family Activity ........................................x Lesson 3-1 Study Guide and Intervention ........................123 Practice: Skills ................................................124 Practice: Word Problems................................125 Reading to Learn Mathematics......................126 Enrichment .....................................................127

Lesson 3-5 Study Guide and Intervention ........................143 Practice: Skills ................................................144 Practice: Word Problems................................145 Reading to Learn Mathematics......................146 Enrichment .....................................................147


Lesson 3-3


Study Guide and Intervention ........................133 Practice: Skills ................................................134 Practice: Word Problems................................135 Reading to Learn Mathematics......................136 Enrichment .....................................................137

Standardized Test Practice Student Recording Sheet ............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A25



iii

3 Test, Form 1 ..........................149–150 3 Test, Form 2A ........................151–152 3 Test, Form 2B ........................153–154 3 Test, Form 2C........................155–156 3 Test, Form 2D........................157–158 3 Test, Form 3 ..........................159–160 3 Extended Response Assessment .161 3 Vocabulary Test/Review.................162 3 Quizzes 1 & 2................................163 3 Quizzes 3 & 4................................164 3 Mid-Chapter Test ...........................165 3 Cumulative Review........................166 3 Standardized Test Practice....167–168


Vocabulary Builder Pages vii-viii include a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar.

Practice: Skills


When to Use Give these pages to students before beginning Lesson 3-1. Encourage them to add these pages to their mathematics study notebook. Remind them to add definitions and examples as they complete each lesson.



Family Letter and Family Activity Page ix is a letter to inform your students’ families of the requirements of the chapter. The family activity on page x helps them understand how the mathematics students are learning is applicable to real life.


One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques.

When to Use Give these pages to students to take home before beginning the chapter.


When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students.

iv





Enrichment













v

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics This is an alphabetical list of new vocabulary terms you will learn in Chapter 3. As you study this chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add this page to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term

Found on Page


clustering

equivalent [ih-KWIHV-uh-luhnt] decimals

expanded form

front-end estimation

standard form


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____

Family Letter

on our bills, on our car Decimals are all around us. They are derstanding decimals and odometer, and on our calculators. Un useful, but important in how to work with them is not only today’s world. ing Decimals, your child In Chapter 3, Adding and Subtract ing them, ordering them, will learn all about decimals–compar cting them, and estimating rounding them, adding them, subtra dy of this chapter, your their sums and differences. In the stu classroom assignments child will complete a variety of daily a chapter project . and activities and possibly produce it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 3 to the real world. You math we will be learning in Chapter line Study Tools for may also wish to log on to the On t Study Guide pages, self-check quizzes, Parent and Studen 1.net. If you have any and other study help at www.msmath contact me at school. questions or comments, feel free to Sincerely,



ix


Family Letter


NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Adding and Subtracting Decimals Knowing how to add and subtract decimals is very important when balancing a checkbook. Work with a family member to complete the sample check register below. Add any deposits and subtract withdrawals to determine the balance of the account. The balance in the account on November 1st was $337.88. Date 11/1 11/7 11/10 11/15 11/21 11/22 11/26 12/1

Transaction

Withdrawal Amount

Deposit Amount

Balance $337.88

Groceries Transfer from Savings Account Electric Bill Deposit from Paycheck Oil Change Birthday Present for Friend Demember Rent

$42.59 $125.00 $35.67 $415.00 $769.63 $17.54 $500.00

For Exercises 1–3, use the completed check register. 1. How much did the oil change cost on November 22?

2. What was the balance on December 1st after rent had been paid?

3. Compare the balance on November 1st with the balance after rent was paid on December 1st. What is difference in the two balances?

4. Work with a family member to develop a personal budget. What income and expenses do you expect to have?

2. $252.09

3. $85.79

4. See students’ work.

x

1. $29.99



NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Representing Decimals Decimals can be written in standard form and expanded form. Standard form is the usual way to write a decimal, such as 3.52. Expanded form is a sum of the products of each digit and its place, such as (3 3 1) 1 (5 3 0.1) 1 (2 3 0.01).

Write 128.0732 in word form.

Write ninety-nine and two hundred seven thousandths in standard form and expanded form.

tens

ones

tenths

hundredths

thousandths

ten-thousandths

thousands

hundreds

tens

ones

tenths

hundredths

thousandths

ten-thousandths

0

1

2

8 • 0

7

3

2

0

0

9

9 • 2

0

7

0

In words, 128.0732 is one hundred twenty-eight and seven hundred thirty-two ten-thousandths.

Standard form: 99.207 Expanded form: (9 3 10) 1 (9 3 1) 1 (2 3 0.1) 1 (0 3 0.01) 1 (7 3 0.001)

Write each decimal in word form. 1. 2.3 2. 0.68 3. 32.501 4. 0.0036 Write each decimal in standard form and expanded form. 5. twenty and two hundredths 6. seven and five tenths 7. three hundred four ten-thousandths 8. eleven thousandths


123


Lesson 3–1

hundreds

Place-Value Chart

thousands

Place-Value Chart

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Representing Decimals Write each decimal in word form. 1. 6.5

2. 0.3

3. 39.2

4. 0.83

5. 5.67

6. 14.006

7. 12.001

8. 0.5214

9. 12.0905

Write each decimal in standard form and expanded form. 10. three tenths

11. fifteen and one tenth

12. eight and four hundredths

13. seventy-two and sixteen thousandths

14. one hundred and one hundredth

15. four hundred seven thousandths

16. four hundred seven tenthousandths

17. one hundred and one thousandth

18. Express (2 3 100) 1 (3 3 10) 1 (1 3 1) 1 (4 3 0.1) 1 (5 3 0.01) in word form.


124


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Representing Decimals BASEBALL For Exercises 1–4, use the table.

The table shows lifetime batting averages for leading baseball players.

Lifetime Batting Averages for Leading Players Team

Batting Average

Tony Gwynn

San Diego Padres

0.338

Mike Piazza

New York Mets

0.325

Derek Jeter

New York Yankees

0.320

Vladimir Guerrero

Montreal Expos

0.319

Edgar Martinez

Seattle Mariners

0.319

1. Write Mike Piazza’s batting average in word form.

2. Which digit is in the thousandths place of each player’s batting average?

3. What is the batting average for the New York Yankees player in expanded form?

4. Which player’s average has a 3 in the hundredths place?

5. BUILDING When measuring board footage for some exotic woods, a carpenter must use 1.25 for thickness rather than 1 in her calculations. Write 1.25 in expanded form.

6. TRAVEL The summer camp Jason attends is exactly four hundred twentythree and four tenths of a mile from his home. Write four hundred twenty-three and four tenths in standard form.


125


Lesson 3–1

Player

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Representing Decimals Pre-Activity Complete the Mini Lab at the top of page 102 in your textbook. Model each decimal using a place-value chart, money, a decimal model, and base-ten blocks. 1. 1.56

2. 0.85

3. 0.08

4. $2.25

Reading the Lesson 5. What does the decimal point do?

6. How does changing the decimal point in 5.78 to 57.8 affect the value of the decimal?

Helping You Remember 7. Look up the words dime and decimal in a dictionary. How is dime related to decimal? Explain how our money system (dollars, dimes, pennies) and the place-value chart use base ten.


126


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Decimal Letters The letter A at the right was created by shading part of a hundreds square. There are 26 parts shaded, so the value of the letter A is 26 hundredths, or 0.26. Find the value of each letter. 2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

Lesson 3–1

1.

26. CHALLENGE Use the values of the 26 letters as a set of data. What is the frequency of the value 0.26? Which value is the mode?


127


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Comparing and Ordering Decimals Use . or , to compare 68.563 and 68.5603. Then, starting at the left, find the first place the digits differ.

First, line up the decimal points.

Compare the digits.

Since 3 . 0,

3.0

68.563 . 68.5603

68.563 68.5603 So, 68.563 is greater than 68.5603.

Order 4.073, 4.73, 4.0073, and 4 from least to greatest. First, line up the decimal points.

Annex zeros so that each has the same number of decimal places.

Use place value to compare

4.0730 4.7300 4.0073 4.0000

4.0000 4.0073 4.0730 4.7300

4.073 4.73 4.0073 4

and order the decimals.

The order from least to greatest is 4, 4.0073, 4.073, and 4.73.

Use ., ,, or 5 to compare each pair of decimals. 1. 4.08 d 4.080

2. 0.001 d 0.01

3. 23.659 d 22.659

4. 50.031 d 50.030

5. 7 d 7.0001

6. 18.01 d 18.010

Order each set of decimals from least to greatest. 7. 0.006, 0.6, 0.060, 6 8. 456.73, 465.32, 456.37, 456.23 9. 3.01, 3.009, 3.09, 3.0001 10. 45.333, 45.303, 45.03, 45.003, 45.0003


128


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Comparing and Ordering Decimals 1. 2.4 d 2.04

2. 6.23 d 6.32

3. 0.02 d 0.020

4. 12.05 d 12.50

5. 0.92 d 0.095

6. 39.21 d 39.021

7. 0.849 d 0.0851

8. 12.1 d 12.10

9. 21.967 d 2.1968

10. 0.0128 d 0.128

11. 1.4601 d 1.460

12. 19.08 d 19.079

13. 28.003 d 28.03

14. 0.831 d 0.0835

15. 39.020 d 39.0200

16. 15.6243 d 15.6234

17. 12.0905 d 12.10

18. 56.7 d 5.67

Order each set of decimals from least to greatest. 19. 1.25, 1.52, 1.02, 1.50

20. 67.39, 68.004, 67.039, 67.04

21. 15.0421, 14.52, 14.521, 15.421

22. 0.0012, 0.0211, 0.0002, 0.0022

Order each set of decimals from greatest to least. 23. 4.99, 4.001, 5.0, 4.01

24. 12.0012, 120.012, 12.012, 12.12

25. 3.5, 3.05, 3.55, 3.555

26. 45.0, 40.5, 40.09, 49.5


129


Lesson 3–2

Use ., ,, or 5 to compare each pair of decimals.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Comparing and Ordering Decimals MUSIC For Exercises 1–4, use the table.

The table shows the percent of the music market for each type of music. Music Industry Sales Statistics, 2001 Type of Music

Percent of Market

Pop

12.1

Country

10.5

Rock

24.4

Rap/Hip-Hop

11.4

R&B

10.6

1. Use . or , to compare the percents for pop and rap/hip-hop. Which is greater?

2. Use . or , to compare the percents for country and R&B. Which is greater?

3. If you owned a store that sells CDs, which kind of music would you want to sell, based on the table? Explain.

4. Suppose children’s songs have 12.05 percent of the market. Is this greater or less than the percent for pop music? Explain.

5. CONSTRUCTION Alberto is setting out four boards of lumber. The lengths of the boards are 4.5 feet, 4.52 feet, 4 feet, and 4.505 feet. Order the lengths from longest to shortest.

6. CONSTRUCTION Ella set out a board of pine lumber that was 0.8 feet long and a board of cedar lumber that was 0.80 feet long. Alberto said the cedar board was longer. Is he correct? Explain.


130


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Comparing and Ordering Decimals Pre-Activity Read the introduction at the top of page 108 in your textbook. Write your answers below. 1. Which player had the highest score? Explain.

Reading the Lesson For Exercises 2–4, refer to the paragraph above Example 2 on page 109. 2. What are equivalent decimals?

3. What does it mean to annex a zero in a decimal? What happens to the value of the decimal?

5. Look at Example 2 on page 109. Why is annexing zeros used in ordering decimals?

6. What does the expression 7.6 , 7.8 mean?

7. What symbol would you use to compare 7.6 and 7.3? Explain.

Helping You Remember 8. Explain how using a number line to compare decimals is similar to using a number line to compare whole numbers.


131


Lesson 3–2

4. List three decimals that are equivalent to 0.7.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment A Look at Nutrients The table below gives data about a few of the nutrients in an average serving of some common foods.

Food

Protein Fat Carbohydrates (grams) (grams) (grams)

Vitamins (milligrams)

Minerals* (milligrams)

B

B-1

B-2

Na

K

Ca

apple (medium)

0.3

0.5

21.1

8

0.02

0.02

1

159 10

chocolate bar (1.02 oz)

2.2

9.4

16.5

0

0.02

0.08

29

119 55

cola (12 fl oz)

0.0

0.0

40.7

0

0.00

0.00

20

7

11

21.8

14.5

0.0

0

0.13

0.15

40

382

6

1.7

0.1

26.8

97

0.20

0.05

2

474 22

peas (1/2 cup)

4.5

0.4

10.8

19

0.22

0.09

128 137 17

wheat bread (1 slice)

2.3

1.0

11.3

0

0.11

0.08

129

whole milk (8 fl oz)

8.0

8.2

11.4

2

0.09

0.40

120 370 291

hamburger (1 medium) orange juice (8 fl oz)

33

30

*Na 5 sodium, K 5 potassium, Ca 5 calcium

Use the data in the table to answer each question. 1. Is there more potassium in one apple or in one serving of peas? 2. Does one serving of milk contain more fat or more carbohydrates? 3. Which foods contain less than 0.05 milligram of vitamin B-2? 4. Which foods contain an amount of carbohydrates between 15 grams and 25 grams? 5. Which food contains the least amount of calcium? 6. Which food contains the greatest amount of vitamin B-1? 7. List the foods in order of their protein content from least to greatest. 8. List the foods in order of their fat content from greatest to least. 9. Make up two questions about the data in the table. Exchange questions with a classmate. Then answer your classmate’s questions.


132


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Rounding Decimals To round a decimal, first underline the digit to be rounded. Then look at the digit to the right of the place being rounded. d d

If the digit is 4 or less, the underlined digit remains the same. If the digit is 5 or greater, add 1 to the underlined digit.

Round 6.58 to the nearest tenth.

Underline the digit to be rounded.

Look at the digit to the right of the underlined digit.

Since the digit to the right is 8, add one to the underlined digit.

6.58

6.58

6.6

To the nearest tenth, 6.58 rounds to 6.6. Round 86.943 to the nearest hundredth.

Underline the digit to be rounded.

Look at the digit to the right of the underlined digit.

Since the digit is 3 and 3 , 5, the digit 4 remains the same.

86.943

86.943

86.94

To the nearest hundredth, 86.943 rounds to 86.94.

1. 3.21; tenths

2. 2.0505; thousandths

3. 6.5892; hundredths



6. 34.35; tenths


8. 2.5134; tenths

9. 0.0052; thousandths 11. 131.1555; thousandths


10. 0.0052; hundredths 12. 232.88; tenths

133


Lesson 3–3

Round each decimal to the indicated place-value position.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Rounding Decimals Round each decimal to the indicated place-value position. 1. 54.38; ones

2. 2.671; tenths

3. $87.01; tens

4. 12.0905; tenths

5. 441.031; ones

6. 7.892; tenths


8. 5.5252; ones

9. 16.01; tens

10. 0.58; tenths



13. $10.65; ones




17. 0.830528; ten-thousandths





134


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Rounding Decimals POPULATION For Exercises 1 and 2, use the table.

The table shows the number of people in the United States per square mile. U.S. Population Year

Number of people per square mile of land area

1970

57.4

1980

64.0

1990

70.3

2000

79.6

1. Round the decimal for the number of people per square mile in 2000 to the nearest tens. Then round it to the nearest ones.

2. Round the decimal for the number of people per square mile in 1970 to the nearest tens. Then round it to the nearest ones.

EVERGLADES For Exercises 3–7, use the following information.

3. How much rain does the Everglades National Park receive each year rounded to the nearest inch?

4. How many visitors did the park have rounded to the nearest tenth of a million?

5. How many visitors did the park have rounded to the nearest ten-thousandth of a million?

6. What is the budget to the nearest million?

7. What is the budget to the nearest hundredth of a million?

8. SNOWBOARDING Mike, Jake, and Aaron are buying snowboards. Mike is getting his snowboard on sale for $219.49. Jake’s costs $279.97. Aaron’s costs $234.95. Round each snowboard price to the nearest dollar.


135


Lesson 3–3

The Everglades National Park gets an average of 59.10 inches of rainfall a year. It had 1.08025 million visitors in 2001, and its budget for 2003 was $13.958 million.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Rounding Decimals Pre-Activity Read the introduction at the top of page 111 in your textbook. Write your answers below. 1. Round each cost to the nearest dollar.

2. How did you decide how to round each number?

3. Make a conjecture about how to round each cost to the nearest dime.

Reading the Lesson For Exercises 4 and 5, see Examples 1 and 3 on pages 111 and 112. 4. In Example 1, what is the underlined digit? What place is it in? Why does the 1 remain the same when the decimal is rounded?

5. In Example 3, why is the digit in the cents place underlined? Why is it increased by 1 when the decimal is rounded?

Helping You Remember 6. Explain how to round a number. Give an example.


136


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Everybody into the Pool! Answer each question using the “decimal pool” below. 1. Which decimal when rounded to the nearest hundredth is 0.03? 2. Which decimal when rounded to the nearest thousandth is 0.003? 3. Which two decimals when rounded to the nearest hundredth are 0.02? 4. Which five decimals when rounded to the nearest tenth are 0.2? 5. Which decimal when rounded to the nearest thousandth is 0.210? 6. Which two decimals when rounded to the nearest hundredth are 0.20? 7. Add to the pool four different decimals that when rounded to the nearest thousandth are 0.301. 8. Add to the pool a three-place decimal that when rounded to the nearest tenth is 1.0.

0.025

0.1505

029

0.0

0.185

0.301

0.1 099

0.2

01

0.196

51

9

3 0.0

0.019

0.2099

9. CHALLENGE Suppose that you are rounding decimals to the nearest hundredth. How many three-place decimals round to 0.05? List them. How many four-place decimals do you think round to 0.05?


137


Lesson 3–3

0.0209

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Estimating Sums and Differences Estimation Methods Rounding

Estimate by rounding each decimal to the nearest whole number that is easy for you to add or subtract mentally.

Front-End Estimation

Estimate by first adding or subtracting the front digits. Then add or subtract the next digits.

Clustering

Estimate by rounding a group of close numbers to the same number.

Estimate 14.07 1 43.22 using front-end estimation. Add the front digits.

Add the next digits.

14.07 1 43.22 }}} 5

14.07 1}}} 43.22 57.00

An estimate for 14.07 1 43.22 is 57.

Use clustering to estimate $7.62 1 $7.89 1 $8.01 1 $7.99. To use clustering, round each addend to the same number. 7.62 7.89 8.01 1 7.99 }}

→ → → →

8.00 8.00 8.00 1 8.00 }}} 32.00

An estimate for $7.62 1 $7.89 1 $8.01 1 $7.99 is $32.

1-9. Sample answers given. Estimate using rounding. 1. 59.118 1 17.799

2. $45.85 1 $6.82

3. 4.65 1 4.44

Estimate using front-end estimation. 4.

81.23 1 5.51

5.

42.06 1 17.39

6.

754.23 2 23.17

Estimate using clustering. 7. $0.99 1 $1.15 1 $0.52


8. 3.65 1 4.02 1 3.98

138

9. 6.87 1 6.97 1 7.39


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Estimating Sums and Differences Estimate using rounding. 1. 2.32 1 2.52

2. 87.146 – 24.953

3. 18.93 1 27.45

4. $46.83 1 $18.60

5. $13.23 – $2.87

6. 43.058 – 15.726

Estimate using front-end estimation. 7.

51.62 1 6.58 }}}

9.

4.57360 – 0.58256 }}}}

8.

10.

$233.10 – 23.62 }}}}

820.1 1 3.2 }}}

11. $102.34 1 $23.00 1 $32.67

12. 652.355 2 52.736

13. 59.62 1 60.4 1 60 1 61

14. $4.79 1 $5.29 1 $4.99

15. 8.2 1 7.8 1 7.2 1 7.99

16. 89.04 1 87.55 1 90.101 1 91

17. 15.044 1 14.765 1 14.689

18. $1.44 1 $0.86 1 $1.00 1 $0.7


139


Lesson 3–4

Estimate using clustering.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Estimating Sums and Differences SPORTS For Exercises 1–3, use the table.

The table shows the percent of annual hospital visits due to sports injuries by males 15 to 19 years of age. Percent of Male Sports-Related Injuries in the U.S., 2000–2001 Sport

Percent

Sport

Percent

Basketball

25.9

Boxing, Wrestling

4.4

Football

21.3

Exercise

3.8

Baseball/softball

4.1

Bicycling

8.1

Soccer

4.6

Skateboarding

3.6

1. Use clustering to estimate the total number of hospital visits due to injuries in baseball/softball, exercising, skateboarding, and boxing.

2. Use rounding to estimate how many more visits were due to football injuries than to soccer injuries.

3. Use front-end estimation to estimate the total number of visits caused by injuries in basketball and skateboarding.

4. BASKETBALL Len dribbled a basketball for 43 seconds before Greg got the ball away. Then Greg dribbled the ball for 11.525 seconds before Len got the ball. Use front-end estimation to estimate how many more seconds Len dribbled the ball than Greg.

5. GARDENING Kevin is going to plant three new types of vegetables in his garden. The garden store sells packages of tomatillo seeds for $1.67, chili pepper seeds for $0.89, and pumpkin seeds for $2.32. Use rounding to estimate how much Kevin will spend on all three packets of seeds.

6. TRAVEL Gloria drove 53.2 miles to her grandmother’s home. From her grandmother’s home she drove 12.67 miles to her aunt’s home. Use front-end estimation to estimate how many miles Gloria drove to get to her aunt’s home. Then use rounding to estimate the number of miles again.


140


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Estimating Sums and Differences Pre-Activity Read the introduction at the top of page 116 in your textbook. Write your answers below. 1. Round each number to the nearest million.

2. About how many more people travel through Hartsfield Atlanta than San Francisco?

Reading the Lesson 3. Below is a difference estimated by rounding to the nearest tens. Describe in words each step shown. 54.3 2 }}2 }8 }.}7 }

→ 50 → 2 }}3 }0 } 20

4. Below is a difference estimated by using front-end estimation. Describe in words each step shown. 68.5 2 34.9 }}}}}} 3

→

68.5 2 34.9 }}}}}} 34.0

5. Below is a sum estimated by using clustering. Describe in words each step shown. 83.20 80.14 79.55 1 80.09 }}}}}}}}

→ → → →

80 80 80 1 80 }}}} 320

6. Suppose you are shopping for groceries. Which method of estimation would you use to estimate the cost of the groceries and why would you pick this method? You may want to consider accuracy, ease or speed of calculation. .


141


Lesson 3–4


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Horizontal Estimation Many times an addition problem is given to you in horizontal form, with the addends written from left to right. To estimate the sum, you don’t have to rewrite the addition vertically in order to line up the decimal points. Just use place value to figure out which digits are most important. Here is an example. 3.11 1 0.4639 1 8.205 The most important digits are in the ones place. 3 1 0 1 8 5 11 The next group of important digits are in the tenths place. 1 tenth 1 4 tenths 1 2 tenths 5 7 tenths Add to make your estimate: 11 1 7 tenths → about 11.7 Estimate each sum. 1. 7.44 1 0.2193

2. 0.4015 1 9.3 1 3.264

3. 0.4208 1 0.16

4. 0.52 1 0.1 1 0.308 1 0.0294

5. 10.2 1 0.519

6. 12.004 1 1.5 1 4.32 1 0.1009

7. 6.72 1 0.5037

8. 0.805 1 1.006 1 0.4 1 2.0305

9. 1.208 1 3.1 1 0.04 1 6.143 1 0.3075

10. 0.9005 1 5.03 1 7.108 1 0.004 1 10.7

This same method works when you need to estimate a sum of much greater numbers. Estimate each sum. 11. 53,129 1 420,916 12. 6,048 1 2,137 1 509 13. 723 1 4,106 1 4,051 1 318 14. 7,095 1 12,402 1 3,114 1 360 15. 650,129 1 22,018 1 107,664 1 10,509 © Glencoe/McGraw-Hill

142


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention To add or subtract decimals, line up the decimal points then add or subtract digits in the same placevalue position. Estimate first so you know if your answer is reasonable.

Find the sum of 61.32 1 8.26. First, estimate the sum using front-end estimation. 61.32 1 8.26

→ 61 1 8 5 69

61.32 1 8.26 }}} 69.58 Since the estimate is close, the answer is reasonable. Find 2.65 2 0.2. Estimate: 2.65 2 0.2

2.65 2 0.20 }}} 2.45

→32053

Annex a zero.

Since the estimate is close, the answer is reasonable.

Add or subtract. 1.

5.

2.3 1 4.1

2.

113.7999 1 6.2001

6.

9. 0.2 1 5.64 1 9.005

11. 216.8 – 34.055


$13.67 2 7.19

3.

0.0058 2 0.0026

7.

0.0123 2 0.0028

4.

$5.63 1 4.10

8.

1

132.346 0.486

5.00921 24.00013

10. 12.36 2 4.081

12. 4.62+ 3.415 + 2.4

143


Lesson 3–5

Adding and Subtracting Decimals

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Adding and Subtracting Decimals Add or subtract. 1.

0.581 1 11 }}}}

2.

4.78 1 6 }}}

3.

9.6 1}} 5.2

4.

7.8 2 4.3 }}

5.

16.79 2 0.51 }}}

6.

1.02 2 0.38 }}}

7.

20.1 1 3.2 }}

8.

0.86 1 0.38 }}}

9.

3.84 1 2.69 }}}

10.

4.17 2 2.58 }}}

11.

47.06 2 38.27 }}}

12.

96.293 2 68.501 }}}}

Add or subtract. 13. 8.5 1 0.5

14. 8.3 1 7.9

15. 5.21 1 4 1 0.2

16. 3.4 1 3.2 2 6

17. 0.485 1 9.32

18. 362 2 145.9

19. 19.4 2 7.86

20. 4 1 8.5 1 2

21. 8.3 1 5.41 1 3.2

22. ALGEBRA Evaluate b 2 a if a 5 113.04 and b 5 241.931.

23. ALGEBRA Evaluate x 1 y if x 5 2.057 and y 5 16.3.

Find the value of each expression. 24. 3.4 3 2 2 6


25. 16.9 2 22

26. 7 1 2.3 2 5.8

144


NAME ________________________________________ DATE ______________ PERIOD _____


1. MICE The average length of the head and body of a western harvest mouse is 2.9 inches. The average length of the tail is 2.8 inches. First, estimate the total length of the mouse. Then find the actual total length.

2. MUSIC A piano solo on a CD is 5.33 minutes long. A guitar solo is 9.67 minutes long. How much longer is the guitar solo than the piano solo? First estimate the difference. Then find the actual difference.

3. WHALES The average length of a humpback whale is 13.7 meters. The average length of a killer whale is 6.85 meters. How much longer is the humpback whale than the killer whale?

4. GARDENING Alan is connecting three garden hoses to make one longer hose. The green hose is 6.25 feet long, the orange hose is 5.755 feet long, and the black hose is 6.5 feet long. First, estimate the total length. Then find the actual total length.

5. ASTRONOMY Distance in space can be measured in astronomical units, or AU. Jupiter is 5.2 AU from the Sun. Pluto is 39.223 AU from the Sun. How much closer to the Sun is Jupiter than Pluto?

6. ALGEBRA It is x miles from James City to Huntley and y miles from Huntley to Grover. How many miles is it from James City to Grover? To find out, evaluate x 1 y if x 5 4.23 and y 5 16.876.


145


Lesson 3–5

Adding and Subtracting Decimals

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Adding and Subtracting Decimals Pre-Activity Read the introduction at the top of page 121 in your textbook. Write your answers below. 1. Estimate the total amount of money earned by the top five movies.

2. Add the digits in the same place-value position. Use estimation to place the decimal point in the sum.

Reading the Lesson For Exercises 3–5 look at the paragraph just above Example 1 on page 121 in your textbook. 3. Before you add or subtract decimals, what do you need to do?

4. Then, starting on the right, what do you do next?

5. Why do you think the first sentence of that paragraph says “in the same place-value position”? Give an example.

6. In Examples 1–5 on pages 121 and 122 in your textbook, the first step is to estimate the sum or difference. How does the estimate help?

Helping You Remember 7. Tell what steps you would use to evaluate the algebraic expression x 1 y if x 5 3.4 and y 5 5.68.


146


NAME ________________________________________ DATE ______________ PERIOD _____

Palindromes A palindrome is a number that reads the same from left to right and from right to left. Decimals like 4.4 and 73.37 are examples of palindromes. A decimal like 5.14 is not a palindrome, of course, but it can be transformed into one using this trick. Write the number. “Flip it” around the decimal point.

5.14

←

Be sure to line up the decimal points.

1 41.5 46.64

Add.

Use the addition trick shown above to transform each number into a palindrome. 1. 41.22

2. 50.9

3. 1.092

4. 0.0008

Use two additions to transform each number into a palindrome. (Exercise 5 has been started for you.) 5.

25.61 1 16.52 }}} 42.13 1 31.24 }}}

7. 3.904

6. 5.92

8. 415.9

Transform each number into a palindrome, using as many additions as necessary. 9. 49.6

10. 8.9

11. 517.6

12. 6.58

13. CHALLENGE Words can be palindromes, too, when they read the same from left to right and from right to left. Can you think of two words that are palindromes?


147


Lesson 3–5

Enrichment


Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860067-7 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03







Chapter 4 Assessment Chapter 4 Test, Form 1 ..........................199–200 Chapter 4 Test, Form 2A ........................201–202 Chapter 4 Test, Form 2B ........................203–204 Chapter 4 Test, Form 2C........................205–206 Chapter 4 Test, Form 2D........................207–208 Chapter 4 Test, Form 3 ..........................209–210 Chapter 4 Extended Response Assessment .................................................211 Chapter 4 Vocabulary Test/Review.................212 Chapter 4 Quizzes 1 & 2................................213 Chapter 4 Quizzes 3 & 4................................214 Chapter 4 Mid-Chapter Test ...........................215 Chapter 4 Cumulative Review........................216 Chapter 4 Standardized Test Practice....217–218 Unit 2 Test/Review..................................219–220 Standardized Test Practice Student Recording Sheet ............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A28

iii



Practice: Skills











iv





Enrichment













v

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


center

circle

circumference [suhr-KUHM-fuh-ruhns]

diameter [deye-A-muh-tuhr]

radius

perimeter [puh-RIH-muh-tuhr]

scientific notation


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: decimals is a valuable skill. Knowing how to multiply and divide ch money we will spend We use decimals to calculate how mu how much of our on sports equipment or to determine movie. Skill in using allowance will be left after seeing a isions about purchasing decimals helps us make informed dec goods and services. viding Decimals, your In Chapter 4, Multiplying and Di find the products and child will learn how to estimate and the perimeter and quotients of decimals as well as find In the study of this circumference of polygons and circles. iety of daily classroom chapter, your child will complete a var ly produce a chapter assignments and activities and possib project . it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get r child that also relates the an activity that you can do with you 4 to the real world. You math we will be learning in Chapter line Study Tools for selfmay also wish to log on to the On dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any other study help at www.msmath1.n contact me at school. questions or comments, feel free to Sincerely,



ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Multiplying and Dividing Decimals Work with a family member. Research the current Federal minimum wage at your local library or on the Internet. Use this information for Exercises 1–5. Whenever necessary, round to the nearest hundredth. 1. What is the current Federal minimum wage?

2. Suppose you worked 5.5 hours last Saturday and were paid minimum wage. How much money would you have earned?

3. Suppose you earned $110.00 last week. If you are paid the Federal minimum wage, how many hours did you work?

4. Federal, state, and local labor laws limit the number of hours that a person under a certain age can work in a day or week. Research the number of hours you can legally work. Use this information to determine the maximum amount you could earn in a day or week if you are earning the Federal minimum wage.

5. Visit a local retail store or look at store advertisements for three or more items you would like to purchase. If you were earning the Federal minimum wage, how many hours would you have to work to earn enough money to purchase each item? Item 1: Item 2: Item 3:

1–5. See students’ work. © Glencoe/McGraw-Hill

x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Multiplying Decimals by Whole Numbers When you multiply a decimal by a whole number, you multiply the numbers as if you were multiplying all whole numbers. Then you use estimation or you count the number of decimal places to decide where to place the decimal point. If there are not enough decimal places in the product, annex zeros to the left.

Find 6.25 3 5. Method 1 Use estimation.

Method 2 Count decimal places.

Round 6.25 to 6. 6.25 3 5 → 6 3 5 or 30 12

6.25 3 5 31.25

There are two places to the right of the decimal point.

6.25 3 5 31.25

Since the estimate is 30 place the decimal point after 31.

Count the same number of decimal places from right to left.

Lesson 4–1

Find 3 3 0.0047. 2

0.0047 3 3 0.0141

There are four decimal places. Annex a zero on the left of 141 to make four decimal places.

When you write a number greater than ten as the product of a decimal and 10 raised to a whole number power, you are writing the number in scientific notation. The whole number factor is a power of ten. Write 8.2 3 105 in standard form. Method 1 Use order of operations. Evaluate

105

first. Then multiply.

8.2 3 105 5 8.2 3 100,000

Method 2 Use mental math. Move the decimal point 5 places. 8.2 3 105 5 8.20000 3 105

5 820,000

5 820,000

So, 8.2 3 105 5 820,000.

Multiply. 1. 8.03 3 3

2. 6 3 12.6

Write each number in standard form. 5. 2.32 3 102 6. 6.8 3 102


3. 2 3 0.012

4. 0.0008 3 9

7. 5.2 3 103

8. 1.412 3 104

169


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Multiplying Decimals by Whole Numbers Multiply. 1. 1.5 33

2. 0.9 36

3. 0.45 3 5

4. 3.12 3 8

5. 3.47 3 5

6. 2.08 3 6

7. 9.14 3 2

8. 0.82 3 9

6.3 3 9

10. 0.02 3 3

11. 9.12 3 4

12. 27.3 3 8

13. 4.007 3 4

14. 3.13 3 3

15. 5.02 3 8

16. 6.31 3 6

17. 8.01 3 5

18. 4.325 3 7

19. 0.762 3 2

20. 0.08 3 8

9.

21. 6 3 3.04

22. 2.6 3 9

23. 13 3 2.5

24. 1.006 3 4

25. Evaluate 42.3t if t = 110.

26. Evaluate 231a if a = 3.6

Write each number in standard form. 27. 3.15 3 104


28. 2.6 3 105

29. 5 3 106

170


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. COOKING Norberto uses three 14.7 oz cans of chicken broth when he makes his delicious tortilla soup. How many total ounces of chicken broth does he use?

2. TIME Amanda works on a farm out in the hills. It takes her 2.25 hours to drive to town and back. She usually goes to town twice a week to get supplies. How much time does Amanda spend driving if she takes 8 trips to town each month?

3. EXERCISE The local health club is advertising a special for new members: no initiation fee to join and only $34.50 per month for the first year. If Andy joins the health club for one year, how much will he spend on membership?

4. BIKING In order to train for a crossstate biking trip, Julie rides her bike 34.75 miles five times a week. How many total miles does she ride each week?

5. MONEY David wants to buy 16 bolts from a bin at the hardware store. Each bolt costs $0.03. How much will David pay for the bolts?

6. INSECTS One wing of a Royal Moth is 0.75 inch across. How wide is the moth’s wingspan when both wings are open?

7. COSTUMES KJ is making costumes for this year’s samba parade. The pattern she is using calls for 2.125 yards of fabric for each costume. How many yards of fabric will she need to make 34 costumes?

8. PLANETS Earth is 1.496 3 108 kilometers from the Sun. What is this distance written in standard form?


171


Lesson 4–1

Multiplying Decimals by Whole Numbers

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Multiplying Decimals by Whole Numbers Pre-Activity Read the introduction at the top of page 135 in your textbook. Write your answers below. 1. Use the addition problem and the estimate to find 2 3 $7.99. 2. Write an addition problem, an estimate, and a multiplication problem to find the total cost of 3 CDs, 4 CDs, and 5 CDs.

3. Make a conjecture about how to find the product of $0.35 and 3.

Reading the Lesson 4. When multiplying a whole number and a decimal, it is very important that the decimal point in the product is in the right place. What are two methods for determining the placement of the decimal point in the product?

5. If you place the decimal point in the product of a whole number and a decimal by counting decimal places, how is this done?

6. What does it mean to annex zeros in the product? Why is it sometimes necessary to do this?

Helping You Remember 7. Work with a partner. Explain the difference between standard form and scientific notation, and give examples of each.


172


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Multiplying by 10, 100, and 1,000 Can you see a pattern in these multiplications? 5.931 5.931 3 10 3 100 59.310 5 59.31 593.100 5 593.1

5.931 3 1,000 5,931.000 5 5,931

When you multiply a number by 10, 100, or 1,000, the product contains the same digits as the original number. However, the decimal point “moves” according to these rules. multiply by 10 multiply by 100 multiply by 1,000

move to the right one place move to the right two places move to the right three places

Many people use this fact as a mental math strategy.

1. 10 3 7.402

2. 100 3 7.402

3. 1,000 3 7.402

4. 10 3 0.84

5. 1,000 3 0.5362

6. 100 3 3.83

7. 24.07 3 10

8. 1.918 3 1,000

9. 0.075 3 100 11. 0.0046 3 100

Lesson 4–1

Find each product mentally.

10. 6.1 3 10 12. 0.005 3 1,000

Now you can use this mental math strategy to estimate some products. The secret is to recognize when one of the factors is fairly close to 10, 100, or 1,000. An example is shown at the right.

32.83 3 97

32.83 3 100 3,283

So, 32.83 3 97 is about 3,283.

Estimate by rounding one number to 10, 100, or 1,000. 13. 6.57 3 9

14. 14.32 3 96

15. 1,225 3 3.548

16. 0.6214 3 11.05

17. 98.04 3 26.331

18. 0.0358 3 9.3145

19. CHALLENGE Find the product 1,000 3 16.5 mentally. How is this different from the other exercises on this page?


173


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Multiplying Decimals When you multiply a decimal by a decimal, multiply the numbers as if you were multiplying all whole numbers. To decide where to place the decimal point, find the sum of the number of decimal places in each factor. The product has the same number of decimal places.

Find 5.2 3 6.13. Estimate: 5 3 6 or 30

5.2 3 6.13 156 52 312 31.876

one decimal place two decimal places

three decimal places

The product is 31.876.

Compared to the estimate, the product is reasonable.

Evaluate 0.023t if t 5 2.3. 0.023t 5 0.023 3 2.3 0.023 3 2.3 69 46 0.0529

Replace t with 2.3.

three decimal places one decimal place

Annex a zero to make four decimal places.

Multiply. 1. 7.2 3 2.1

2. 4.3 3 8.5

3. 2.64 3 1.4

4. 14.23 3 8.21

5. 5.01 3 11.6

6. 9.001 3 4.2

Evaluate each expression if x 5 5.07, y 5 1.5, and z 5 0.403. 7. 3.2x 1 y


9. z 3 7.06 2 y

8. yz 1 x

174


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Multiplying Decimals Multiply. 1. 0.3 3 0.5

2. 1.2 3 2.1

3. 2.5 3 6.7

4. 0.4 3 8.3

5. 2.3 3 1.21

6. 0.6 3 0.91

7. 6.5 3 0.04

8. 8.54 3 3.27

9. 5.02 3 1.07

10. 0.003 3 2.9

12. 7.1 3 0.004

13. 3.007 3 6.1

14. 2.52 3 0.15

15. 2.6 3 5.46

16. 16.25 3 1.3

17. 3.5 3 24.09

18. 0.025 3 17.1

19. 11.04 3 6.18

20. 14.83 3 16.7

Lesson 4–2

11. 0.93 3 6.8

21. 27.1 3 10.105

Evaluate each expression if x 5 2.1, y 5 0.031, and z 5 3.05. 22. xy 1 z


24. x 3 13.55 2 y

23. y 1 xz

175


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Multiplying Decimals 1. GIFTS Colin is filling 4.5 ounce bottles with lavender bubble bath that he made for gifts. He was able to fill 7.5 bottles. How many ounces of bubble bath did he make?

2. GROCERY Iona’s favorite peaches are $2.50 per pound at the local farmers’ market. She bought 3.5 pounds of the peaches. How much did she spend?

3. SHOPPING Jennifer is buying new school clothes. The items she wants to buy add up to $132.50 before sales tax. Sales tax is calculated by multiplying the total amount by 0.08. What is the amount of sales tax for the items?

4. DRIVING Ana bought a van that holds 20.75 gallons of gas and gets an average of 15.5 miles per gallon. How many miles can she expect to go on a full tank?

5. INCOME Ishi makes $8.50 an hour rolling sushi at Kyoto Japanese Restaurant. His paycheck shows that he worked 20.88 hours over the past two weeks. How much did Ishi make before taxes?

6. TRAVEL Manny is on vacation in France. He rented a car to drive 233.3 kilometers from Paris to Brussels and wants to figure out the distance in miles. To convert from kilometers to miles, he needs to multiply the total kilometers by 0.62. How many miles will Manny drive?


176


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Multiplying Decimals Pre-Activity Read the introduction at the top of page 141 in your textbook. Write your answers below. 1. Suppose you fill a bag with 1.3 pounds of jellybeans. The product 1.3 3 2 can be used to estimate the total cost. Estimate the total cost. 2. Multiply 13 by 200. 3. How are the answers to Exercises 1 and 2 related? Repeat Exercises 1–3 for each amount of candy. 4. 1.7 pounds of gummy worms 5. 2.28 pounds of snow caps 6. Make a conjecture about how to place the decimal point in the product of two decimals.

7. When multiplying decimals, what is the relationship between the number of decimal places in each factor and the number of decimal places in the product? 8. Look at Exercises 1 and 2 above and the answers for these exercises. a. How is 13 related to 1.3 pounds? b.

How is 207 related to $2.07 per pound?

c.

What is the actual cost of 1.3 pounds of jellybeans if each pound costs $2.07 per pound?

d.

How is 2691 related to the actual cost of 1.3 pounds of jellybeans?

Helping You Remember 9. In situations where you are multiplying decimals by whole numbers it is easy to think of the calculation as adding the same value multiple times. What does it mean to multiply decimals? Describe some situations where you would need to multiply decimals.


177


Lesson 4–2

Reading the Lesson

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment A Logic Puzzle Here is a puzzle that will help you brush up on your logical thinking skills. The product 3.3 3 8.1 is in both the circle and the triangle, but not in the square. Place the product in the diagram at the right. 8.1 3 3.3 243 243 2 6.73

26.73

Write 26.73 in the correct region of the diagram.

Use the given information to place the product in the diagram above. 1. The product 14.19 3 1.3 is in both the triangle and the square, but not in the circle.

2. The product 0.08 3 2.7 is in the triangle, but not in the circle or the square.

3. The product 1.24 3 0.16 is not in the circle, the square, or the triangle.

4. The product 2.2 3 0.815 is in both the square and the circle, but not in the triangle.

5. The product 0.02 3 0.03 is in the circle, but not the triangle or the square.

6. The product 21.7 3 0.95 is in the circle, the square, and the triangle.

7. The product 2.5 3 12.8 is in the square, but not the circle or triangle.

8. If you did all the calculations correctly, the sum of all the numbers in the diagram should be a “nice” number. What is the sum?


178


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Dividing Decimals by Whole Numbers When you divide a decimal by a whole number, place the decimal point in the quotient above the decimal point in the dividend. Then divide as you do with whole numbers.

Find 8.73 4 9. Estimate: 9 4 9 5 1

0.97 9q8 w.7 w3 w 20 87 28 1 63 263 0

Place the decimal point directly above the decimal point in the quotient.

Divide as with whole numbers.

8.73 4 9 5 0.97

Compared to the estimate, the quotient is reasonable.

Find 8.58 4 12. Estimate: 10 4 10 5 1

0.715 12q8 w.5 w8 w0 w 28 4 18 212 60 260 0

Place the decimal point.

Annex a zero to continue dividing.

Divide. 1. 4q9 w.2 w

2. 5q4 w.5 w

3. 8.6 4 2

4. 2.89 4 4

w.2 w 5. 4q3

6. 3q7 w.2 w

7. 7.5 4 5

8. 3.25 4 5


179


Lesson 4–3

8.58 4 12 5 0.715 Compared to the estimate, the quotient is reasonable.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Dividing Decimals by Whole Numbers Divide. Round to the nearest tenth if necessary. 1. 3q9 w.6 w

2. 5q5 w.1 w5 w

3. 2q1 w6 w.0 w8 w

4. 7q2 w4 w.6 w4 w

5. 11q1 w3 w2 w.2 w2 w

6. 16q1 w4 w2 w.4 w

7. 79.2 4 9

8. 47.4 4 15

9. 217.14 4 21

10. 5q3 w4 w.6 w5 w

11. 8q2 w0 w.7 w2 w

12. 10q7 w2 w.6 w

13. 15q5 w7 w.4 w8 w

14. 25q2 w6 w4 w.5 w

15. 34q3 w1 w7 w.5 w9 w4 w

16. 122.32 4 11

17. 42.48 4 18

18. 323.316 4 24


180


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. ENTERTAINMENT Frank, Gina, Judy, and Connie are splitting their dinner bill. After tip, the total is $30.08. How much does each owe if they split the bill four ways?

2. FOOD There are 25 servings in a 12.5 ounce bottle of olive oil. How many ounces are in a serving?

3. RUNNING Isabella has found that she stays the most fit by running various distances and terrains throughout the week. On Mondays she runs 2.5 miles, on Tuesdays 4.6 miles, on Thursdays 6.75 miles, and on Saturdays 4.8 miles. What is the average distance Isabella runs on each of the days that she runs? Round to the nearest hundredth of a mile.

4. BUSINESS Katherine spends $1,089.72 each month for rent and supplies to run her hair salon. If she charges $18 for a haircut, how many haircuts must Katherine do to cover her monthly expenses? Round to the nearest whole number.

5. CONSTRUCTION It took Steve and his construction crew 8 months to build a house. After expenses, he was left with $24,872.67 for himself. On average, how much did Steve make per month? Round to the nearest dollar.

6. GRADES Shane wants to figure out what grade he is getting in math. His test scores were 85.6, 78.5, 92.5, 67, and 83.7. What was his average test score? What grade will he receive?


181

Grade

Average Score

A

90 – 100

B

80 – 89

C

70 – 79

D

60 – 69

F

50 – 59


Lesson 4–3

Dividing Decimals by Whole Numbers

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Dividing Decimals by Whole Numbers Pre-Activity Do the Mini Lab at the top of page 144 in your textbook. Write your answers below. Use base-ten blocks to show each quotient. 1. 3.4 4 2

2. 4.2 4 3

3. 5.6 4 4

Find each whole number quotient. 4. 34 4 2

5. 42 4 3

6. 56 4 4

7. Compare and contrast the quotients in Exercises 1–3 with the quotients in Exercises 4–6.

8. MAKE A CONJECTURE Write a rule about how to divide a decimal by a whole number.

Reading the Lesson 9. In the equation 4.8 4 8 5 0.6, how can you check to see if the division sentence is true? 10. Where do you place the decimal point in the quotient when dividing by a whole number?

Helping You Remember 11. Work with a partner. Pretend your partner missed the class that covered this lesson. Explain to your partner the method for knowing where to place the decimal point when you are dividing with decimals. © Glencoe/McGraw-Hill

182


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Unit Pricing The unit price of an item is the cost of the item given in terms of one unit of the item. The unit might be something that you count, like jars or cans, or it might be a unit of measure, like ounces or pounds. You can find a unit price using this formula. unit price 5 cost of item 4 number of units For example, you find the unit price of the tuna in the ad at the right by finding the quotient 0.89 4 6. The work is shown below the ad. Rounding the quotient to the nearest cent, the unit price is $0.15 per ounce.

TUNA 89¢ 6 ounce can 0.148 6q0 w.8 w9 w0 w 6 29 24 50 48 2

Find a unit price for each item. 1.

2.

5-pound bag CARROTS $1.29

18-ounce jar PEANUT BUTTER $2.49

3.

Grade A Jumbo EGGS Dozen $1.59

Give two different unit prices for each item. Frozen BURRITOS 5-ounce pkg 2 for $1.39

5.

Purr-fect CAT FOOD 3/$1 3-ounce can

6.

Old Tyme SPAGHETTI SAUCE 12-ounce jars 2/$3

Lesson 4–3

4.

Circle the better buy. 7.

Mozarella Cheese 3/$4 10-ounce pkg


Mozarella Cheese 2/$3 18-ounce pkg

8.

183

Dee-light Chicken Wings $9.99 5-pound bag

Top Q Chicken Wings $2.29 18-ounce bag


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Dividing by Decimals When you divide a decimal by a decimal, multiply both the divisor and the dividend by the same power of ten. Then divide as with whole numbers.

Find 10.14 4 5.2. Estimate: 10 4 5 5 2 Multiply by 10 to make a whole number.

1.95 52q1 w0 w1 w.4 w0 w 2 52 494 2 468 260 2 260 0

5.2q1 w0 w.1 w4 w N N Multiply by the same number, 10.

10.14 divided by 5.2 is 1.95. Check: 1.95 3 5.2 5 10.14 ✓

Place the decimal point. Divide as with whole numbers.

Annex a zero to continue.

Compare to the estimate.

Find 4.09 4 0.02. 0.02q4 w.0 w0 w NN NN Multiply each by 100.

204.5 2q4 w0 w9 w.0 w 24 00 20 09 28 10 2 10 0

Place the decimal point. Divide.

Write a zero, in the dividend and continue to divide.

4.09 4 0.02 is 204.5. Check: 204.5 3 0.02 5 4.09 ✓

Divide. 1. 1.4q9 w.8 w

2. 2.1q4 w.4 w1 w

3. 0.72q1 w6 w.8 w4 w8 w

4. 8.652 4 1.2

5. 0.5 4 0.001

6. 9.594 4 0.06


184


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Dividing by Decimals Divide. Round to the nearest hundredth if necessary. w.8 w6 w 1. 0.2q4

2. 0.7q2 w.5 w2 w

3. 1.2q1 w4 w.4 w

4. 3.8q1 w7 w.1 w

5. 1.32q3 w.9 w6 w

6. 34.9q6 w2 w8 w.2 w

7. 0.105 4 0.5

8. 1.296 4 0.16

10. 0.5q8 w.2 w5 w3 w

11. 0.8q0 w.9 w9 w4 w4 w

12. 0.32q1 w.5 w0 w0 w4 w8 w

13. 0.75q1 w3 w.5 w9 w

14. 1.8q4 w.4 w2 w0 w8 w

15. 4.02q1 w6 w.1 w6 w0 w4 w

16. 160.3639 4 25.1

17. 246.3293 4 13.3

18. 106.288 4 6.5


185


Lesson 4–4

9. 3.825 4 2.5

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Dividing by Decimals MARATHON For Exercises 1 and 2, use the table that shows course

records for the Boston Marathon. Course Records for the Boston Marathon Division

Record-holder

Year

Time (hours)

Men’s Open

Cosmas Ndeti

1994

2.121

Women’s Open

Margaret Okayo

2002

2.345

Men’s Wheelchair

Heinz Frei

1994

1.356

Women’s Wheelchair

Jean Driscoll

1994

1.523

1. The Boston Marathon is 26.2 miles. Use the times shown in the table to calculate the miles per hour for each division winner. Round to the nearest thousandth.

2. To the nearest hundredth, how many times greater was the men’s open time than the women’s wheelchair time?

3. DRIVING The Martinez family drove 48.7 miles to the river. It took them 1.2 hours to get there. How fast did they drive? Round to the nearest whole number.

4. SHOPPING Nikki is buying some refrigerator magnets for her friends. Her total bill is $16.80. If magnets are $0.80 each, how many magnets is she buying?

5. SCALE MODEL Matt is making a scale model of a building. The model is 3.4 feet tall. The actual building is 41.48 feet tall. How many times smaller is the model than the actual building?

6. COOKING Yori has 14.25 cups of cupcake batter. If each cupcake uses 0.75 cup of batter, how many cupcakes can Yori make?


186


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Dividing by Decimals Pre-Activity Do the Mini Lab at the top of page 152 in your textbook. Write your answers below. Use a calculator to find each quotient. 1. 0.048 4 0.06 0.48 4 0.6 4.8 4 6 48 4 60

2. 0.0182 4 0.13 0.182 4 1.3 1.82 4 13 18.2 4 130

3. Which of the quotients in Exercises 1 and 2 would be easier to find without a calculator? Explain your reasoning.

Rewrite each problem so you can find the quotient without using a calculator. Then find the quotient. 4. 0.42 4 0.7 5. 1.26 4 0.3 6. 1.55 4 0.5

Reading the Lesson 7. When dividing decimals, what happens to the decimal point in the divisor and the dividend when you multiply both by the same power of 10?

Helping You Remember 9. Write a short song or come up with a clever saying that will help you remember that whatever change you make to the decimal point of the divisor you must also make to the decimal point of the dividend.


187


Lesson 4–4

8. Without doing any dividing, describe what you must do to start dividing 0.07 by 1.5.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment It’s in the Cards Below each set of cards, a quotient is given. Use the digits on the cards to form a division sentence with that quotient. Use as many zeros as you need to get the correct number of decimal places. For example, this is how to find a division for the cards at the right.

2

You know that 24 4 3 5 8. So, one division is 0.0024 4 30 5 0.0008.

Quotient: 0.0008

1.

2. 4

5

2

4. 3

6. 1

7

Quotient: 0.0074

2

1

4

8

9. 1

Quotient: 0.0004

4

6

8

1

3

Quotient: 20.65

4

6

12. 2

3

4

6

3

Quotient: 0.0208

188

4

5

6

Quotient: 0.08

13. CHALLENGE Use the cards at the right. Write four different divisions that have the quotient 0.4.


5

Quotient: 0.005

11. 2

3

1

Quotient: 0.03

10.

3

Quotient: 0.0025

8. 2

2

1

3

Quotient: 0.0155

7.

7

Quotient: 0.0005

5. 5

5

3

3

Quotient: 0.04

Quotient: 0.009

4

3. 1

6

3

2

4

6


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention The distance around any closed figure is called its perimeter. To find the perimeter, add the measures of all the sides of the figure. Finding Perimeter Figure

Words

Symbols

Rectangle

The perimeter P of a rectangle is the sum of the lengths and widths. It is also two times the length ø plus two times the width w.

Square

The perimeter P of a square is four times the measure of any of its sides s.

P5ø1ø1w1w P 5 2ø 1 2w P 5 4s

Find the perimeter of the rectangle.

3 ft

Estimate: 5 1 5 1 5 1 5 5 20

P 5 2ø 1 2w P 5 2(5) 1 2(3) P 5 10 1 6 P 5 16

Write the formula. Replace ø with 5 and w with 3. Multiply. Add.

5 ft

5 ft

The perimeter of the rectangle is 16 feet. Compared to the estimate, the answer is reasonable.

3 ft

Find the perimeter of the square. P 5 4s P 5 4(6) P 5 24

Write the formula. Replace s with 6. Multiply.

6 in.

The perimeter of the square is 24 inches.

Find the perimeter of each figure. 1.

2.

4 in. 1 in.

3 yd

1 in. 4 in. 10 yd

3.

10 yd

5 ft

5 ft 3 yd


189


Lesson 4–5

Perimeter

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Perimeter Find the perimeter of each figure. 1.

2.

5 ft 2 ft

4.3 in.

2 ft 8.7 in.

5 ft

8.7 in.

4.3 in.

3.

4.

4 in.

4 in.

4 in.

11.5 yd

13.2 yd

13.2 yd

4 in. 11.5 yd

5.

6.

9.8 km

2 mi

9.8 km 9.3 mi

9.3 mi

2 mi

7.

8.

7.6 km

2. 1

2 km

cm

2.

1

cm

5.6 c m

9.2 km 7.2 km

5.6 cm

4.3 km

3.3 km


190


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. GEOGRAPHY The state of Colorado is nearly rectangular. It is about 589 kilometers by 456 kilometers. What is the perimeter of Colorado?

2. FRAMING How many inches of matting is needed to frame an 8.5 inch by 11 inch print?

3. GARDENING Jessica wants to put a fence around her 10.5 foot by 13.75 foot rectangular garden. How many feet of fencing will she need?

4. SEWING Amy is making pillows to decorate her bed. She is going to make three square pillows that are each 2 feet by 2 feet. She wants to use the same trim around each pillow. How many feet of trim will she need for all three pillows?

5. JOGGING Before soccer practice, Jovan warms up by jogging around a soccer field that is 100 yards by 130 yards. How many yards does he jog if he goes around the field four times?

6. POSTER Ted is making a stop sign poster for a talk on safety to a first grade class. He will put a strip of black paper around the perimeter of the stop sign. Each of the stop sign’s eight sides is 16.34 inches. How long a strip of paper will he need?

7. FLAG Jo is making a triangular banner. Each of the three sides is 14.567 inches long. If she puts a braided trim around the banner, how much trim will she need?

8. PYRAMIDS The Great Pyramid at Giza, Egypt, has a square base, with each side measuring 0.229 kilometer. If you could walk once all the way around the pyramid at its base, how far could you walk?


191


Lesson 4–5

Perimeter

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Perimeter Pre-Activity Do the Mini Lab at the top of page 158 in your textbook. Write your answers below. 1. Find the distance around your textbook by adding the measures of each side.

2. Can you think of more than one way to find the distance around your book? If so, describe it.

Reading the Lesson 3. The perimeter of a rectangle is equal to 2ø 1 2w. What does the formula tell you about the lengths and widths of a rectangle?

4. The formula for the perimeter of a square is P 5 4s. What does that tell you about the sides of a square?

5. Can you use the formula for the perimeter of a rectangle to find the perimeter of a square? Why or why not?

Helping You Remember 6. Think of a way to remember the formula for the perimeter of a rectangle, P 5 2ø 1 2w. For example, use the letters of the variables as the first letters of words in a sentence.


192


NAME ________________________________________ DATE ______________ PERIOD _____

Getting From Here to There At the right, you see a rectangle on a grid of squares. The rectangle is 4 units wide and 7 units long. The diagonal path of this rectangle crosses 10 squares of the grid. width length diagonal path

For each rectangle, record the width, the length, and the diagonal path. 1.

2.

3.

4 7 10

4.

5. Refer to your answers to Exercises 1–4. What is the pattern?

Now record the width, length, and diagonal path for each of these rectangles. 6.

7.

8.

9. Refer to your answers to Exercises 6–8. Does the pattern that you found in Exercise 5 still hold? 10. What is the difference between the rectangles in Exercises 1–4 and the rectangles in Exercises 6–8?

Predict the diagonal path for each rectangle. 11. 4 units by 9 units

12. 10 units by 21 units




193


Lesson 4–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Circumference The circumference is the distance around a circle.

Center

The radius, r, is the distance from the center to any point on a circle.

The diameter, d, is the distance across a circle through its center.

The circumference of a circle is equal to p times its diameter or p times twice its radius.

C 5 pd or C 5 2pr

Find the circumference of a circle whose diameter is 4.2 meters. Round to the nearest tenth. C 5 pd < 3.14 3 4.2 < 13.188 < 13.2

Write the formula. Replace p with 3.14 and d with 4.2. Multiply. Round to the nearest tenth.

The circumference of the circle is about 13.2 meters. Find the circumference of a circle whose radius is 13 inches. Round to the nearest tenth. C 5 2pr < 2 3 3.14 3 13 < 81.64 < 81.6

Write the formula. Replace p with 3.14 and r with 13. Multiply. Round to the nearest tenth.

The circumference of the circle is about 81.6 inches.

Find the circumference of each circle shown or described. Round to the nearest tenth. 1.

2.

3. 0.65 ft

3.25 in. 4m

4. The radius of a circle measures 16 miles. What is the measure of its circumference to the nearest tenth? 5. Find the circumference of a circle whose diameter is 12.5 yards to the nearest tenth. 6. What is the circumference of a circle with a radius of 2.05 inches to the nearest tenth? © Glencoe/McGraw-Hill

194


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Circumference Find the circumference of each circle shown or described. Use 3.14 for p. Round to the nearest tenth. 2. 2.5 cm

4.

3. 3.4 in.

5.

11 m

6. 8.6 mm

7.1 yd

21 mi

7.

8.

9. 14.04 m

12.5 cm 4.83 ft

10.

11.

12. 0.875 yd

25.3 ft 16.2 in.

13. r 5 13 cm

14. d 5 4.1 ft

15. r 5 22 mm

16. d 5 1.25 in.

17. r 5 10.6 mi

18. d 5 14.23 yd


195


Lesson 4–6

1.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Circumference AUDIO MEDIA For Exercises 1–3, use the table that shows the sizes of three main audio media: vinyl, CD, and mini-disc. Use 3.14 for p.

Diameters of Audio Media Medium

Diameter (inches)

Vinyl Disc

12

Compact Disc (CD)

5

Mini Compact Disc (Mini-disc)

2.5

1. What is the circumference of a CD?

2. When a record player needle is placed on the outside edge of a vinyl record, how far does the needle travel in one rotation?

3. What is the difference between the circumference of a vinyl disc and a mini-disc?

4. CROP CIRCLES On June 8, 1992 a crop circle with an 18-meter radius was found in a wheat field near Szekesfehervar, 43 miles southwest of Budapest. What was its circumference?

5. SEQUOIAS The largest living thing in the world is the General Sherman sequoia in Sequoia National Park, California. It is 272 feet high, has a diameter of 36.5 feet, and has an estimated weight of 2,150 tons. What is the sequoia’s circumference to the nearest tenth of a foot?

6. MONSTER TRUCKS A monster truck fleet uses 23 degree tires 66 inches tall, 43 inches wide, mounted on 25-inch diameter wheels. What is the circumference of a monster truck wheel to the nearest tenth of an inch?


196


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Circumference Pre-Activity Do the Mini Lab at the top of page 161 in your textbook. Write your answers below.

2. What conclusion can you make about the circumference and diameter of a circle?

3. Predict the distance around a circle that is 4 inches across.

Reading the Lesson 4. What is the real value of p? What does it mean that the real value never ends?

5. Why is the symbol < used in the solutions of the circumference problems in the examples?

6. What are the two formulas that you can use to find the circumference of a circle? When would you use each of them?

Helping You Remember 7. Make a model of a circle and its parts using materials from your home. Label the center, radius, diameter, and circumference.


197


Lesson 4–6

1. What do you notice about each quotient?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Estimating the Area of a Circle You have learned that area is the number of square units needed to cover a surface. Counting square units on a circular surface can be challenging. Here is a counting method that gives a fairly good estimate of the area of a circle. Count the squares that cover any part of the circular region.

Count the squares that are entirely within the circle. Find the mean of the two numbers. 60 1 32 92 }} 5 }} 5 46 1 2

So the area of the circle is about 46 square units. 60

32

Estimate the area of each circle or oval. 1.

2.

3.

4.

5.

6.


198



Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860068-5 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03






Lesson 5-4






iii




Practice: Skills











iv





Enrichment













v

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


common multiples

equivalent fractions

greatest common factor (GCF)

improper fraction

least commmon denominator (LCD)

least common multiple (LCM)


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


mixed number

multiple

repeating decimal

simplest form

terminating decimal

Venn diagram


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: is part of our daily lives. Using fractions, ratios, and decimals ret these types of Knowing how to represent and interp measure lengths, and numbers helps us analyze statistics, the importance of math compare prices. In order to emphasize cepts to everyday events. skills, we try to relate classroom con als, your child will learn In Chapter 5, Fractions and Decim anized list , and to find the to solve problems by making an org mon multiple of numbers greatest common factor and least com r child will also learn to to simplify and compare fractions. You fractions and to write express mixed numbers as improper In the study of this decimals as fractions and vice versa. iety of daily classroom chapter, your child will complete a var ly produce a chapter assignments and activities and possib project . it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 5 to the real world. You math we will be learning in Chapter line Study Tools for selfmay also wish to log on to the On dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any other study help at www.msmath1.n contact me at school. questions or comments, feel free to Sincerely,



ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Writing Decimals as Fractions Work with a family member. Batting averages are written as decimals to the thousandth place. For example, a sample batting average could be .266. Research three different baseball players and their batting averages in your local newspaper, library, or on the Internet. 1. Write your players’ names and their batting averages. Players’ Name

Batting Average

2. Which player has the greatest batting average? 3. Write each batting average as a fraction with a denominator of 1,000. Then if the fraction is not already written in simplest terms, write an equivalent fraction in simplest terms. For example, the batting average 266 .266 would be written as } }. Then an equivalent fraction in simplest 1,000

133 terms is } }. 500

Player’s Name

Batting Average

4. Suppose a baseball player has 16 hits from 53 times at bat. What is his batting average as a decimal to the nearest thousandth? Is it better or worse than the averages of the players you chose? Explain.

4. .302; See students’ work.

x

1–3. See students’ work.



NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Greatest Common Factor The greatest common factor (GCF) of two or more numbers is the greatest common factor of the numbers. To find the GCF, you can make a list or use prime factors.

Find the GCF of 12 and 30 by making a list. List the factors of 12 and 30. 12: 1, 2, 3, 4, 6, 12 30: 1, 2, 3, 5, 6, 10, 15, 30 The common factors are 1, 2, 3, and 6. The greatest is 6. The GCF of 12 and 30 is 6. Find the GCF of 18 and 27 by using prime factors.

18

27

2 ? 9

3 ? 9

2 ? 3 ? 3

3 ? 3 ? 3

The common prime factors are 3 and 3. So, the GCF of 18 and 27 is 3 3 3 or 9.

Find the GCF of each set of numbers by making a list. 1. 8 and 12

2. 10 and 15

3. 81 and 27

Find the GCF of each set of numbers by using prime factors. 4. 15 and 20

5. 6 and 12

6. 28 and 42

Find the GCF of each set of numbers. 7. 21 and 9

8. 15 and 7

10. 30 and 45

11. 44 and 55


9. 54 and 81

221

12. 35, 20, and 15


Lesson 5–1

Write the prime factorizations of 18 and 27.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Greatest Common Factor Find the GCF of each set of numbers by making a list. 1. 12 and 20

2. 24 and 30

3. 18 and 27

Find the GCF of each set of numbers by using prime factors. 4. 10 and 25

5. 6 and 21

6. 14 and 42

Find the GCF of each set of numbers. 7. 15 and 40

8. 16 and 36

9. 12 and 54

10. 24 and 64

11. 39 and 26

12. 35 and 63

13. 36 and 48

14. 35 and 28

15. 40 and 56

16. 56 and 14

17. 27 and 63

18. 88 and 66

19. 60 and 84

20. 45 and 90

21. 85 and 51

22. 54 and 72

23. 48 and 80

24. 63 and 108

25. 21, 30, 44

26. 16, 24, 56

27. 27, 54, 81


222


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. WAREHOUSE A warehouse has three shelves that can hold 8, 12, or 16 skateboards. Each shelf has sections holding the same number of skateboards. What is the greatest number of skateboards that can be put in a section? Explain.

2. FRUIT Mei has 15 oranges, 9 peaches, and 18 pears. She wants to put all of the fruit into decorative baskets. Each basket must have the same number of pieces of fruit in it. Without mixing fruits, what is the greatest number of pieces of fruit Mei can put in each basket? Explain.

3. SHIPPING Oscar needs to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs. He can pack only one type of CD in each box, and he must pack the same number of CDs in each box. What is the greatest number of CDs Oscar can pack in each box? Explain.

4. GARDENING Jill wants to put 45 sunflower plants, 81 corn plants, and 63 tomato plants in her garden. If she puts the same number of plants in each row and if each row has only one type of plant, what is the greatest number of plants Jill can put in one row? Explain.

5. MONEY The list Wednesday $36 shows the Thursday $54 amounts of Friday $72 money the club leader collected from members for a camping trip. Each member paid the same amount. What is the most the camping trip could cost per member? Explain.

6. MONEY Use the information from Exercise 5. How many members have paid to go on the camping trip if the price is the greatest possible price per member?


223


Lesson 5–1

Greatest Common Factor

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Greatest Common Factor Pre-Activity Read the introduction at the top of page 177 in your textbook. Write your answers below. 1. Who rode Rainbow Falls? 2. Who rode Gold Rush? 3. Who rode both Rainbow Falls and Gold Rush?

Reading the Lesson 4. Look at the diagram at the top of page 177 in your textbook. What does a Venn diagram do?

For Exercises 5–8, use the Venn diagram in Example 1 at the bottom of page 177. 5. What elements are listed in the circle on the left?

6. What does the name tell you about each of the numbers inside the circle on the left?

7. What does the area where the two circles overlap represent?

8. What does GCF mean and what is the GCF of 42 and 56?

Helping You Remember 9. Work with a partner to find the GCF for these two sets of numbers: 12 and 13, and 14 and 42. Have one partner find each GCF by listing factors. Have the other partner find each GCF by using prime factors. Then exchange papers and check each other’s work.


224


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment GCFs By Successive Division Here is a different way to find the greatest common factor (GCF) of two numbers. This method works well for large numbers. Find the GCF of 848 and 1,325. Step 1 Divide the smaller number into the larger. 1 R477 848q1 w,3 w2 w5 w 848 477

Step 3 The last divisor is the GCF of the two original numbers. The GCF of 848 and 1,325 is 53. Use the method above to find the GCF for each pair of numbers. 1. 187; 578

2. 161; 943

3. 215; 1,849

4. 453; 484

5. 432; 588

6. 279; 403

7. 1,325; 3,498

8. 9,840; 1,751

9. 3,484; 5,963

11. 45,787; 69,875


10. 1,802; 106

12. 35,811; 102,070

225


Lesson 5–1

Step 2 Divide the remainder into the divisor. Repeat this step until you get a remainder of 0. 1 R371 1 R106 3 R53 2 R0 477q8 w4 w8 w 371q4 w7 w7 w 106q3 w7 w1 w 53q1 w0 w6 w 477 371 318 106 371 106 53 0

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Simplifying Fractions Fractions that name the same number are equivalent fractions. To find equivalent fractions, you can multiply or divide the numerator and denominator by the same nonzero number.

d Replace the d with a number so that }1} 5 }}. 2

10

Since 2 3 5 5 10, multiply the numerator and denominator by 5. 35

35

d 1 }} 5 }} 10 2

5 1 }} 5 }} 10. 2

35

35

When the GCF of the numerator and denominator is 1, the fraction is in simplest form. To write a fraction in simplest form, you can divide the numerator and denominator by the GCF. 12 Write } } in simplest form. 30

The GCF of 12 and 30 is 6. 46 12 2 }} 5 }} 30 5

Divide the numerator and denominator by the GCF, 6.

46 The GCF of 2 and 5 is 1, so }2} is in simplest form. 5

Replace each d with a number so that the fractions are equivalent. 1. }1} 5 }d} 5

15

12 2 2. } } 5 }} 18

27 3. }d} 5 } } 14

d

42

Write each fraction in simplest form. If the fraction is already in simplest form, write simplest form. 4. }6}

5. }2}

6. }6}

21 7. } }

15 8. } }

9. }7}

30

28


3

8

10

30

226


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Simplifying Fractions Replace each d with a number so that the fractions are equivalent. 1. }1} 5 }d} 35

2. }d} 5 }2}

3. }1} 5 }d}

10 2 4. } } 5 }} d

20 5. }4} 5 } } 45

6. }1} 5 }4}

27 7. }1} 5 } }

8. }d} 5 }8}

18 d 9. } } 5 }}

5

15

3

d

15

d

7

5

6

d

28

24

24

16

4

Write each fraction in simplest form. If the fraction is already in simplest form, write simplest form. 10. }1}

11. }8}

20 12. } }

13. }6} 15

15 14. } }

15. }7}

27 16. } }

17. }7} 12

28 18. } }

90 19. } }

20. }8} 21

14 21. } }

23 22. } }

23. }9}

12 24. } }

25. }4}

75 26. } }

60 27. } }

10 28. } } 25

15 29. } } 19

20 30. } }

49 31. } }

49 32. } }

24 33. } }

81

100

46

12

56


60

10

60

8

36

35

13

27

100

110

28

70

64

227


Lesson 5–2

2

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Simplifying Fractions For Exercises 1–3, use the following information and the table at the right. Write your answers in simplest form. In a frequency table, the relative frequency of a category is the fraction of the data that falls in that class. To find relative frequency, divide the frequency by the total number of items.

1. STATISTICS What is the relative frequency of people with brown eyes?

Eye Color Survey Color

Tally

Frequency

Brown

552

12

Blue

5

5

Green

4

4

Hazel

53

8

Violet

1

1

2. STATISTICS What is the relative frequency of people with hazel eyes?

4 }} 15

3. STATISTICS What is the relative frequency of people with brown or hazel eyes?

4. ANIMALS Lions sleep about 20 hours a 20 day. Write } } as a fraction in simplest 24

form.

5 }} 6

5. MARBLES Carlota has 63 marbles. Twenty-eight of her marbles are aggies. What fraction of Carlota’s marbles are aggies? Write the answer in simplest form.

6. MOVIES Fourteen of the top thirty alltime grossing children’s films were 14 animated films. Write } } as a fraction 30

in simplest form.

7 }} 15


228


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Simplifying Fractions Pre-Activity Read the introduction at the top of page 182 in your textbook. Write your answers below. 1. How many students were surveyed? 2. How many students prefer music magazines?

Reading the Lesson 3. The word equivalent [ih-KWIH-vuh-luhnt] means “equal in quantity, strength, value, and so forth.” What are equivalent fractions?

4. How can you find equivalent fractions?

5. Which of the following fractions are equivalent? How can you tell?

6. How can you tell if a fraction is in simplest form?

7. What are two ways you can use to write a fraction in simplest form?

Helping You Remember 8. Look at the bar graph at the top of page 182 in your textbook. Write a fraction that shows how many of the total number of students say comics is their favorite type of magazine. Write an equivalent fraction that uses greater numbers. Write this fraction in simplest form. Be sure to show all your work.


229


Lesson 5–2

5 15 20 }}, }}, }} 9 27 45

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Fraction Mysteries Here is a set of mysteries that will help you sharpen your thinking skills. In each exercise, use the clues to discover the identity of the mystery fraction. 1. My numerator is 6 less than my denominator. I am equivalent to }3}. 4

2. My denominator is 5 more than twice my numerator. I am equivalent to }1}. 3

3. The GCF of my numerator and denominator is 3. I am equivalent to }2}. 5

4. The GCF of my numerator and denominator is 5. I am equivalent to }4}. 6

5. My numerator and denominator are prime numbers. My numerator is one less than my denominator. 6. My numerator and denominator are prime numbers. The sum of my numerator and denominator is 24. 7. My numerator is divisible by 3. My denominator is divisible by 5. My denominator is 4 less than twice my numerator. 8. My numerator is divisible by 3. My denominator is divisible by 5. My denominator is 3 more than twice my numerator. 9. My numerator is a one-digit prime number. My denominator is a one-digit composite number. I am equivalent to }8}. 32

10. My numerator is a prime number. The GCF of my numerator and denominator is 2. I am equivalent to }1}. 5

11. CHALLENGE Make up your own mystery like the ones above. Be sure that there is only one solution. To check, have a classmate solve your mystery.


230


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Mixed Numbers and Improper Fractions The number 2}2} is a mixed number. A mixed number indicates the sum of a whole number and a 3

fraction. The number }5} is an improper fraction. Improper fractions are fractions greater than or equal 3 to 1. Mixed numbers can be written as mixed numbers or as improper fractions.

Draw a model for 2}1}. Then write 2}1} as an improper fraction. 3

3

The model shows there are seven }1}s. 3 You can also multiply the denominator and the whole number. Then add the numerator. (2 3 3) 1 1 7 2}1} → } } 5 }} 3

3 3 1 So 2}} can be written as }7}. 3 3

Write }9} as a mixed number. 4

Divide 9 by 4. Use the remainder as the numerator of the fraction. 2}1} 4 4q9 w 28 1

9 4

So, }9} can be written as 2}1}. 4

4

2

1 4

Write each mixed number as an improper fraction. 1. 3}1} 8

2. 2}4}

3. 2}1} 2

4. 1}2}

5. 2}1}

6. 3}7}

7. 2}3}

8. 1}3}

10

3

8

4

Write each improper fraction as a mixed number. 9. }7}

10. }5}

11. }3}

11 12. } }

22 13. } }

15 14. } }

25 15. } }

16 16. } }

4

5


3

7

2

4

231

8

3


Lesson 5–3

9

5

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Mixed Numbers and Improper Fractions Draw a model for each mixed number. Then write the mixed number as an improper fraction. 1. 4}1} 3

2. 3}3} 8

3. 2}2} 5

Write each mixed number as an improper fraction. 4. 6}1} 2

5. 1}5} 6

6. 1}3} 8

7. 3}1}

8. 3}7} 8

9. 2}1}

10. 2}8}

11. 4}5}

12. 8}3}

13. 5}4}

14. 10}2}

15. 9}1}

5

4

7

3

9

6

3

4

Write each improper fraction as a mixed number. 16. }9}

17. }5}

15 18. } }

17 19. } }

19 20. } }

27 21. } }

25 22. } }

31 23. } }

52 24. } }

41 25. } }

37 26. } }

77 27. } }

5

6

9


2

4

3

4

2

5

232

8

7

8


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Mixed Numbers and Improper Fractions 1. MILEAGE Brownsville is 7}5} miles away

47 2. SWIMMING Steven swam } } meters

8

6

from Frisco. Write the distance as an improper fraction.

crossing Lady Jay Creek. Write the distance he swam as a mixed number.

7}5} m 6

3. FOOD Kenji’s favorite recipe calls for

4. PUPPY Nikki’s puppy weighs

3}3} cups of flour. Write the amount of 4

25 }} pounds. Write the puppy’s weight as 7

flour he needs as an improper fraction.

a mixed number.

3}4} lb 7

10

87 6. GEOGRAPHY Hampshire Hill is } }

she is too tired to keep going. Write the distance she can run as an improper fraction.

9

meters tall. Write its height as a mixed number.

9}2} m 3


233


Lesson 5–3

5. EXERCISE Koto can run 4}7} miles before

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Mixed Numbers and Improper Fractions Pre-Activity Complete the Mini Lab at the top of page 186 in your textbook. Write your answers below. 1. How many shaded }1}s are there? 3

2. What fraction is equivalent to 1}1}? 3

Make a model to show each number. 3. the number of fourths in 2}3} 4

4. the number of halves in 4}1} 2

Reading the Lesson 5. What is a mixed number? Write three examples.

6. You read 4}1} as four and one-sixth. How do you read the following mixed 6

numbers: 3}3}, 2}2}, 8}1}? 5

3

2

7. What is an improper fraction? Write three examples.

8. Look at Example 2 on page 187. What does the (6 3 2) 1 1 represent?

Helping You Remember 9. Work with a partner. Have one person show the other how to write a mixed number as an improper fraction. Then have the other partner show how to write an improper fraction as a mixed number. © Glencoe/McGraw-Hill

234


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Nice Fractions

?

Can fractions be nice? When you see fractions like the ones at the right, it is hard to think of them as anything but nasty. Sometimes, all you need to do is write a simple fraction—a “nice” fraction—as an estimate. You can do this by using compatible numbers.

18

→

→ }6}

17 is close to 18, and 18 5 3 3 6.

6 1 }} 5 }} 18 3

149 }} 98

150 →} } 100

53 44

?

→ →

6 }} 17

14 25

198 ? 147

6 17 ?

1 49 98

?

149 is close to 150. 98 is close to 100.

150 3 }} 5 }} 100 2

Choose the best estimate for each fraction from the choices at the right. 15 1. } } 21

35 2. } } 24

21 3. } } 29

24 4. } }

49 5. } }

89 6. } }

59 7. } }

19 8. } }

41

46

49

48

81

a. about }1} b. about c. about d. about e. about

147 9. } }

118 10. } }

298

61

39 11. } }

76 12. } }

158

51

4 1 }} 2 3 }} 4 1}1} 4 1}1} 2

f. about 2

Write a nice fraction as an estimate of each fraction. 13. }4} 19

12 14. } } 25

15. }7} 31

16. }8}

14 17. } } 25

30 18. } }

23 19. } }

79 20. } }

53 21. } }

50 22. } }

121 23. } }

198 24. } }

44

19

35

98

79

147

Write a fraction that fits each description. 25. It’s close to }1}. 2

The denominator is 55. 27. It’s close to 1}1}. 2

The denominator is 49.


26. It’s close to }2}. 3

The numerator is 99. 28. It’s close to }2}. 3

The denominator is 89.

235


Lesson 5–3

37

53

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Least Common Multiple A multiple of a number is the product of the number and any whole number. The multiples of 2 are below. 13252

23254

33256

43258

5 3 2 5 10

The smallest number other than 0 that is a multiple of two or more whole numbers is the least common multiple (LCM) of the numbers.

Find the LCM of 4 and 6 by making a list. Step 1 List the nonzero multiples. multiples of 4: 4, 8, 12, 16, 20, … multiples of 6: 6, 12, 18, 24, 30, … Step 2 Identify the LCM from the common multiples. The LCM of 4 and 6 is 12. Find the LCM of 6 and 15 by using prime factors. Step 1 Write the prime factorization of each number. 6

15

2 3 3

3 3 5

Step 2 Identify all common prime factors. 65233 15 5 3 3 5 Step 3 Find the product of all of the prime factors using each common prime factor once and any remaining factors. The LCM is 2 3 3 3 5 or 30.

Find the LCM of each set of numbers. 1. 2 and 4

2. 5 and 10

3. 3 and 7

4. 5 and 6

5. 6 and 9

6. 4 and 10

7. 9 and 27

8. 4 and 6

9. 5 and 7


236


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Least Common Multiple 1. 4 and 36

2. 5 and 25

3. 3 and 42

4. 4 and 5

5. 3 and 8

6. 5 and 13

7. 7 and 10

8. 7 and 49

9. 6 and 9

10. 6 and 30

11. 5 and 6

12. 12 and 18

13. 8 and 28

14. 6 and 14

15. 5 and 14

16. 12 and 15

17. 9 and 24

18. 15 and 18

19. 12 and 14

20. 3, 5, and 12

21. 6, 16, and 24

22. 12, 18, and 24

23. 7, 10, and 14

24. 2, 5, and 12


237


Lesson 5–4

Find the LCM of each set of numbers.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Least Common Multiple 1. FORESTRY Omar is planting trees. He has enough trees to plant 6, 7, or 14 trees in each row. What is the least number of trees Omar could have?

2. BUSES The Line A bus arrives at the bus stop every 25 minutes, and the Line B bus arrives every 15 minutes. They are both at the bus stop right now. In how many minutes will they both be at the bus stop again?

3. MARCHING BAND The high school marching band rehearses with either 6 or 10 members in every line. What is the least number of people that can be in the marching band?

4. TIME In a clock, a large gear completes a rotation every 45 seconds, and a small gear completes a rotation every 18 seconds. How many seconds pass before the gears align again?

5. ROSES Dante is planting his rose garden. He knows he can plant all of his roses by planting 12 or 15 rose bushes in every row. What is the least number of rose bushes Dante could have?

6. FAMILY Every 7 years the Lancaster family has a family reunion. Every 6 years they update their family tree. If they both had a photo taken and updated their family tree in 1997, in what year will both events occur again?


238


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Least Common Multiple Pre-Activity Read the introduction at the top of page 194 in your textbook. Write your answers below. 1. Write the products of 8 and each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. 2. Describe the pattern you see in the way the numbers increase. 3. Study the products of any number and the numbers from 1 to 10. Write a rule for the pattern you find. Give examples to support your rule.

Reading the Lesson Look at page 194 in your textbook. Complete each sentence. 4. The multiples 0, 8, 16, and 24 are found on the lists of multiples for both 8 and 4. They are multiples that are common to both 8 and 4. Multiples that are common to both 8 and 4 are ____________________ of 8 and 4. 5. The smallest multiple other than 0 that is on the list for both 8 and 4 is 8. It has the least value of all the multiples that 8 and 4 have in common other than 0. This smallest common multiple is the ____________________ or _____________ of 8 and 4. Look at Example 2 on page 195. Complete each sentence. 6. A prime factor is a factor that is a ________________. 7. The example says to use each common prime factor once and then any remaining prime factors. The common prime factor in the example is 5 because __________________________________.

8. Work with a partner to find the least common multiple of 8 and 12. Have one person find the LCM by making a list and have the other by using prime factors. Then exchange papers and check each other’s work.


239


Lesson 5–4


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Perfect! A proper factor of a number is any factor of the number except the number itself. You can use proper factors to classify numbers. A number is abundant if the sum of its proper factors is greater than the number itself.

A number is deficient if the sum of its proper factors is less than the number itself.

Proper factors of 12: 1, 2, 3, 4, 6 1 1 2 1 3 1 4 1 6 5 16, and 16 . 12. So, 12 is abundant.

Proper factors of 16: 1, 2, 4, 8 1 1 2 1 4 1 8 5 15, and 15 , 16. So, 16 is deficient.

Now you can probably guess the definition of a perfect number. A number is perfect if the sum of its proper factors is equal to the number itself.

Proper factors of 6: 1, 2, 3 1121356 So, 6 is perfect!

Tell whether each number is abundant, deficient, or perfect. 1. 8

2. 9

3. 15

4. 18

5. 20

6. 24

7. 25

8. 28

9. 30

10. 35

11. What is the least whole number that is abundant? 12. Is it possible for a prime number to be perfect? Explain.

13. Is it possible for the sum of two deficient numbers to be an abundant number? Explain.

14. CHALLENGE Show why 496 is a perfect number.


240


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention To compare two fractions, • Find the least common denominator (LCD) of the fractions; that is, find the least common multiple of the denominators. • Rewrite each fraction as an equivalent fraction whose denominator is the LCD. • Compare the numerators.

Replace d with ,, ., or 5 to make }1} d }5} true. 3

12

• The LCM of 3 and 12 is 12. So, the LCD is 12. • Rewrite each fraction with a denominator of 12. 34 1 d 4 1 }} 5 }}, so }} 5 }}. 12 3 12 3

5 5 } } 5 }} 12 12

34 • Now, compare. Since 4 , 5, }4} , }5}. So }1} , }5}. 12

3

12

12

Order }1}, }2}, }1}, and }3} from least to greatest. 6 3 4

8

The LCD of the fractions is 24. So, rewrite each fraction with a denominator of 24. 34

38

1 d }} 5 }}, so }1} 5 }4}. 6 24 24 6

2 d 2 16 }} 5 }} , so }} 5 }}. 24 3 3 24

34

38

36

33

1 d }} 5 }}, so }1} 5 }6}. 24 4 4 24

3 d 3 9 }} 5 }} , so }} 5 }}. 8 24 8 24

36

33

The order of the fractions from least to greatest is }1}, }1}, }3}, }2}. 6 4 8 3

Replace each d with ,, ., or 5 to make a true sentence. 1. }5} d }3} 12

8

2. }6} d }3} 8

3. }2} d }1}

4

7

6

Order the fractions from least to greatest. 4. }3}, }3}, }1}, }1} 4 8 2 4


5. }2}, }1}, }5}, }7} 3 6 18 9

241

6. }1}, }5}, }5}, }5} 2 6 8 12


Lesson 5–5

Comparing and Ordering Fractions

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Comparing and Ordering Fractions Replace each d with ,, ., or 5 to make a true sentence. 1. }2} d }3}

2. }3} d }6}

3. }5} d }7}

4. }1} d }6}

5. }3} d }1}

6. }1} d }9}

7. }5} d }7}

8. }5} d }5}

9. }4} d }2}

10. }6} d }4}

11. }5} d }3}

12. }3} d }2}

13. }5} d }7}

14. }2} d }1}

15. }5} d }2}

16. }3} d }5}

17. }4} d }3}

18. }3} d }5}

19. }1} d }2}

20. }7} d }4}

11 21. }9} d } }

22. }1} d }2}

23. }8} d }7}

24. }2} d }4}

3

2

6

7

7

10

6

4

4

7

8

5

10

14

12

8

8

9

8

12

15

9

9

9

16

8

3

6

12

5

16

4

6

12

7

5

10

7

8

9

12

10

3

9

5

9

12

15

Order the fractions from least to greatest. 25. }3}, }2}, }5}, }1}

26. }1}, }2}, }3}, }1}

27. }2}, }4}, }5}, }7}

13 7 28. }4}, }2}, } }, }}

11 5 3 9 29. } }, }}, }}, }}

30. }7}, }3}, }5}, }1}

4 5 8 2

5 3 15 9


3 7 14 6

12 6 4 16

242

3 9 6 12

15 5 12 2


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. SHOES Toya is looking in her closet. If

2. BUDGET Daniel spends }3} of his money 7 4 on rent and }} of his money on food. 9

1 2 }} of her shoes are black and }} are 3 5

brown, does she have more black shoes or more brown shoes? Explain.

Does he spend more money on food or rent? Explain.

food; }4} . }3} 9

3. WOODWORKING Isi drilled a hole that

7

4. FOOD In a recent survey, }2} of the 5

is }5} inch wide. She has a screw that is

people surveyed said their favorite food

9 5 }} inch wide. Is the hole wide enough to 6

was pizza, }1} said it was hot dogs, and

4 3 }} said it was popcorn. Which food was 10

fit the screw? Explain.

favored by the greatest number of people? Explain.

pizza; }2} . }3} . }1} 5

5. OFFICE SUPPLIES A blue paper clip is

10

4

6. GUMBALLS A red gumball is }5} inch

8 5 across. A green gumball is }} inch 6 across, and a blue gumball is }7} inch 9

1 }} inch wide. A silver paper clip is 6 3 }} inch wide, and a red paper clip is 8 1 }} inch wide. What color paper clip has 3

across. List the gumballs in order from smallest to largest.

the smallest width? Explain.

red, blue, green


243


Lesson 5–5

Comparing and Ordering Fractions

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Comparing and Ordering Fractions Pre-Activity Read the introduction at the top of page 198 in your textbook. Write your answers below. 1. Use the models to determine which marble is larger.

Reading the Lesson For Exercises 2–4, look at the key concept box on page 198. 2. How is LCM related to LCD?

3. How can you find the least common denominator?

4. For the second step, it says to rewrite each fraction as an equivalent fraction using the LCD. What are equivalent fractions?

5. When comparing numbers, you can use the signs ,, ., and 5. What does each sign mean?

Helping You Remember 6. Explain how to order fractions having different denominators from least to greatest.


244


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment If someone asked you to name a fraction between }4} and }6}, you 7

7

probably would give the answer }5} pretty quickly. But what if you 7

were asked to name a fraction between }4} and }5}? At the right, you 7 7

can see how to approach the problem using “fraction sense.” So, one

4 d }} 5 }} 7 14 5 d }} 5 }} 14 7

→ }4} 5 }8} →

7 14 5 10 }} 5 }} 7 14

fraction between }4} and }5} is }9}. 7

7

14

Use your fraction sense to solve each problem. 1. Name a fraction between }1} and }2}. 3

3

2. Name a fraction between }3} and }4}. 5

5

3. Name five fractions between }1} and 1. 2

4. Name five fractions between 0 and }1}. 4

5. Name a fraction between }1} and }1} whose denominator is 16. 4

2

6. Name a fraction between }2} and }3} whose denominator is 10. 3

4

7. Name a fraction between 0 and }1} whose numerator is 1. 6

8. Name a fraction between 0 and }1} whose numerator is not 1. 10

9. Name a fraction that is halfway between }2} and }5}. 9

9

10. Name a fraction between }1} and }3} that is closer to }1} than }3}. 4

4

4

4

11. Name a fraction between 0 and }1} that is less than }3}. 2

10

12. Name a fraction between }1} and 1 that is less than }3}. 2

5

13. Name a fraction between }1} and }3} that is greater than }4}. 2

4

5

14. How many fractions are there between }1} and }1}? 4


245

2


Lesson 5–5

Developing Fraction Sense

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Writing Decimals as Fractions Decimals like 0.58, 0.12, and 0.08 can be written as fractions. To write a decimal as a fraction, you can follow these steps. • Identify the place value of the last decimal place. • Write the decimal as a fraction using the place value as the denominator. • If necessary, simplify the fraction.

Write 0.5 as a fraction in simplest form. 0.5 5 }5}

0.5 means five tenths.

10 1

5 5 }@ }

Simplify. Divide the numerator and denominator by the GCF, 5.

10 @ 2

5 }1}

So, in simplest form, 0.5 is }1}.

2

2

Write 0.35 as a fraction in simplest form. 35 0.35 5 } }

0.35 means 35 hundredths.

100 7

@ 35 5} }


100 @ 20

5 }7}

So, in simplest form, 0.35 is }7}.

20

20

Write 4.375 as a mixed number in simplest form. 375 4.375 5 4} } 1,000

0.375 means 375 thousandths.

3

@ 3 75 5 4} } 1@ ,000

5 4}3}

Simplify. Divide by the GCF, 125.

8

8

Write each decimal as a fraction or mixed number in simplest form. 1. 0.9

2. 0.8

3. 0.27

4. 0.75

5. 0.34

6. 0.125

7. 0.035

8. 0.008

9. 1.4

13. 12.05 © Glencoe/McGraw-Hill

10. 3.6

11. 6.28

12. 2.65

14. 4.004

15. 23.205

16. 51.724

246


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Writing Decimals as Fractions 1. 0.6

2. 10.9

3. 0.08

4. 6.25

5. 4.125

6. 0.075

7. 9.35

8. 3.56

9. 8.016

10. 21.5

11. 0.055

12. 7.42

13. 5.006

14. 3.875

15. 1.29

16. 2.015

17. 6.48

18. 0.004

19. 4.95

20. 8.425

21. 9.74

22. 0.47

23. 5.019

24. 1.062

25. 3.96

26. 0.824

27. 20.8

28. 6.45

29. 4.672

30. 0.375


247


Lesson 5–6

Write each decimal as a fraction or mixed number in simplest form.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Writing Decimals as Fractions 1. FIELD TRIP About 0.4 of a biology class will be going on a field trip. Write the decimal as a fraction in simplest form.

2. EARTH Eighty percent of all life on Earth is below the ocean’s surface. Write 0.80 as a fraction in simplest form.

4 }} 5

3. VENUS The planet Venus is 67.24 million miles away from the Sun. Write the decimal as a mixed number in simplest form.

4. SATURN If you weighed 138 pounds on Earth, you would weigh 128.34 pounds on Saturn. Write the weight on Saturn as a mixed number in simplest form.

17 128} } lb 50

5. MERCURY If you were 10 years old on Earth, you would be 41.494 years old on Mercury. Write the age on Mercury as a mixed number in simplest form.

6. INTERNET According to recent figures, 4.65 million people in the Middle East are online. Write the decimal as a mixed number in simplest form.

13 4} } 20


248


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Writing Decimals as Fractions Pre-Activity Complete the activity at the top of page 202 in your textbook. Write your answers below.

2. Write this decimal as a fraction.

3. Repeat Exercises 1 and 2 with each of the other decimals.

Reading the Lesson For Exercises 4–6, look at Example 1 on page 202. 4. Why is the denominator of the fraction 10?

5. How does the example tell you to simplify the fraction?

6. What do the letters GCF stand for?

7. Look at Example 3 on page 203. What is the place value of the last decimal place? What does that mean when you go to write the corresponding fraction?

Helping You Remember 8. Work with a partner. Each of you write several decimals with varying numbers of digits. Next, exchange papers and write the decimals as fractions. Then, exchange the papers again and check one another’s work.


249


Lesson 5–6

1. Write the word form of the decimal that represents the amount of people who prefer Italian ice.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Estimating with Decimals and Fractions Often you only need to give a fractional estimate for a decimal. To make fractional estimates, it helps to become familiar with the fraction-decimal equivalents shown in the chart at the right. You also should be able to identify the fraction as an overestimate or underestimate. Here’s how. The decimal 0.789 is a little less than 0.8, so it is a 42 little less than }4}. Write } }. 5

11 a little more than 1}1}. Write 1} }. 8 8

7. 0.09

10. 2.76

10 8

0.2

5 }1}

0.25

5 }1}

0.3

5 }3}

5 4

10

0.375 5 }3} 8

Write a fractional estimate for each decimal. Be sure to identify your estimate as an overestimate or an underestimate.

4. 0.741

5 }1}

0.125 5 }1}

5

The decimal 1.13 is a little more than 1.125, so it is

1. 0.243

0.1

2. 0.509

3. 0.429

5. 0.88

6. 0.63

8. 0.57

0.4

5 }2}

0.5

5 }1}

0.6

5 }3}

12. 5.218

13. The scale in the delicatessen shows 0.73 pound. Write a fractional estimate for this weight.

2 5

0.625 5 }5} 8

0.7

5 }7}

0.75

5 }3}

0.8

5 }4}

9. 1.471

11. 1.289

5

10 4 5

0.875 5 }7} 8

0.9

5 }9} 10

14. Darnell ordered a quarter pound of cheese. The scale shows 0.23 pound. Is this more or less than he ordered?

15. On the stock market, prices are listed as halves, fourths, and eighths of a dollar. Yesterday the price of one share of a stock was $25.61. Write a fractional estimate for this amount. 16. Charlotte used a calculator to figure out how many yards of ribbon she needed for a craft project. The display shows 2.53125. Write a fractional estimate for this length.


250


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Writing Fractions as Decimals Any fraction can be written as a decimal using division. Decimals like 0.5 and 0.516 are called terminating decimals because the digits end. A decimal like 0.8 w7 w 5 0.878787… is called a repeating decimal because the digits repeat.

Write }3} as a decimal. 8

Divide. 0.375 8 q3 w.0 w0 w0 w 22 4 60 256 40 240 0

Lesson 5–7

Therefore, }3} 5 0.375. 8

Write }7} as a decimal. 11

Divide. 0.6363 11q7 w.0 w0 w0 w0 w 26 6 40 233 70 266 40 233 7 The pattern repeats. Therefore, }7} 5 0.6 w3 w. 11

Write each fraction or mixed number as a decimal. 1. }3}

2. }3}

3. }1}

4. }3}

5. }1}

6. 2}1} 4

7. 1}5}

8. 3}8}

10. 1}5}

11. 3}1}

12. 4}5}

10

8

9. 1}3} 11


4

8

3

6

6

251

5

9

11


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 1. }9}

1 2. }2}

3. }3}

4. }1}

5. }1}

6. }5}

7. }4}

8. 3}7} 8

9. 9}2}

10. }8}

11. 4}2}

12. 6}5}

13. 5}1}

14. 12}3}

17 15. 10} }

11 16. 2} }

11 17. 3} }

18. 6}4}

19. 1}5}

20. 10}1}

13 21. 2} }

22. 3}7}

23. 5}8}

24 24. 3} }

10

2

9

11

3

18

9

12


4

100

6

6

5

3

8

8

20

16

5

8

18

9

25

252


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Writing Fractions as Decimals 1. PLANETS The planet Mercury is roughly

2. MARBLES Lin has a marble that is

2 }} the size of Earth. Write the fraction 5

5 }} inch wide. Write the marble’s width 8

as a decimal.

as a decimal.

0.625 in.

4. EXERCISE Tate has been dancing for }5}

3. HOMEWORK Miko has finished }6} of

6

11

of an hour. Write this fraction as a decimal.

Lesson 5–7

her homework. Write the fraction as a decimal.

6. COOKING A recipe calls for 2}2} cups of

5. SPORTS Charlie played tennis for

3

3}3} hours. Write the mixed number as a

milk. Write the mixed number as a decimal.

4

decimal.

7. HEIGHT Winona is 2}4} the height of her 11

8. RECESS Jennifer has been spinning in circles for 4}3} minutes. Write the

little brother. Write the mixed number as a decimal.


16

mixed number as a decimal.

253


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Writing Fractions as Decimals Pre-Activity Read the introduction at the top of page 206 in your textbook. Write your answers below. 1. Write the decimal for }9}. 10

2. Write the fraction equivalent to }1} with 10 as the denominator. 2

3. Write the decimal for }5}. 10

4. Write }3} and }2} as decimals. 5

5

Reading the Lesson 5. Look at Exercise 4 at the top of page 206. What do you need to do to the fractions in order to write the decimals?

6. Look at Example 1 on page 206. How can you tell that 0.875 is a terminating decimal?

7. How are repeating decimals different from terminating decimals?

8. What two methods are used to indicate repeating decimals?

9. Why is it necessary to use an indicator for repeating decimals?

Helping You Remember 10. Write the following fractions as decimals. First, use the paper and pencil method. Then, use a calculator and compare your answers. 3 3 1 5 }}, }}, }}, }} 11 20 12 8


254


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Tagging Along Which of }2}, }3}, }4}, and }9} belongs in the “tag” 3 4 5

10

on the number line at the right? The tag is to the right of 0.75, so the fraction must be greater than 0.75. Express each fraction as a decimal. 2 w, }} 5 0.6 3

3 }} 5 0.75, 4

4 }} 5 0.8, 5

?

0

0.25

0.5

0.75

1

9 }} 5 0.9 10

Only 0.8 and 0.9 are greater than 0.75, and 0.9 is much closer to 1 than to 0.75. Choose 0.8, which is equal to }4}. 5

On each number line, fill in the tags using the given fractions. 15 2. }4}, }3}, }6}, }5}, } }

8 2 3 9 8

0

0.25

3 4 5 8 16

0.5

0.75

1

15 3 4 3. }7}, }6}, } }, }}, }} 4 5

0

8

0.5

0.75

1

1.25

1.5

2

2.25

2.5

13 8 4. }9}, }7}, }8}, } }, }}

2 3

1.25

Lesson 5–7

1. }3}, }1}, }2}, }1}, }7}

5 3 5

1.5

1.75

2

1.5

6

1.75

4

5. Write a fraction in simplest form for each tag on this number line. Use only the denominators 2, 3, 4, 5, 8, and 10. Express numbers greater than 1 as improper fractions.

0


0.5

1

255

1.5

2



Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860069-3 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03






Lesson 6-4





iii




Practice: Skills











iv

Enrichment





Assessment Options



The assessment masters in the Chapter 6 Resources Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use.










v

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics This is an alphabetical list of vocabulary terms you will use in Chapter 6. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you first found the term. Add this page to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term

Found on Page


denominator

fraction

least common denominator (LCD)

like fractions

mixed number

numerator

simplest form

unlike fractions


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____

Family Letter

h fractions is hard. However, Sometimes people think dealing wit nt situations, such as we encounter fractions in many differe owing how to add and cooking, building, and investing. Kn that can help us in our subtract fractions is a valuable skill daily lives. ing Fractions, your child In Chapter 6: Adding and Subtract tract fractions and mixed will learn how to round, add, and sub r, your child will complete numbers. In the study of this chapte nts and activities and a variety of daily classroom assignme possibly produce a chapter project . it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 6 to the real world. You math we will be learning in Chapter line Study Tools for may also wish to log on to the On t Study Guide pages, and self-check quizzes, Parent and Studen et. If you have any other study help at www.msmath1.n contact me at school. questions or comments, feel free to Sincerely,



ix


Family Letter


NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Adding and Subtracting Fractions Work with a family member to record the amount of time (in hours) each of you spends doing each activity on a typical day. Then write a fraction in simplest form to represent the fraction of a day spent on each activity. Remember that the total number of hours for all six categories must be 24. Name _____________ Activity

Hours

Name _____________ Fraction

Activity

work

work

school

school

eating

eating

sleeping

sleeping

recreation/ entertainment

recreation/ entertainment

other

other

Hours

Fraction

Use the fractions from the tables above to answer the following questions. Express all answers as fractions in simplest form. 1. Together, how much of a day do you both spend sleeping? 2. Who spends more time on recreation or entertainment? What is the difference in time expressed as a fraction of the day? 3. Together, how much of a day do you both spend on work and/or school? 4. Find the activity that you each spend the most time doing. Find the difference in time between these activities expressed as a fraction of the day. 5. Together, what fraction of a day do you both spend doing activities that are included in the other category?


x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Rounding Fractions and Mixed Numbers Use these guidelines to round fractions and mixed numbers to the nearest half. Rounding Fractions and Mixed Numbers

Round to }1} 2

When the numerator is almost as large as the denominator, round up to the next whole number.

7 }} rounds to 1. 8

When the numerator is about half of the denominator, round the fraction to }1}.

4}3} rounds to 4}1}.

When the numerator is much smaller than the denominator, round down to the previous whole number.

1 }} rounds to 0. 5

7

2

Round down

Round 2}3} to the nearest half.

2

3

8

28

The numerator of }3} is about half of the

8 denominator. So, 2}3} rounds to 2}1}. 8 2

2

2 12

3

Round up when it is better for a measure to be too large than too small. Round down when it is better for a measure to be too small than too large. 1 MUSIC You have 4}} minutes left on a mixed tape you are making 2

for a friend. Should you choose a song that is 5 minutes long or a song that is 4 minutes long? In order for the entire song to be recorded, you should round down the number of minutes left on the tape and choose the song that is 4 minutes long.

Round each number to the nearest half. 1. }2}

2. }1} 18

3. }6}

4. 6}2}

5. 5}4}

6. 8}4}

7. 4}1}

8. }2}

5

7

13

5

9

7

7

Tell whether each number should be rounded up or down. 9. the weight of a package you are mailing

10. the length of a rug for your bathroom


277


Lesson 6–1

Round up

Example

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Rounding Fractions and Mixed Numbers Round each number to the nearest half. 1. }2}

2. 2}1} 9

3. 1}4} 7

11 4. } }

5. 2}1} 5

6. 1}1} 3

7. 7}3} 4

8. 3}2}

9. }5}

10. }1}

11. 9}7} 8

12. 4}3}

13. 8}6} 7

14. 1}5}

15. }1}

16. 3}8}

17. }9}

11 18. 2} }

19. 5}3} 20

20. 7}9}

21. 10}1}

13 22. } }

23. 6}4}

24. 8}9}

3

12

16

7

10

12

13

15

12

5

8

9

18

11

25

19

Tell whether each number should be rounded up or down. 25. the amount of wrapping paper for a

26. the length of a strip of wallpaper to hang

gift that is 2}4} feet wide 7

27. the width of a CD player to fit into a

on a wall 7}5} feet high 6

28. the height of a notebook that must

width of 18}2} inches 5

fit inside a backpack 1}3} feet tall 4

Find the length of each line segment to the nearest half inch. 29.

30.

31.

32.


278


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Rounding Fractions and Mixed Numbers 1. EXERCISE Judy walked 6}5} miles. To the 8

2. ANIMALS Maria’s hamster weighs 3}4} 9

pounds. How many pounds is this to the nearest half pound?

nearest half mile, how many miles did she walk?

3}1} lb 2

10

4. CARPENTRY Jan has cut a board to make a shelf. The board is 3}2} feet long.

library to the school. How many miles is this to the nearest half mile?

5. LUMBERING Pat needs to haul away

7

How many feet is this to the nearest half foot?

6. CLOTHING Mandy is making table place

1}3} tons of wood from the lot. The 8

mats that will take 2}1} yards of cloth. If

maximum weight his pickup truck is supposed to carry is 1 ton. How many trips should Pat make to haul all the wood away? Explain.

cloth is sold in half yards, how many yards of cloth will Mandy need to buy? Explain.

4

2}1} yd; }1} is more than a whole 2

4

yd and less than a half yd.

7. EXERCISE Julien is preparing for a 5-mile race. He can choose from a

8. CRAFTS Marisa wants to glue her 6}1}-inch by 8}4}-inch painting onto 4

4}7}-mile course to train on or a 5}2}-mile 8 5

5

foam backing. The foam backing comes in sheets that are 6 inches by 9 inches or 7 inches by 9 inches. Which sheet of foam should Marisa buy? Explain.

course. Which course should he choose? Explain.

7 in. by 9 in.; 6}1} in. is greater 4 than 6 in.


279


Lesson 6–1

3. TRAVEL It is 9}7} miles from the

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Rounding Fractions and Mixed Numbers Pre-Activity Complete the Mini Lab at the top of page 219 in your textbook. Write your answers below. 1. Compare the numerators and denominators of the fractions in each list. How do they compare?

2. Write a rule about how to round to the nearest half inch.

Reading the Lesson For Exercises 3–5, look at the Concept Summary on page 219 in your textbook. 3. When do you round the number up to the next whole number? 4. When do you round the fraction to }1}? 2

5. When do you round the number down to the whole number? 6. Look at Example 3 on page 220 in your textbook. Name another example of when it is better to round up even if the rules say to round down.

Helping You Remember 7. Work with a partner. Write several different fractions and mixed numbers on a piece of paper. Make a table with three columns headed Round up to the Next Whole Number, Round to }1}, and Round Down to the Whole Number. 2 Then have your partner write your numbers in the correct columns. Now, have your partner write some numbers and you write the numbers in the correct columns.


280


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Greatest Possible Error When you measure a quantity, your measurement is more precise when you use a smaller unit of measure. But no measurement is ever exact—there is always some amount of error. The greatest possible error (GPE) of a measurement is one half the unit of measure. At the right, you see how the GPE for the

INCHES

1

2

length of line segment:

ruler shown is calculated as }1} inch. Since 16 1}3} 5 1}6}, the actual measure of the line 16 8

1}3} inches, to the nearest }1} inch

segment may range anywhere from

GPE: half of }1} inch, or }1} inch

8

8

16

8

16

Use the GPE to give a range for the measure of each line segment. 1.

2. INCHES

1

2

3.

INCHES

1

2

4. INCHES

1

2

5. Using this scale, the weight of a bag of potatoes is measured as 3 pounds. What is the range for the actual weight of the potatoes?

CM 1

pounds

3

4

5

6. Using this container, the amount of a liquid is measured as 20 milliliters. What is the range for the actual amount of the liquid?

0 3

2

50 mL 40 mL

1

30 mL

2

20 mL 10 mL


281


Lesson 6–1

1}5} inches to 1}7} inches. 16

8

unit of measure: }1} inch

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Estimating Sums and Differences Round fractions to the nearest half to estimate sums and differences.

Estimate }2} 1 }9}.

Estimate }3} 2 }1}.

10

5

8

2 1 }} rounds to }}. 5 2 9 }} rounds to 1. 10 9 2 1 1 }} 1 }} is about }} 1 1 or 1}}. 10 5 2 2

4

3 1 }} rounds to }}. 8 2 1 }} rounds to 0. 4 3 1 1 1 }} 2 }} is about }} 2 0 or }}. 8 4 2 2

Round mixed numbers to the nearest whole number to estimate sums and differences. When you have a fraction and a mixed number, round in the manner that makes the most sense.

Estimate 8}1} 1 6}1}. 7

Estimate 3}5} 2 }2}.

5

8 5 1 3}} rounds to 3}}. 8 2 2 1 }} rounds to }}. 5 2 3}5} 2 }2} is about 3}1} 2 }1} or 3. 8 5 2 2

8}1} rounds to 8. 7 6}1} rounds to 6. 5 8}1} 1 6}1} is about 8 1 6 or 14. 7 5

5

Estimate. 1. }9} 1 }3}

2. }5} 2 }1}

4. }7} 1 }3}

5. 1}5} 1 6}2}

6. 3}5} 2 2}1}

8. 4}2} 1 3}1} 7

9. 3}5} 2 }3}

11. 5}5} 2 }4}

12. 1}5} 2 }4}

11

8

8

8

4

8

7. 6}2} 2 2}3} 11

4

10. 6}3} 1 }2} 8

5


3. }3} 1 }3} 10

9

7

11

7

5

6

8

9

9

282

4

7

9


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Estimating Sums and Differences Estimate. 2. }5} 2 }1} 7

3. }9} 1 }7}

7 11 4. } } 2 }}

5. }5} 1 }4}

6. 1}1} 2 }3}

7. 2}6} 1 1}1}

8. }9} 2 }3}

9. }7} 1 2}2}

1. }2} 1 }7} 3

8

12

7

6

16

8

8

10

5

10

8

3

8

15

5

9

7 15 10. 3} } 2 }}

13 11. 8}3} 1 5} }

13 4 12. 4} } 2 }}

13. }1} 1 7}1}

11 5 14. 12} } 2 7}}

15. }4} 1 3}5}

16. 4}1} 2 }1} 10

17. 8}3} 1 8}7}

18. 10}2} 2 9}5}

19. 3}1} 1 3}5}

20. 6}7} 2 }1}

14 21. 8}1} 1 } }

10

3

8

16

3

8


10

15

14

10

13

7

8

15

16

7

8

7

6

283

9

Lesson X–2 6–2

16

9

15


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Estimating Sums and Differences CLOTHING For Exercises 1–4, use the table. It shows articles of clothing and the yardage of cloth needed to make them.

Amount of Cloth Needed to Make Clothing Article of Clothing

Amount of Cloth (yards)

Bandana

1 }} 3

Vest

7 }} 8

Pants

4}1}

Shirt

3}3}

Jacket

6}4}

1. Jan wants to make a bandana and a vest from the same cloth. About how many yards of cloth will she need?

5 8 9

2. About how much more cloth will a vest need than a bandana?

1 2 }1} or about }1} yd more 2

3. Gloria wants to make pants and a matching shirt from the same cloth. About how much cloth will she need?

2

4. Sam is trying to decide whether to make a jacket or a shirt. About how much more cloth would he need to buy for a jacket than for a shirt?

62 3 or about 3 yd more

5. GARDENING Juan is building a fence around a triangular garden. About how much fencing should he buy to be sure he has enough?

6. GARDENING Refer to the drawing in Exercise 5. About how much longer is the longest side of the garden than the shortest side, to the nearest whole number?

7

3

3 8 ft

2 8 ft 1

5 8 ft


284


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Estimating Sums and Differences Pre-Activity Read the introduction at the top of page 223 in your textbook. Write your answers below. 1. To the nearest whole number, how tall is the largest cowboy boot?

2. To the nearest whole number, how tall is the largest tricycle wheel?

3. About how much taller is the tricycle wheel than the cowboy boots?

Reading the Lesson

5. In this lesson, what happens to fractions that keep the calculations from being exact?

6. Look at Example 5 on page 224 in your textbook. When is it necessary to round up when you are forming an estimate?

Helping You Remember 7. Work with a partner. Write an addition problem and a subtraction problem using mixed numbers. Then write a problem where you need to estimate by rounding all fractions up or down. Exchange papers with your partner. Use rounding to estimate answers to your partner’s problems.


285


Lesson X–2 6–2

4. Why is it important to use the word about when you are expressing an estimate?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Using 1 as a Benchmark When you estimate sums of proper fractions, it often helps to use the number 1 as a benchmark, like this. Two halves make a whole, so }1} 1 }1} 5 1. 2

If two fraction are each less than }1}, 2 their sum is less than 1.

If two fractions are each greater than }1}, 2 their sum is greater than 1.

3 4 }} 1 }} , 1 8 9

Fill in each 1. }2} 1 }5} 3

7 27 4. } } 1 }} 50

10

5 7 }} 1 }} . 1 8 9

with , or . to make a true statement. 2. }2} 1 }3}

1

8

2

5

50 38 5. } } 1 }}

1

Fill in each

1

7

99

1

24 32 6. } } 1 }}

1

10

1

75

3. }3} 1 }5} 11

49

65

with one of the given fractions to make a true statement.

7. }2} }3} }4} }5}

1 }} 1 2

.1

1 }} 1 2

,1

8. }8} }7} }6} }5}

1 }} 1 2

.1

1 }} 1 2

,1

5 5 5 5

9 }} 1 16

.1

9 }} 1 16

,1

12 13 24 10. }1} } } } } }}

6 }} 1 13

.1

6 }} 1 13

7 7 7 7

11 11 11 11

9. }1} }2} }3} }4}

25 25 25 25

Fill in each

with , or . to make a true statement.

11. 1}5} 2 1}1}

1 }} 2

8

2

49 14. 1 2 } } 99

1 }} 2


,1

12. 1 2 }5}

1 }} 2

10 13. 1 2 } }

1 }} 2

15. 4}3} 1 }1}

5

16. 3 2 }4}

2}1}

11

7

3

286

19

7

2


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Adding and Subtracting Fractions with Like Denominators Fractions with the same denominator are called like fractions. • To add like fractions, add the numerators. Use the same denominator in the sum. • To subtract like fractions, subtract the numerators. Use the same denominator in the difference.

Find the sum of }3} and }3}. 5

3 5

5

Estimate }1} 1 }1} 5 1

3 5

2 2 3 3 313 Add the numerators. }} 1 }} 5 }} 1 15 5 5 5 5 }6} Simplify. 5 5 1}1} Write the improper fraction as a mixed number. 5

Compared to the estimate, the answer is reasonable. Find the difference of }3} and }1}. 4

4

Estimate 1 2 0 5 1 3 1 321 }} 2 }} 5 }} 4 4 4 2 5 }} or }1} 4 2

Subtract the numerators. Simplify.

Compared to the estimate, the answer is reasonable.

Add or subtract. Write in simplest form. 1. }1} 1 }4}

2. }9} 2 }7}

3. }9} 1 }5}

9 11 4. } } 2 }}

5. }4} 1 }5} 7

6. }4} 2 }1} 9

7. }7} 1 }5}

8. }6} 2 }4}

9. }3} 1 }3}

10. }4} 2 }1}

11. }5} 1 }1}

12. }7} 2 }1}

7

4

9

4


11

9

5

11

5

10

8

6

287

10

8

6

12

7

10

12

7

10


Lesson 6–3

9

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Adding and Subtracting Fractions with Like Denominators Add or subtract. Write in simplest form. 1. }2} 1 }4} 9

2. }2} 1 }4}

3. }2} 2 }1}

4. }3} 1 }1} 4

5. }7} 2 }3} 8

6. }9} 1 }3}

7. }5} 2 }1}

8. }1} 1 }5}

11 7 9. } } 2 }}

10. }7} 1 }3}

11. }9} 2 }4}

12. }3} 1 }1}

10 2 13. } } 2 }}

14. }7} 1 }2}

15. }5} 1 }4}

16. }3} 2 }1}

17. }3} 1 }3}

18. }5} 1 }3}

19. }5} 2 }3}

20. }5} 2 }2}

21. }6} 1 }5}

9

4

6

8

11

10

8

5

5

8

6

6

9

11

10

12

10

8

9

10

8

12

6

10

8

3

7

6

6

10

7

7

3

12

12

8

6

6

7

22. How much is }2} pound plus }1} pound? 9

9

23. How much longer is }3} foot than }1} foot? 8

8

24. How much more than }1} cup is }3} cup? 4

4

25. What is the sum of }2}, }7}, and }1}? 11 11


11

288


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Adding and Subtracting Fractions with Like Denominators St at eB ui ld in g

{

{

{

Ra di o

Em pi re

drawing at the right that shows distances between major sites on the Avenue of the Americas in New York City.

Ci ty M M us us ic eu Ha m ll of M od er n Ar Ce t nt ra lP ar kS ou th

MAPS For Exercises 1–3, use the

16 mi 20

3 mi 20

6 mi 20

Avenue of the Americas, New York City

1. Carla walked from the Empire State Building to the Museum of Modern Art. How far did she walk?

2. Julie walked from Central Park South to the Museum of Modern Art. Jolene walked from Radio City Music Hall to the Museum. How much farther did Julie walk than Jolene?

3 }} mi 20

3. Dion walked from Central Park South to the Empire State Building. How far did he walk?

4. COOKING Tiffany made a glass of punch from fruit juice concentrate. She used }1} cup concentrate and }3} cup 4

4

water. How much more water than concentrate did Tiffany use?

5. ART Beng is creating a painting. He

6. CONSTRUCTION Mr. Hayashi is

has }5} of a tube of red paint and }3} of a 8 8

repairing his sidewalk. He mixed }5}

tube of green paint. How much more red paint does he have than green paint?

pound of cement with sand and water to make concrete. The next day he

9

mixed }7} pound of cement with sand 9

and water. How many pounds of cement altogether did Mr. Hayashi use?


289


Lesson 6–3

1 }} c 2

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Adding and Subtracting Fractions with Like Denominators Pre-Activity Complete the Mini Lab at the top of page 228 in your textbook. Write your answers below. Find each sum using grid paper. 1. }4} 1 }3} 12

12

2. }1} 1 }1} 6

6

3. }3} 1 }5} 10

10

4. What patterns do you notice with the numerators?

5. What patterns do you notice with the denominator?

6. Explain how you could find the sum of }3} 1 }1} without using grid paper. 8

8

Reading the Lesson Look at the paragraph below the Mini Lab on page 228 in your textbook. 7. Write a definition for like fractions. 8. What meaning does your textbook give for denominator? 9. The units being added are twelfths. Write a fraction that indicates one twelfth.

Helping You Remember 10. In your own words, explain how to add like fractions. Then explain how to subtract like fractions.


290


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Mystic Hexagons A hexagon is a six-sided figure. In a mystic hexagon, the sum of the numbers along each side is the same number. This number is called the mystic sum. For example, the mystic sum for the hexagon at the right is 20.

6

9

12

10 20

2

1

15

For each mystic hexagon, write the mystic sum in the blank in the middle. Then find the missing fractions along the sides. 1.

5

15 13

3

4

2. 13 35

7 35

9 25 7 25 6 35

9 35

4 25

16 35 3 35

16 25 18 25

2 35

3 25

1 25

Complete each mystic hexagon. Be sure to express all your answers in simplest form. 4. 14 45 8 25

23 45

16 25 6 25

7 45

3 25

16 45 37 45

7 25


13 25

1 45

12 25

291

34 45


Lesson 6–3

3.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Adding and Subtracting Fractions with Unlike Denominators To find the sum or difference of two fractions with unlike denominators, rename the fractions using the least common denominator (LCD). Then add or subtract and simplify.

Find }1} 1 }5}.

3 1 5 The LCD of }} and }} is 6. 3 6

Rename }1} as }2}.

Write the problem.

1 }} 3 1}5} 6

6

3

→

}

Add the fractions.

6

1 2 2 }} 3 }} 5 }} 3 2 6 5 }} 6

2 }} 6 1}5} 6 } 7 1 }} or 1}} 6 6

→

Find }2} 2 }1}.

3 4 2 1 The LCD of }} and }} is 12. 3 4

Rename }2} as }8} and }1} as }3}.

Write the problem.

2 }} 3 2}1} 4

12

3

2 4 8 }} 3 }} 5 }} 3 4 12 3 1 3 }} 3 }} 5 2}} 12 4 3

→

}

Subtract the fractions.

12

4

8 }} 12 2}3} 12 }} 5 }} 12

→

Evaluate x 2 y if x 5 }1} and y 5 }2}. 2

x 2 y 5 }1} 2 }2} 2 5 1 5 }} 3 }5} 2 }2} 3 }2} 2 5 5 2 5 4 5 }} 2 } } 10 10 1 5 }} 10

5

Replace x with }1} and y with }2}. 2 5 Rename }1} and }2} using the LCD, 10. 2

5

Simplify. Subtract the numerators.

Add or subtract. Write in simplest form. 1. }1} 1 }1}

2. }2} 2 }1}

3. }1} 1 }7}

4. }9} 2 }3}

5. }2} 1 }1}

6. }5} 2 }1}

7. }7} 1 }1}

8. }4} 2 }1}

6 7

2 2

3 6

2

4

12

10

9. Evaluate x 1 y if x 5 }1} and y 5 }1}. 12


6

8

2

10 9

5

3

10. Evaluate a 1 b if a 5 }1} and b 5 }3}. 2

292

4


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Adding and Subtracting Fractions with Unlike Denominators Add or subtract. Write in simplest form. 1.

2 }} 3 1 }5} 6

2.

}

3.

}

2 }} 3 2 }1} 6

4.

1 }} 2 1 }7} 8 }

4 }} 7 2 }1} 2 }

6.

1 }} 6 2 }1} 12 }

}

5.

5 }} 6 1 }3} 4

7. }5} 2 }1}

8. }1} 1 }5}

9. }1} 1 }5} 6

11 10. }3} 1 } }

11. }1} 2 }2}

11 3 12. } } 2 }}

13. }3} 2 }1}

14. }4} 1 }1}

15. }3} 1 }2}

16. }2} 2 }1}

11 1 17. } } 2 }}

18. }3} 1 }9}

8

5

2

4

5

12

4

3

4

5

12

12

5

3

3

6

5

7

12

4

2

4

10

19. How much more is }3} gallon than }1} gallon? 8

4

20. How much more is }3} ounce than }1} ounce? 3

Lesson 6–4

4

21. Evaluate x 2 y if x 5 }7} and y 5 }3}. 10

5

22. Evaluate s 1 t if s 5 }2} and t 5 }5}. 3


6

293


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Adding and Subtracting Fractions with Unlike Denominators BUSINESS For Exercises 1–4, use the table below. It lists the fractions of United States car sales held by several companies in 2001.

Leading Car Sales in U.S. in 2001 Company

Fraction of Sales

Company A

1 }} 5

Company B

4 }} 25

Company C

2 }} 5

Company D

3 }} 20

1. What fraction of the U.S. sales did Company C and Company B hold together?

2. How much greater was the fraction of the market of Company A than of Company D?

1 }} 20

3. How much more than Company A’s fraction of the market did Company C have?

4. Find the total fraction of the market that Company D and Company B hold together.

31 }} 100

5. TRAVEL Gabriella’s travel shampoo

6. EXERCISE Bill and Andy were racing to see who could run the farthest in

bottle holds }1} cup of shampoo. Before 2 leaving on vacation, she filled the bottle

5 minutes. Bill ran }5} of a mile, and

to the top with }1} cup of shampoo. How

Andy ran }3} of a mile. How much

much shampoo was already in the bottle?

farther did Andy run than Bill?

8


8

4

294


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Adding and Subtracting Fractions with Unlike Denominators Pre-Activity Complete the Mini Lab at the top of page 235 in your textbook. Write your answers below. 1. How can you describe the sum of 3 pennies and 2 nickels using a common name?

2. How can you describe the sum of 2 pens and 2 pencils using a common name?

3. Explain why you need a common unit name to find the sum. 4. What do you think you need to do to find the sum of }1} and }3}? 2

4

Reading the Lesson 5. Look at the paragraph in the middle of page 235 in your textbook. What does it mean to rename a fraction? 6. What do the letters LCD stand for? 7. What is the LCD of }1} and }1}? 6

4

Helping You Remember 8. Work with a partner. Pretend you are a teacher. You are teaching your partner how to add and subtract fractions with unlike denominators. Simplify }1} 1 }3}, showing and explaining the steps to your partner. Then 2

4

have your partner simplify }1} 2 }2}, showing and explaining each step. 5

Lesson X–4 6–4

2


295


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Unit Fractions A unit fraction is a fraction whose numerator is 1 and whose denominator is any counting number greater than 1. unit fractions: }1} }1} }1} 2 3 10

A curious fact about unit fractions is that each one can be expressed as a sum of two distinct unit fractions. (Distinct means that the two new fractions are different from one another.) 1 1 1 }} 5 }} 1 }} 12 3 4

1 1 1 }} 5 }} 1 }} 2 3 6

1 1 1 }} 5 }} 1 } } 10 11 110

Did you know? The Rhind Papyrus indicates that fractions were used in ancient Egypt nearly 4,000 years ago. If a fraction was not a unit fraction, the Egyptians wrote it as a sum of unit fractions. The only exception to this rule seems to be the fraction }2}. 3

1. The three sums shown above follow a pattern. What is it?

2. Use the pattern you described in Exercise 1. Express each unit fraction as a sum of two distinct unit fractions. a. }1}

b. }1}

4

5

c. }1}

d. }1}

12

100

Does it surprise you to know that other fractions, such as }5}, can be 6

expressed as sums of unit fractions? One way to do this is by using equivalent fractions. Here’s how. 5 10 }} 5 }} 6 12

➝

6 4 10 1 1 }} 5 }} 1 }} 5 }} 1 }} 12 12 12 2 3

➝

5 1 1 }} 5 }} 1 }} 6 2 3

3. Express each fraction as a sum of two distinct unit fractions. b. }4}

a. }2}

15

3

c. }5}

d. }2}

9

5

4. Express }4} as the sum of three distinct unit fractions. 5

5. CHALLENGE Show two different ways to express }1} as the sum of three 2

distinct unit fractions.


296


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Lesson X–5 6–5

Adding and Subtracting Mixed Numbers To add or subtract mixed numbers: 1. Add or subtract the fractions. 2. Then add or subtract the whole numbers. 3. Rename and simplify if necessary.

Find 2}1} 1 4}1}. 3

4

Estimate 2 1 4 5 6 The LCM of 3 and 4 is 12.

Rename the fractions.

Add the fractions.

2}4}

2}1} 3 }4}

3 4 1 4}1} 3 }3} 4 3 }}}}

2}4}

12 1 4}3} 12

→

Add the whole numbers.

12 1 4}3} 12 }} 7 }} 12

→

}}

2}4}

12 1 4}3} 12 }} 6}7} 12

→

2}1} 1 4}1} 5 6}7}. Compared to the estimate, the answer is reasonable. 3

12

4

Find 6}1} 2 2}1}. 2

3

Estimate 6}1} 2 2 5 4}1} 2 2 The LCM of 2 and 3 is 6.

Rename the fractions.

Subtract the fractions.

6}3}

6}1} 3 }3}

2 3 1 2 2}} 3 }2} 3 2 }}}}

6}3}

6 2 2}2} 6

→

Subtract the whole numbers.

6 2 2}2} 6 }} 1 }} 6

→

}}

6}3}

6 2 2}2} 6 }} 4}1} 6

→

6}1} 2 2}1} 5 4}1}. Compared to the estimate, the answer is reasonable. 2

3

6

Add or subtract. Write in simplest form. 1.

3}2}

3 2 2}1} 3

}}

5. 3}2} 2 1}1} 3

2


2.

4}3}

3.

4 1 1}3} 4

}}

5}1}

6}7}

4.

2 1 4}1} 3

8 2 3}1} 2

}}

6. 4}2} 1 2}1} 3

}}

7. 5}1} 2 2}1}

4

3

297

4


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Adding and Subtracting Mixed Numbers Add or subtract. Write in simplest form. 1.

2}1}

2.

4 1 3}3} 4

}}

4.

4}5}

3.

6 2 3}1} 6

}}

2}3}

5.

7 1 4}2} 7

}}

4

2

12 2 1}1} 12

}}

6}2}

6.

3 1 3}4} 9

}}

7. 9}3} 2 7}1}

8}5}

8}7}

12 2 5}5} 12

}}

8. 2}1} 1 5}7} 8

9. 1}2} 1 4}8}

8

3

9

10. 10}3} 2 2}1}

11. 6}5} 1 }3}

12. 9}4} 1 2}2}

13. 5}2} 2 }1}

14. 8}1} 2 5}3}

15. 4}3} 1 9}1}

17. 5}8} 2 3}1}

18. 8}3} 1 6}2}

5

3

2

6

2

7 11 16. 7} } 2 3}} 12

6

12

9

8

5

10

5

6

4

3

3

5

Evaluate each expression if a 5 1}2}, b 5 }1}, and c 5 3}5}. 3

4

6

19. a 1 b

20. c 1 a

21. c 2 b

22. c 2 a


298


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Solve. Write answers in simplest form. 1. SCHOOL Liwanu spent 2}2} hours on his 5

2. FARMING Mr. Garcia planted 4}7} acres 8 5 of wheat and 1}} acres of corn. How 8

math homework and 1}3} hours on his 5 science homework. How much time did he spend doing math and science homework?

3. COOKING Trey wants to make biscuits and muffins. He needs 2}1} cups of flour 4 for the biscuits and 1}5} cups of flour for 8

much more wheat did he plant than corn?

3}1} acres 4

4. COOKING Gina wants to make cookies. The recipe for blueberry muffins calls for 2}3} cups of flour. The recipe for 4

cornmeal muffins calls for 1}1} cups of

the muffins. How much flour does Trey need altogether?

3

flour. How many more cups of flour would Gina need for blueberry muffins than corn muffins?

1}5} c 12

5. WEIGHT Crystal’s baby brother weighed

6. BOOKS Kyle read 3}5} books and Jan

6 1 read 2}} books. How many more books 3

7}1} pounds at birth. After one month, 2

her brother weighed 8}4} pounds. How

did Kyle read than Jan?

5

much weight did the baby gain?

7. ANIMALS The average length of a

8. RECYCLING The class collected

Rufous hummingbird is 3}1} inches. The 2

9}5} pounds of glass bottles and

average length of a Broad-tailed

6}1} pounds of aluminum cans. How

7

hummingbird is 4}1} inches. How much

2

many pounds of glass and aluminum did the class collect in all?

2

shorter is the Rufous hummingbird?


299


Lesson 6–5

Adding and Subtracting Mixed Numbers

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Adding and Subtracting Mixed Numbers Pre-Activity Complete the Mini Lab at the top of page 240 in your textbook. Write your answers below. 1. How many whole paper plates can you make?

2. What fraction is represented by the leftover pieces?

3. What is the sum 1}3} 1 2}1}? 4

2

Reading the Lesson 4. What is a mixed number? Give an example.

5. In Example 2 on page 241 in your textbook, the letters LCM are used. What does LCM stand for?

6. How are LCM and LCD related?

Helping You Remember 7. In your own words, summarize how to add or subtract mixed numbers.


300


NAME ________________________________________ DATE ______________ PERIOD _____

Equations with Fractions and Decimals Sometimes an equation involves both fractions and decimals. To solve an equation like this, you probably want to work with numbers in the same form. One method of doing this is to start by expressing the decimals as fractions. The example at the right shows how you might solve the equation m 1 }1} 5 0.6 w.

m 1 }1} 5 0.6 w 3

m 1 }1} 5 }2} 3

←

3

Write 0.6 w as a fraction.

m 5 }2} 2 }1} 3

3

m 5 }1} 3

3

Name the number that is a solution of the given equation. 1. z 5 }1} 1 0.375; }1}, }3}, }1}, }3}

2. 0.75 2 }3} 5 b; 0, }1}, 1, 1}1}

3. c 1 0.6 5 }4}; }1}, }3}, 1}1}, 1}2}

4. 0.6 w 5 j 2 }1}; }1}, }2}, 1, 1}1}

5. }1} 1 r 5 0.75; }1}, }1}, }3}, 1

6. d 2 0.1 5 }7}; }1}, }3}, }4}, }9}

8

8 8 2 4

5 5 5

4

5

4 2 4

5

4

4

3 3 3

4

3

10 2 5 5 10

Solve each equation. If the solution is a fraction or a mixed number, be sure to express it in simplest form. 7. }2} 1 0.4 5 k

8. s 5 }7} 2 0.125

5

8

9. 0.6 w 5 n 2 }2}

10. t 1 0.2 5 }4}

3

5

11. 0.375 1 g 5 }5}

12. y 2 0.25 5 }3}

13. 0.8 2 }1} 5 x

14. q 1 0.125 5 }5}

8

4

5

8

15. w 5 }1} 1 0.375 1 }5}

16. 0.7 1 }1} 2 0.3 5 a

17. p 1 }1} 5 0.8 2 }3}

18. k 2 0.875 5 0.375 1 }1}

8

5


8

5

10

8

301


Lesson 6–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Subtracting Mixed Numbers with Renaming Sometimes it is necessary to rename the fraction part of a mixed number as an improper fraction before you can subtract.

Find 5 2 2}1}. 4

Write the problem.

Rename 5 as 4}4}.

Subtract.

4

4}4}

→

5 22}1} 4 }}

→

4}4}

→

4 22}1} 4

4 22}1} 4 }} 2}3} 4

→

}}

So, 5 2 2}1} 5 2}3}. 4

←

Rename 5 as 4 44 .

1

Then cross out 2 4 .

4

Find 6}1} 2 2}3}. 2

Write the problem.

The LCM of 2 and 4 is 4.

6}1}

6}2}

→

2 22}3} 4

4 22}3} 4

→

}}

4

Since }3} is greater than 4 2 2 6 }}, rename 6}} as 5}}. 4

4

→

5}6}

4 22}3} 4

→

}}

Subtract.

4

→ →

}}

So, 6}1} 2 2}3} is 3}3} . 2

4

5}6}

4 22}3} 4 }} 3}3} 4

4

Subtract. Write in simplest form. 6

1.

5

2.

21}1} 3

3.

23}2} 9

}}

}}

6. 8}3} 2 3}5}

9. 5}1} 2 1}5}

10. 9}1} 2 4}3}

6

3

6


8

2

4.

3 22}2} 3

}}

5. 5}1} 2 3}2} 3

6}1}

8

4

5

11. 8}1} 2 }7}

302

6 21}1} 3

}}

7. 12 2 1}2}

2

4}1}

8

8. 7}1} 2 3}5} 2

6

12. 8}1} 2 6}5} 3

6


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Subtracting Mixed Numbers with Renaming Subtract. Write in simplest form. 4}5}

2.

7 21}6} 7

}}

4 23}1} 3 }}

5 5. 10}9}

1 6. 11}4}

22}2} 3 }}

25}3} 8 }}

2 9. 12}5}

10. 10 25}1} 4 }}

24}3} 4 }}

1 13. 13}2}

14.

27}4} 5 }}

8}1}

3 22}5} 9

3.

7}1}

4.

6 23}5} 6

}}

7.

3}1}

1 8. 15}3}

}}

26}1} 2 }}

4 21}5} 8

12.

23}3} 4 }}

}}

9}7}

25}7} 11 }}

}}

8

18. 4}1} 2 1}1}

19. 7 2 2}3}

20. 7}1} 2 6}5}

21. 6 2 5}5}

22. 8}3} 2 2}1}

8

6


2

4

6

10

303

5 27}9} 10

16. 12

10 26}4} 5

5

9}2}

}}

17. 5}1} 2 }5} 2

5 22}7} 10

}}

5 11. 12}8}

15.

6}1}

2


Lesson X–6 6–6

1.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Subtracting Mixed Numbers with Renaming Solve. Write in simplest form. 1. EXERCISE Seth has already walked 5 3 }} miles. It takes 1}} miles to get to 8 8

2. COOKING Aviva needs fresh lemon juice to make cheesecake. She bought 2 lemons but needed only 1}1} lemons

school. How much further does he have to go?

4

for the amount of juice she needs. How much lemon does she have left over?

3 }} of a lemon 4

3. WORK In 2000, 17 million workdays were lost due to strikes and labor disputes. In 2001, there were only

4. TRAVEL It usually takes Amalie 1}3} 4

hours to get to her aunt’s house. Due to Thanksgiving traffic, this year it took

1}1} million days lost. How many more

3}1} hours. How much longer did it take

5

3

workdays were lost in 2000?

5. CARS A 2002 SUV can accelerate from

this year?

6. SCULPTURE Jose has 8}1} cups of Plaster 2

59 0 to 60 mph in 10} } seconds. A sports

of Paris powder. If Jose uses 5}3} cups

86 car takes 9} } seconds to get from 0

for a sculpture, how much plaster will he have left?

100

5

100

to 60 mph. How much faster does the sports car get to 60 mph?


2}9} c 10

304


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Subtracting Mixed Numbers with Renaming Pre-Activity Read the introduction at the top of page 244 in your textbook. Write your answers below. 1. Which sport’s ball has the greater weight?

Lesson X–6 6–6

2. Explain how you would find the difference between the greatest weights allowed for a softball and a baseball.

Reading the Lesson 3. Look at Example 1 in the middle of page 244 in your textbook. What is renamed? Why is it necessary to do this renaming?

4. In Example 2 at the bottom of page 244, both fractions have a common denominator. Why is it necessary to rename 4}1}? Explain what happened 3

in the renaming.

Helping You Remember 5. Explain why renaming is sometimes necessary when subtracting mixed numbers.


305


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment The Stock Market When you buy stock in a company, you become a part owner in that company. You buy stock in units called shares. The stock report that you see in a newspaper lists high and low prices per share of stock. Historically, stock prices were given as whole dollars or as halves, fourths, or eighths of a dollar. Find the difference between the high and low prices for each stock listed. The difference for Stock A is shown as an example. High

Low

Stock

Difference

49}3} 8

32}1}

A

49}3} 2 32}1} 5 17}1}

1.

23}3} 4

12}5}

B

2.

44}3} 8

26}3}

C

3.

45}1} 4

36}1}

D

4.

51}1} 4

29}3}

E

5.

67

38}1}

F

6.

45

26}3}

G

7.

75}3} 4

46}7}

H

8.

43}1}

25}1}

I

9.

39}3}

28

J

10.

78

43}1}

K

2 8

4 8 4 2 8 4 8 8 8

8

8

4

8

11. What stock listed above had the greatest difference between high and low prices? the least difference? 12. What would be the price of Stock H if it rose 2}1} dollars above the high? 2


306



Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860070-7 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03







Chapter 7 Assessment Chapter 7 Test, Form 1 ..........................357–358 Chapter 7 Test, Form 2A ........................359–360 Chapter 7 Test, Form 2B ........................361–362 Chapter 7 Test, Form 2C........................363–364 Chapter 7 Test, Form 2D........................365–366 Chapter 7 Test, Form 3 ..........................367–368 Chapter 7 Extended Response Assessment .369 Chapter 7 Vocabulary Test/Review.................370 Chapter 7 Quizzes 1 & 2................................371 Chapter 7 Quizzes 3 & 4................................372 Chapter 7 Mid-Chapter Test ...........................373 Chapter 7 Cumulative Review........................374 Chapter 7 Standardized Test Practice....375–376 Unit 3 Test/Review..................................377–378 First Semester Test ................................379–382 Standardized Test Practice Student Recording Sheet ............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A30

iii



Practice: Skills











iv





Enrichment













v

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics This is an alphabetical list of new vocabulary terms you will learn in Chapter 7. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add this page to your math study notebook to review vocabulary at the end of the chapter.

Vocabulary Term

Found on Page


compatible [kuhm-PA-tuh-buhl] numbers

reciprocal [rih-SIH-pruh-kuhl]

sequence


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: en measuring distances We often use fractions, especially wh fractions helps us solve and amounts. Knowing how to use miles a jogger runs everyday problems such as how many needed for a bread recipe. around a track or how much flour is viding Fractions, your In Chapter 7, Multiplying and Di ts, multiply fractions and child will learn how to estimate produc mixed numbers, and find mixed numbers, divide fractions and of this chapter, your child patterns and sequences. In the study oom assigments and will complete a variety of daily classr pter project . activities and possibly produce a cha it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that relates the math we an activity you can do with your chi real world. You may also will be learning in Chapter 7 to the Tools for self-check wish to log on to the Online Study Guide Pages, and other quizzes, Parent and Student Study you have any questions or study help at www.msmath1.net. If school. comments, feel free to contact me at Sincerely,



ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Fractions and Recipes Have a family member help you find a recipe. You can find recipes in cookbooks, the newspaper, or maybe someone’s memory. In the space below, write the amount of each ingredient of the recipe.

Suppose you want to triple the recipe. Calculate how much of each ingredient you will need to use.

Suppose you want to cut the recipe in half. Calculate how much of each ingredient you will need to use.


x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Estimating Products Numbers that are easy to divide mentally are called compatible numbers. One way to estimate the products of fractions is to use compatible numbers.

Estimate }2} 3 8.

3 2 Estimate }} 3 8. Make it easier by finding }1} 3 8 first. 3 3 1 Change 8 to 9 since 3 and 9 are compatible numbers. }} 3 9 5 ? 3 1 1 }} of 9, or 9 divided by 3, is 3. }} 3 9 5 3 3 3 2 Since }1} of 9 is 3, }2} of 9 is 2 3 3 or 6. }} 3 9 5 6 3 3 3 2 So, }} 3 8 is about 6. 3

Lesson 7–1

1 You can estimate the product of fractions by rounding to 0, }}, or 1. 2

Estimate }1} 3 }5}. 3

6

1 5 1 1 }} 3 }} → }} 3 1 5 }}. 3 6 2 2 1 5 So, }} 3 }} is about }1}. 3 6 2

You can estimate the product of mixed numbers by rounding to the next whole number.

Estimate 3}1} 3 5}7}. 4

8

Since 3}1} rounds to 3 and 5}7} rounds to 6, 3}1} 3 5}7} → 3 3 6 5 18. 4 1 So, 3}} 3 5}7} is about 18. 4 8

8

4

8

1–12. Sample answers given. Estimate each product. Show how you found your estimate. 1. }1} 3 24

2. }7} 3 }3}

5. }2} 3 19

6. 2}4} 3 6}1}

5

8

11 6 9. } } 3 }} 12

7


8

5

5

10. }3} 3 17 8

3. 7}2} 3 5}3}

4. }4} 3 20

7. }1} 3 }1}

8. 3}7} 3 10}1}

7

12

4

12

9

327

10

8

11. 4 }7} 3 2}9} 8

7

10

11 1 12. } } 3 }} 12

3


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Estimating Products Estimate each product. 1. }1} 3 26

10 1 2. } } 3 }}

3. }1} 3 17

4. }6} 3 }1}

5. }1} 3 }4}

6. 2}4} 3 5}1}

7. }3} 3 29

8. }5} 3 }2}

9. 6}3} 3 4}7}

5

7

11

8

2

11

3

7

9

6

5

7

4

9

10

10. }3} 3 }6}

11. }7} 3 }8}

12. 4}1} 3 3}7}

13. 9}1} 3 }1}

14. }2} 3 26

15. }5} 3 41

16. }7} 3 30

17. 7}2} 3 9}3}

18. }3} 3 35

19. }5} 3 }1}

20. }1} 3 }5}

21. 3}1} 3 7}7}

22. }2} 3 35

23. 6}7} 3 8}5}

5

7

8

8

3

3

9

8

9

9

3

12

7

8

8

4

9

12

3

8

4

12

8

24. }6} 3 32 11

25. Estimate }4} of 49. 5

26. Estimate the product of 2}4} and 16}1}. 11


5

328


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Estimating Products Estimate by using rounding or compatible numbers. Show how you found your estimates. Grams of Saturated Fat per Tablespoon 4 }} 5 4 1}} 5 7}1} 5 3}1} 5

Safflower Oil Olive Oil Butter Cream Cheese

1. Jenny is making muffins. The recipe calls for 4 tablespoons of oil. If she uses safflower oil, about how many grams of saturated fat would she be adding to the muffin batter?

2. Curtis spread 2 tablespoons of butter on his slice of bread. About how many grams of saturated fat did Curtis add to the slice of bread?

3. Rubin is fond of bagels and cream

4. WATER Marcia is making a habit of drinking at least 7 cups of water a day. About how many cups of water did she

cheese. He spread 5}2} tablespoons of 3

cream cheese on his bagel and ate the bagel. About how many grams of saturated fat did Rubin eat by eating the cream cheese?

5. TRAVEL Seth has been driving for 4}3} hours at 62 miles per hour. About 4

7}1} 3 2 Æ 7 3 2 5 14 5

drink if she drank }3} the number of 4

cups she wanted to drink? about

6 c; }3} 3 7 Æ }3} 3 8 5 6 4

4

6. MAIL The U.S. Postal Service delivers about 199 billion pieces of mail each year. Of this mail, }4} is sent by big

how many miles has he driven?

5

commercial users. About how many pieces of mail are sent by big commercial users each year?

199 3 }4} Æ 200 3 }4} 5 160 5


329

5


Lesson 7–1

FOOD For Exercises 1–3, use the table. The table lists the grams of saturated fat per tablespoon of some common fats.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Estimating Products Pre-Activity Complete the activity at the top of page 256 in your textbook. Write your answers below. 1. For the shots attempted, what is the nearest multiple of 3? 2. How many basketballs should be added to reflect the nearest multiple of 3? 3. Divide the basketballs into three groups each having the same number. How many basketballs are in each group? 4. About how many field goals did Kayla make?

Reading the Lesson For Exercises 5 and 6, look at Example 1 on page 256. The statement 1 1 }} 3 13 → }} 3 12 is read one-fourth of 13 is changed to one-fourth of 12. 4

4

5. What does the → mean? 6. Why is 13 changed to 12? 7. Three combinations of fractions, whole numbers, and mixed numbers are talked about in this lesson. Complete the table to summarize the information in the lesson. Kind of Product Kind of Product How to Estimate How to Estimate fraction fraction and and whole whole number number Use compatible numbers, numbers that are easy to divide mentally. two fractions two fractions Round each fraction to 0, }1}, or 1 2 two mixed numbers two mixed numbers Round each mixed number to the nearest whole number.

Helping You Remember 8. In this lesson, compatible numbers are defined as numbers that are easy to divide mentally. Look up the word compatible in a dictionary. How could you relate one of the meanings you find in the dictionary to numbers like 4 and 12 (rather than 4 and 13) and 4 and 24 (rather than 4 and 23)?


330


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Shopping with Compatible Numbers Suppose that you are meeting a friend for lunch and come across the sale advertised at the right. For weeks, you have wanted to buy a set of CDs that is regularly priced at $31.98. Here is how compatible numbers can help you find the sale price of the set. • }1} of $31.98 is about }1} of $32, or $8. 4 4 • “}1} off” means that you pay 1 – }1}, or }3}. 4

4

One-Day Discounts

ff 1/ 4 O ry E ve C D in S t oc k

4

• Since }1} of $32 5 $8, }3} of $32 5 $24. 4

gs n i v Sa iot R

4

1/3 Of f

Each exercise gives the regular price of one or more items. Use the information at the right to estimate the sale price.

Every VIDEO CASS ETTE in Stoc k

1. video cassette: $8.95 2. CD: $14.95 1/2 Off

3. headphones: $10.98

ALL HEADPHONES TRUE-CELL BATTERIES

4. three packs of TRUE-CELL batteries; $5.98 per pack $2.00 OFF ALL DVDs

5. one CD: $20.95 one video cassette: $11.95 6. one set of headphones: $15.79 two video cassettes: $4.98 and $6.98

7. one CD: $16.95 one set of headphones: $14.50 one DVD: $19.98 8. two CDs: $14.95 and $12.95 one video cassette: $7.98 two DVDs: $14.95 each


331


Lesson 7–1

The sale price is about $24.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Multiplying Fractions Type of Product

What To Do

Example

two fractions

Multiply the numerators. Then multiply the denominators.

fraction and a whole number

Rename the whole number as an improper fraction. Multiply the numerators. Then multiply the denominators.

Find }2} 3 }3}. 5

3 3 7 6 18 }} 3 6 5 }} 3 }} 5 }} 5 1}} 11 11 11 1 11

Estimate: }1} 3 1 5 }1} 2

4

2 3 233 }} 3 }} 5 }} 5 4 534 5 }6} or }3} 20 10

2

Multiply the numerators. Multiply the denominators. Simplify. Compare to the estimate.

Find }4} 3 8.

Estimate: }1} 3 8 5 4 2

9

4 4 8 }} 3 8 5 }} 3 }} 9 9 1

Write 8 as }8}. 1

438 5} }

Multiply.

931

32 5 5} } or 3}} 9

8 2 4 234 }} 3 }} 5 }} 5 }} 335 15 3 5

Simplify. Compare to the estimate.

9

Find }2} 3 }3}. 5

Estimate: }1} 3 }1} 5 }1} 2

8

2

4

1

2 3 233 @ }} 3 }} 5 } 5 8 538 @

Divide both the numerator and denominator by the common factor, 2.

4

5 }3}


20

Multiply. Write in simplest form. 1. }1} 3 }5}

2. }3} 3 }3} 4

3. 4 3 }1}

4. }5} 3 2

5. }3} 3 10

6. }2} 3 }3}

7. }1} 3 }1}

8. }2} 3 }1}

4

6

5


7

3

8

5

7

332

7

12

9

2


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Multiplying Fractions Multiply. Write in simplest form. 1. }3} 3 }1}

2. }1} 3 }2}

3. }1} 3 6

4. }2} 3 }3} 7

5. }3} 3 10

6. }1} 3 }3}

7. }2} 3 3

8. }9} 3 }4}

9. }7} 3 }2}

5

2

3

5

3

8

9

10

6

5

8

5

9

10. 11 3 }3}

11. }5} 3 }1}

12. }4} 3 }2}

13. }7} 3 }6}

14. 16 3 }5}

15. }4} 3 }1}

10 16. }1} 3 } } 11

17. }5} 3 }3}

18. }1} 3 }4}

19. 21 3 }4}

20. }5} 3 18

21. }5} 3 }8}

4

12

5

6

11

4

9

9

12

12

7

8

10

9

6

3

8

7

9

For Exercises 22–24, evaluate each expression if x 5 4, y 5 }2}, and 3

z 5 }1}. 4 22. }3} x 8

23. xz

24. 3x

25. xy

26. 9y

27. }1}x

28. yz

29. 8z

30. xyz

3

31. If a 5 }6}, what is }2}a? 7

3

32. Evaluate st if s 5 }3} and t 5 24. 8


333


Lesson 7–2

4

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Multiplying Fractions COOKING For Exercises 1 and 2, use the recipe for chocolate frosting.

Chocolate Frosting Recipe 1 }} cup butter 3

2 ounces melted unsweetened chocolate 2 cups powdered sugar 1 }} teaspoon vanilla 2

2 tablespoons milk

1. Georgia wants to cut the recipe for chocolate frosting in half for a small cake that she’s making. How much of each ingredient will she need?

2. Suppose Georgia wanted to double the recipe; what would the measurements be for each ingredient?

3. COMPUTERS }1} of today’s college 5 students began using computers between the ages of 5 and 8. If a college has 3,500 students, how many of the students began using computers between the ages of 5 and 8?

4. EXERCISE A paper published in a medical journal reported that about

5. ANIMALS Catherine walks her dog }3} 4 mile every day. How far does she walk

6. MUSIC If you practice a musical

11 }} of girls ages 16 to 17 do not exercise 25

at all. The entire study consisted of about 2,500 girls. About how many did not exercise?

instrument each day for }2} of an hour, 3

each week?

how many hours of practice would you get in each week?


334


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Multiplying Fractions Pre-Activity Complete the activity at the top of page 261 in your textbook. Write your answers below. 1. What part of Earth’s surface is covered by the Pacific Ocean?

2. What is the relationship between the numerators and denominators of the factors and the numerator and denominator of the product?

Reading the Lesson

3. What must the numerator and denominator have in order to simplify before you multiply?

4. Why is it helpful to simplify before you multiply?

Helping You Remember 5. Work with a partner. Look at each example on pages 261 and 262 in your textbook. Use a piece of paper to cover up the words that are beside the equations. Explain to your partner in your own words what is happening in each step. Then uncover the words and check.


335


Lesson 7–2

For Exercises 3 and 4, look at Example 3 and the sentence before it on page 262 in your textbook.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Word Sums Can one sixth plus one third equal one? It is possible if the fractions are fractions of words! Here is an example. Find the last one sixth of the word TOMATO: O Find the middle one third of the word FINEST: NE Add the letters O 1 NE 5 ONE!

Match each word sum in the first column with its definition in the second column. 1. the first one fourth of CHECKERS 1 the last one half of AFFAIR

a. purchased

2. the first one half of CLOSET 1 the last one fourth of DOWNTOWN

b. clock sound

3. the first one fifth of BACKGROUND 1 the middle one third of WONDER

c. capital of Georgia

4. the middle one third of ADVENTURE 1 the last one third of LEADER

d. to come into a room

5. the middle one third of BUGLER 1 the last one fourth of SATISFACTORY

e. where we live

6. the first two thirds of TICKET 1 the last four fifths of STOCK

f. honor

7. the middle one half of SEAT 1 the last one half of FOURTH

g. circus act

8. the first two fifths of BOARD 1 the middle one half of DAUGHTER

h. place to sit

9. the first one half of MARBLE 1 the last three fifths of SUGAR 1 the last one fourth of CLARINET

i. woman’s name

10. the last two thirds of EAT 1 the first one third of LANDSLIDE 1 the first one fifth of TABLESPOON

j. music makers


336


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Multiplying Mixed Numbers To multiply mixed numbers, write the mixed numbers as improper fractions, and then multiply as with fractions.

Find 2}1} 3 1}2}. 4

2}1} 3 1}2} 5 }9} 3 }5} 4

3

4

Estimate: 2 3 2 5 4.

3

Write mixed numbers as improper fractions.

3

3

935 @ 5 }

Divide the numerator and denominator by their common factor, 3.

43@ 3 1

15 3 5} } or 3}} 4 4


If a 5 1}1} and b 5 2}1}, what is the value of ab? 3

ab 5 1}1} 3 2}1} 3

4

5 }4} 3 }9} 3 4

4

Replace a with 1}1} and b with 2}1}. 3

4


1

3

1

1

9 @ @ 4 5 } 3 } @ 4 3 @

Divide the numerator and denominator by their common factors, 3 and 4.

5 }3} or 3

Simplify.

1

Multiply. Write in simplest form. 2. 1}1} 3 }3}

3. 3 3 1}3}

5. 9 3 1}1}

6. 2}4} 3 }4}

7. 2}1} 3 1}1}

3

3

5

6

9

9. 8 3 1}1}

4

11

10. }3} 3 2}1}

4

8

2

4. }2} 3 3}1}

5

2

3

3

11. 4 3 1}1} 8

2

8. 1}1} 3 }3} 4

5

12. 1}1} 3 3 9

13. Evaluate 5x if x 5 1}2}. 3

14. If t 5 2}3}, what is 4t? 8


337


Lesson 7–3

1. }1} 3 1}1}

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Multiplying Mixed Numbers Multiply. Write in simplest form. 1. }1} 3 1}1} 4

2. 2}1} 3 }3}

3. }3} 3 3}1}

4. 6}1} 3 }1}

5. 1}3} 3 3}2}

6. }5} 3 4}1}

7. }4} 3 3}1}

8. 1}3} 3 2}2}

9. 4}1} 3 }9}

10. 3}1} 3 2}1}

3

4

2

3

5

7

5

3

7

9

6

5

2

5

8

10

7

3

4

11. }8} 3 5}1}

12. 2}5} 3 6

13. 3}3} 3 2}4}

14. }5} 3 4}3}

15. 20 3 1}2}

16. 2}4} 3 }6}

17. 5}3} 3 1}1}

18. 14 3 2}5}

9

7

4

8

5

7

5

4

8

9

11

11

7

For Exercises 19–24, evaluate each expression if r 5 1}2}, s 5 2}1}, and 3 5 t 5 }3}. 4

19. 4t

20. st

21. }1}r

22. rs

23. }1}s

24. rt

2

11

25. Evaluate }2}m if m 5 5}1}. 3

6

26. What is ab if a 5 1}5} and b 5 }7}? 11


8

338


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Multiplying Mixed Numbers FOOD For Exercises 1–3, use the table. The table shows Keith’s food

options for a 7-day outdoor survival course. Food Options for 7-day Outdoor Survival Course 1 plastic jar 5 4}3} cups

peanut butter

5 2 14}} cups 3 6}1} cups 6 8 boxes 5 16}1} cups 4 1 3}} cups 3 1 box 5 8}4} cups 5

dried noodles/rice dried fruit/nuts concentrated juice boxes beef jerky powdered milk

5 packages 5 15}2} cups

dehydrated soup

3

4 cans 5 5}3} cups

canned tuna/meat

5

1. Keith wants to divide his tuna over the seven-day course. How many cups of tuna meat can Keith plan on

2. Keith would like to bring enough concentrated juice in order to have 2}1} cups available per day. How much 4

consuming each day?

juice does he need and is 8 boxes of concentrated juice enough?

15}3} c; yes 4

4. MEASUREMENT Bill wants to put a large mural on a wall that is 9}1} feet long and 8}1} feet wide. Find 3

8

the area of the wall. If the mural is 100 square feet, will it fit on the wall?

75}5} ft2; no 6

5. PAINTING Pam is mixing 3}1} batches of 5

6. COOKING To make a batch of fruit punch, Steve needs 2}2} cups blackberry

paint. If one batch calls for

3

2}3} tablespoons of detergent to add to

juice. If he wants to make 2}3} batches

4

4

the tempera powder, how many tablespoons of detergent will Pam need?


of punch, how many cups of blackberry juice will he need?

339


Lesson 7–3

3. Six other students have been advised to bring the same menu on the course. How many cups of dried fruits and nuts will the students be bringing all together?

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Multiplying Mixed Numbers Pre-Activity Complete the activity at the top of page 265 in your textbook. Write your answers below. 1. How many miles does Jasmine walk in a week? 2. Write a multiplication sentence that shows the total miles walked in a week. 3. Write the multiplication sentence using improper fractions.

Use a number line and improper fractions to find each product. 4. 2 3 1}1}

5. 2 3 2}1}

3

4

0

1

2

3

0

1

2

3

4

5

6. 3 3 1}3} 4

0

1

2

3

4

5

6

7. Describe how multiplying mixed numbers is similar to multiplying fractions.

Reading the Lesson 8. What is an improper fraction?

9. What is a mixed number?

10. Why is it helpful to write a mixed number as an improper fraction?

Helping You Remember 11. Example 2 on page 266 shows how to multiply mixed numbers. Describe a general process you would use to check if your answer is correct. Trade your description with a partner and follow your partner’s process to check the answer for Example 3. Answer any questions your partner may have about your process.


340


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Mixed Numbers and Mental Math Sometimes you can multiply a whole number and a mixed number in your head. The trick is to think of the mixed number in two parts—the whole number and the fraction. Find each product mentally. Think: }1} of 10

Think: 3 3 10

Example 3}1} 3 10 5 2

2

1

5

1. 7}1} 3 6 5

1

5

2. 4 3 9}1} 5

1

5

3. 4}1} 3 6 5

1

5

4. 5}1} 3 8 5

1

5

5. 153 2}1} 5

1

5

6. 12 3 4}1} 5

1

5

7. 1}2} 3 6 5

1

5

8. 5}3} 3 20 5

1

5

2

2

3 4

5

6

3 4

Now you can use this mental math technique to make better estimates. Here’s how. Estimate the product: 4}1} 3 11}7} 2 9 4}1} 3 11}7} → 4}1} 3 12

Lesson 7–3

2 9 2 1 4}} 3 12 5 4 3 12 1 }1} of 12 2 2

5 48 1 6 5 54

So, 4}1} 3 11}7} is about 54. 2

9

Estimate by rounding only one factor. 9. 6}1} 3 4}2} 2

11

15 1 11. 11} } 3 2}} 16 4 2 6 13. 1}} 3 14}} 3 7


10. 5}1} 3 8}9}

10 3 12. 5}7} 3 4}1} 10 6 2 14. 19}} 3 1}3} 7 4

341


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Dividing Fractions When the product of two numbers is 1, the numbers are called reciprocals.

Find the reciprocal of 8. Since 8 3 }1} 5 1, the reciprocal of 8 is }1}. 8

8

Find the reciprocal of }5}. 9

Since }5} 3 }9} 5 1, the reciprocal of }5} is }9}. 9

5

9

5

You can use reciprocals to divide fractions. To divide by a fraction, multiply by its reciprocal.

Find }2} 4 }4}. 3

2 4 2 5 }} 4 }} 5 }} 3 }} 3 5 3 4

5

Multiply by the reciprocal, }5}. 4

1

2 5 @ 5 } 3 3 } 4 @

Divide 2 and 4 by the GCF, 2.

5 }5}

Multiply numerators and denominators.

2

6

Find the reciprocal of each number. 3. }4}

2. }1}

1. 2

4. }3}

11

6

5

Divide. Write in simplest form. 5. }1} 4 }2}

6. }1} 4 }1}

7. }2} 4 }1}

8. }1} 4 }3}

9. }4} 4 2

10. }4} 4 }1}

11. }5} 4 }5}

12. }9} 4 3

13. }3} 4 }7}

14. }9} 4 9

15. }2} 4 }5}

16. 4 4 }7}

3

5

5

4

12


9

5

10

2

10

3

12

3

342

4

6

8

2

4

10

9


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Dividing Fractions Find the reciprocal of each number. 1. }1}

2. }3}

3. 7

4. }8}

5. 12

6. }9}

7. }5}

8. }3}

2

5

10

11

10

8

Divide. Write in simplest form. 9. }5} 4 }1} 3

10. }9} 4 }1}

11. }1} 4 }3}

12. 8 4 }4} 5

13. }7} 4 }5}

14. }9} 4 }1}

15. }3} 4 9

16. }9} 4 }3}

17. }2} 4 }4}

18. 15 4 }5} 9

19. }6} 4 }3}

20. }1} 4 }5}

21. }5} 4 }5}

10 22. } }45

23. }7} 4 }1}

24. }6} 4 }8}

25. }3} 4 }9}

26. 5 4 }4}

6

8

6

7

12

9

2

10

12

4

5

9

11

11

5

5

10

6

10

7

2

9

11

4

7

12

7

9

Find the value of each expression if x 5 }1}, y 5 }3}, and z 5 }2}. 5

3

27. x 4 y

28. z 4 2

29. y 4 z

30. z 4 x

31. }1} 4 x

32. 5 4 y


3

343


Lesson 7–4

4

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Dividing Fractions 1. PIZZA Norberto has }9} of a pizza. The

2. CARPENTRY Laura wants to cut a board

10

pizza will be divided equally among 6 people. How much will each person get?

into three equal pieces. The board is 5 }} feet long. How long will each piece 8 5

be?

3. PETS Errol uses }1} can of wet dog food

}} ft 24

4. ICE CREAM Julia ate }1} pint of mint

3

2

for his dog, Muddy, each day. How many servings will he get from 5 cans of dog food?

chocolate chip ice cream. Mark ate 3 }} pint of malt ice cream. How many 4

times more ice cream did Mark eat?

1}1} times 2

6. SCHOOL Kirsten has }3} hour left to

5. GARDENING Talia wants to give away 6 bundles of rosemary from her herb

4

finish 5 math problems on the test. How much time does she have to spend on each problem?

garden. If she has }1} pound of rosemary, 2

how much will each bundle weigh?

3 }} h 20

7. FOOD Joe has }1} of a cake he would like 2

8. INTERNET }3} of college students use the

to split among 3 people. What part of the cake will each person get?

4

Internet more than the library. }9} use 100

the library more. How many times more students use the Internet?

8}1} times 3


344


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Dividing Fractions Pre-Activity Complete the Mini Lab at the top of page 272 in your textbook. Write your answers below. 1. How many }1}-pizza servings are there? 2

2. The model shows 4 4 }1}. What is 4 4 }1}? 2

2

Draw a model to find each quotient. 3. 3 4 }1} 4

4. 2 4 }1} 6

5. 4 4 }1} 2

Reading the Lesson 6. What is the definition of reciprocals? 7. Show that }1} 3 3 5 1. 3

8. How do you find the reciprocal of a whole number? How do you find the reciprocal of a fraction?

Helping You Remember 9. Work with a partner. Study the model in Example 3 at the top of page 273. Explain how it shows that }1} is }1} of }3}. 6

4

Lesson 7–4

8


345


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Operations with Fractions and Decimals Sometimes an operation involves both fractions and decimals. To perform the operation, you need to express all the numbers in the same form. Here are two examples. Express the decimal as a fraction.

1 w 5 }1} 4 }1} }} 4 0.3 5 5 3 5 }1} 3 }3} 5 1 5 }3} 5

Express the fraction as a decimal.

3 }} 1 0.115 5 0.75 1 0.115 4

5 0.865

Perform the operation. Express the answer as a fraction or mixed number in simplest form. 1. }5} 4 0.25

2. 0.6 w 4 }7} 9

3. 0.125 3 }4}

4. 1}1} 3 0.3 w

5. 0.8 2 }3}

6. 1}3} 2 0.875

16

5

11

5

8

Perform the operation. Express the answer as a decimal. 7. 0.34 4 }1}

8. }1} 4 0.005

5

9. 0.001 3 }3}

8

10. 6.39 1 }7}

5

11. 9.1 2 }1}

8

12. }3} 1 0.709 1 }2}

4

8

5

13. Kevin is making one recipe that calls for 1}1} pounds of hamburger and 4

another that calls for 2 pounds. In the store, he finds a family pack of hamburger that is labeled 3.75 pounds. Is this more or less than he needs? How much more or less? 14. Daneesha needs 1}1} yards of material to make a jacket and 1}3} yards of 2

4

material to make a skirt. The material costs $7.50 per yard. What is the total cost of the material for the skirt and jacket? Round your answer to the nearest cent.


346


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention To divide mixed numbers, express each mixed number as an improper fraction. Then divide as with fractions.

Find 2}2} 4 1}1}. 3

Estimate: 3 4 1 5 3

5

2}2} 4 1}1} 5 }8} 4 }6} 3

5


3 5 5 }8} 3 }5} 3 6


4

835 @ 5 }

Divide 8 and 6 by the GCF, 2.

336 @ 3

20 2 5} } or 2}} 9


9

Find the value of s 4 t if s 5 1}2} and t 5 }3}. 3

s 4 t5 5 5 5

1}2} 4 }3} 3 4 5 3 }} 4 }} 3 4 5 4 }} 3 }} 3 3 20 2 }} or 2}} 9 9

4

Replace s with 1}2} and t with }3}. 3

4

Write 1}2} as an improper fraction. 3


Simplify.

Divide. Write in simplest form. 1. 2}1} 4 }4}

2. 1}2} 4 1}1} 4

3. 5 4 1}3} 7

4. 2}1} 4 }7}

5. 5}2} 4 }9}

6. 7}1} 4 1}2}

7. 3}5} 4 2

8. 2}1} 4 }2}

11. 1}8} 4 5

12. }3} 4 2}1}

2

5

5

3

10

9. 9 4 1}1}

2

3

10. }4} 4 2}6}

9

5

7

6

9

3

4

8

9

7

4

13. If x 5 1}1} and y 5 3, what is x 4 y? 4

14. Evaluate 18 4 t if t 5 }9}. 11


347


Lesson 7–5

Dividing Mixed Numbers

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Dividing Mixed Numbers Divide. Write in simplest form. 1. 2}5} 4 6}4}

2. 4}6} 4 3}2}

3. 31}2} 4 7}3}

4. 1}1} 4 3

5. 6 4 2}2} 5

6. 1}3} 4 }3}

8. 3}1} 4 7

9. 6}2} 4 }4}

6

5

7

3

7. 2}1} 4 4}2} 2

7

5

3

4

9

3

5

4

5

10. 1}2} 4 1}5}

11. 6}3} 4 1}7}

12. }7} 4 2}5}

13. 3}5} 4 1}1}

14. 1}7} 4 }4}

15. 5 4 8}3}

16. 2}2} 4 1}1}

17. 3}1} 4 1}7}

18. 6}1} 4 3}1}

9

6

9

6

4

3

20

9

3

9

5

8

10

4

9

6

3

Evaluate each expression if a 5 1}3}, b 5 4}5}, and c 5 3}3}. 8

19. b 4 a

7

10

20. a 4 c

21. c 4 b

For Exercises 22–24, evaluate each expression if a 5 3}3}, b 5 1}1}, and 4 2 c 5 4}1}. 8

22. a 4 b

23. c 4 a

24. b 4 c

25. What is the value of r 4 t if r 5 4}1} and t 5 2}3}? 3

5

26. If x 5 4}2} what is 1}1} 4 x? 3


6

348


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 2. FOOD DeLila has 4}1} pies to divide

1. VIDEOTAPES Lyle is putting his videotapes on a shelf. The shelf is 12 inches long. If each videotape is

2

equally among 9 people. How much will

1 2

each person get? }} of a pie

1}1} inches wide, how many videotapes 2 can he put side-by-side on the shelf?

3. GARDENING Maurice mows lawns on Saturday. Last week it took him 5}1}

4. COOKING Chris is cutting a roll of cookie dough into pieces that are

2

1 1 }} inch thick. If the roll is 10}} inches 2 2

hours to finish. This week it took only 5 hours. How many times longer did it

long, how many pieces can he make?

take last week than this week?

5. SPORTS Tanya Streeter holds the world record for free-diving in the ocean. She

6. GARDENING Catherine got 9}3} pounds 8

of cherries from her tree this year. Last

dove 525 feet in 3}1} minutes. How many 2 feet per minute did she dive?

year she only got 6}1} pounds. How 4 many times more pounds did she get

1 2

this year than last year? 1}} times

7. SEWING Jeanne has 3}3} yards of fabric. 5

She needs 1}4} yards to make a pair of 5 pants. How many pairs of pants can she make?


8. EXERCISE Del Ray can run 20}1} miles in 2

2}1} hours. How many miles per hour 4

1 9

can he run? 9}} mi per h

349


Lesson 7–5

Dividing Mixed Numbers

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Dividing Mixed Numbers Pre-Activity Complete the activity at the top of page 276 in your textbook. Write your answers below. 1. To the nearest yard, how long is each piece? 2. To the nearest yard, how long is the fabric on the bolt? 3. About how many pieces can you cut?

Reading the Lesson 4. Describe how to write a mixed number as an improper fraction.

5. Describe what is happening at each step below. If you need help, use Examples 1 and 2 on page 276 as a guide. Find the value of a 4 b if a 5 5}5} and b 5 2}1}. 8

a 4 b 5 5}5} 4 2}1} 8

4

4

45 9 5} } 4 }} 8

4

45 4 5} } 3 }} 8

9

5

1

2

1

@ 45 4 @ 5 } 3 } 8 @ @ 9

5 }5} or 2}1} 2

2

Helping You Remember 6. As an experiment, try to find 4}1} 4 2}1} in a different way from the way 4

2

you learned in this lesson. First, divide the whole numbers. Next divide the fractions. Then, put together the whole number you found and the fraction you found to make a mixed number. Now find 4}1} 4 2}1} in the 4

2

way the lesson shows how to divide mixed numbers. What two important steps must you do in order when dividing mixed numbers?


350


NAME ________________________________________ DATE ______________ PERIOD _____

Modeling Division of Fractions on a Ruler How many half-inch lengths are in 4 inches? When you look at a ruler, it is easy to see that the answer is 8. 1 2

1 2

INCHES

1 2

1 2

1

1 2

1 2

2

1 2

1 2

3

4

5

So, this diagram is also a model for the division 4 4 }1} 5 8. 2

Write the division that is modeled in each diagram. 1. INCHES

1

2

3

4

5

INCHES

1

2

3

4

5

INCHES

1

2

3

4

5

INCHES

1

2

3

4

5

2.

3.

4.

5. Use the ruler below. Create a model for the division 4}2} 4 }2} 5 7. 3

INCHES

1


2

3

4

351

3

5


Lesson 7–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Sequences A sequence is a list of numbers in a specific order that follows a pattern or rule.

Describe the pattern in the sequence 41, 37, 33, 29, …. Then find the next two numbers in the sequence. 41, 37, 33, 29, …

NNN

24 24 24

In this sequence, 4 is subtracted from each number. The next two numbers are 29 2 4, or 25, and 25 2 4, or 21. Describe the pattern in the sequence 243, 81, 27, 9, …. Then find the next two numbers in the sequence. 243,

81,

27,

9, …

N N1 N1

3 }1} 3

3 }} 3

3 }} 3

In this sequence, each number is multiplied by }1}.

3 1 The next two numbers are 9 3 }}, or 3, and 3 3 }1}, or 1. 3 3

Describe each pattern. Then find the next two numbers in the sequence. 1. 72, 77, 82, 87, …

2. 3, 6, 12, 24, …

3. 32, 29, 26, 23, …

4. 14}1}, 14, 13}1}, 13, 12}1}, …

5. 1, }1}, }1}, }1}, …

6. 3, 4}1}, 6, 7}1}, …

2 4 8

2

2

2

2

2

Find the missing number in each sequence. 7. ____, 75, 50, 25, …


8. 17}1}, 18}2}, 20, ____, 22}2}, … 3

352

3

3


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Sequences

1. 6, 10, 14, 18, …

2. 31, 26, 21, 16, …

3. 12, 24, 48, 96, …

4. 16, 8, 4, 2, …

5. 108, 36, 12, 4, …

6. 1, 1}1}, 1}2}, 1}3}, …

7. }1}, }1}, }1}, }1}, …

8. 43, 38, 33, 28, …

64 32 16 8

9. 63, 56, 49, 42, …

5

5

5

10. 2, 15, 28, 41, …

11. 5, 20, 35, 50, …

12. 1, 1}2}, 2}1}, 3, …

13. 4, 12, 36, 108, …

14. 1, 5, 25, 125, …

3

3

Find the missing number in each sequence. 15. 54,

17.

? , 42, 36, …

? , 12, 48, 192, …

19. 16, 4,

? , }1}, … 4


16. }1}, }1}, 6 3

18. }1}, }1}, 81 27

20.

353

? , }2}, … 3

? , }1}, … 3

? , 1, 5, 25, …


Lesson 7–6

Describe each pattern. Then find the next two numbers in the sequence.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Sequences 1. SPORTS Thomas is getting in shape for track. He is starting with a 2 mile run

2. WATER Kevin is pumping water from a small pond into a water tank. At 9 A.M. the water level was 2 inches. At 11 A.M.

and will increase the run by }1} mile 2

it was 3}1} inches. At 1 P.M. it was

each week for 4 weeks. What will his distance be for the second, third, and

2

5 inches. If the pattern continues, what will the level be at 3 P.M.? Explain.

fourth weeks?

6}1} in.; The tank is filling at a rate 2 of 0.75 in. per h.

3. BACKPACKING A group of backpackers started with 5 pounds of cheese. On the

4. FROGS The frog population in a Japanese garden is growing at an alarming rate. The counts taken show there were 14 frogs to start, then 28, then 56, then 112. If they continue to grow at this rate, what will the next count be? Explain.

second day they had only 2}1} pounds. 2

On the third day they had 1}1} pounds. 4 If the pattern continues, how much will they have on the fourth day? Explain.

5. MONEY James borrowed $315 from his parents for a snowboard. He agreed to pay them back in monthly payments. In February he owed $265. In March he owed $215. In April he owed $165. What are his monthly payments? How much will he owe in August?


6. TRAVEL Jessica is on a road trip. At noon she still had 372 miles to go. At 1 P.M. she had 307 miles to go. At 2 P.M. she had 242 miles to go. At this rate, how many miles will Jessica have left to go at 5 P.M.? Explain.

354


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Sequences Pre-Activity Complete the activity at the top of page 282 in your textbook. Write your answers below.

2. Write the fraction that represents each of the next three notes.

3. Identify the pattern in the numbers.

Reading the Lesson 4. If you have a list of numbers, how can you tell if they are a sequence, as described in this lesson?

5. In extending a sequence, what are the two necessary steps?

Helping You Remember 6. Work with a partner. Make up a sequence of numbers that follow a certain pattern. Exchange lists with your partner. For the list you receive from your partner, describe the pattern, and write the next two numbers in the pattern.


355


Lesson 7–6

1. What are the names of the next three notes?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Figurate Numbers Figurate numbers are numbers associated with a pattern of geometric figures. For example, the diagram at the right shows the first four triangular numbers. The first number is 1, and then the pattern is add 2, add 3, add 4, and so on.

1

3 12

6

10

13

14

1. Refer to the diagram above. Find the next six triangular numbers. 1, 3, 6, 10,

,

,

,

,

,

2. The diagram at the right represents the first four square numbers. What is the pattern? Use the pattern to list the first ten square numbers in the space below. ,

,

,

,

,

,

,

,

,

,

,

,

,

3. The diagram at the right represents the first four rectangular numbers. What is the pattern? Use the pattern to list the first ten rectangular numbers in the space below. ,

,

,

,

,

4. In the space below, sketch the geometric figure that represents the sixth rectangular number.

5. In the space below, sketch the geometric figure that represents the sixth triangular number.


356



Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860071-5 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03






Lesson 8-4





iii




Practice: Skills











iv





Enrichment













v

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


coordinate [koh-AWR-duhn-uht] plane

coordinate system

graph

integer [IHN-tih-juhr]

negative integer

opposites

ordered pair

origin [AWR-uh-juhn]


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____


(continued)

Found on Page


positive integer

quadrant

x-axis

x-coordinate

y-axis

y-coordinate

zero pair


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: e, keep scores in games, We use integers to count and compar . Integers often play a solve problems, and describe distances mple, you may decide not role in the decisions we make. For exa cost $36 and you only to buy a pair of jeans because they have $30. r child will learn all about In Chapter 8, Algebra: Integers, you them, adding them, integers: comparing them, ordering and dividing them. Your subtracting them, multiplying them, nate system. In the study child will also learn about the coordi te a variety of daily of this chapter, your child will comple and possibly produce a classroom assignments and activities chapter project . it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 8 to the real world. You math we will be learning in Chapter line Study Tools for selfmay also wish to log on to the On dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any other study help at www.msmath1.n contact me at school. questions or comments, feel free to Sincerely,



ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Describing Situations Using Integers Work with a family member to answer the following questions. Write a positive or negative integer to describe each situation. 1. How many minutes does it take you to travel to school?

2. What was today’s low temperature?

3. What is the amount of your last withdrawal from the bank?

4. How many different kinds of vegetables are in your refrigerator?

5. How much money did you spend today?

6. How much time do you spend cleaning your room each week?

7. Give the approximate distance in miles from your house to the movie theater.

8. How much money did you spend on your last trip to the mall?

Estimates will vary. 1. positive 2. positive 3. negative 4. positive 5. negative 6. positive 7. positive 8. negative © Glencoe/McGraw-Hill

x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Integers An integer is any number from the set {…, 23, 22, 21, 0, 1, 2, 3, …} where … means continues without end. You can use a number line to compare integers. On a number line, the number on the left is always less than the number on the right. Opposite integers are the same distance from zero on opposite sides of the number line.

Write an integer to show 3 degrees below zero. Numbers below zero are negative numbers. The integer is 23. Order the integers 1, 22, and 3 from least to greatest. Graph each integer on a number line. Then compare.

Lesson 8–1

25 24 23 22 21 0 1 2 3 4 5

The order from least to greatest is 22, 1, and 3.

Write an integer to describe each situation. 1. 4 degrees below zero

2. a gain of 2 points

Replace each d with <, >, or 5 to make a true sentence. 3. 22 d 0

4. 3 d 23

5. 29 d 29

Write the opposite of each integer. 6. 3

7. 22

8. 1

9. 24

Order each set of integers from least to greatest. 10. 22, 3, 0, 21, 1

11. 3, 23, 22, 1, 21

12. 5, 27, 22, 1, 9

13. 22, 1, 5, 25, 0


383


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Integers Write an integer to describe each situation. 1. a loss of 8 yards

2. an increase of 2 inches

3. 5 feet above sea level

4. a decrease of 6 members

5. scored 10 fewer points

6. earned 7 dollars interest

7. a gain of 5 pounds

8. 4 degrees below normal

Graph each integer on the number line. 28

26

24

22

0

9. 0 13. 25

2

4

6

8

10. 23

11. 4

12. 16

14. 1

15. 28

16. 7

Replace each d with ,, ., or 5 to make a true sentence. 17. 29 d 8

18. 0 d 21

19. 16 d 6

20. 23 d 3

21. 12 d 221

22. 212 d 210

23. 5 d 25

24. 283 d 280

25. 29 d 29

26. 257 d 275

27. 256 d 56

28. 0 d 0

Write the opposite of each integer. 29. 22

30. 16

31. 29

32. 18

33. 27

34. 110

35. 114

36. 112

Order each set of integers from least to greatest. 37. 2, 26, 22, 0

38. 9, 28, 4, 29

39. 5, 23, 211, 9

40. 23, 2, 24, 217


384


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. MONEY Katryn owes her father $25. Write this number as an integer.

2. GEOGRAPHY Mt. Whitney in California is 14,494 feet above sea level. Write this number as an integer.

3. GEOGRAPHY Badwater in Death Valley is 282 feet below sea level. Write this number as an integer.

4. SCHOOL Dick forgot to put his name on his homework. His teacher deducts 5 points for papers turned in without names on them. So, Dick lost 5 points from his score. Write this number as an integer.

5. GEOGRAPHY Multnomah Falls in Oregon drops 620 feet from the top to the bottom. Suppose a log is carried by the water from the top to the bottom of the falls. Write the integer to describe the location of the log now.

6. TRAVEL The train left the station and traveled ahead on the tracks for 30 miles. Write an integer to describe the new location of the train from the station.

7. WEATHER The table shows the average normal January temperature of four cities in Alaska. Compare the temperatures of Barrow and Fairbanks, using ,, ., or 5. Then compare the temperatures of Barrow and Anchorage.

8. WEATHER Use the table from Exercise 7. Write the temperatures of the four cities in order from highest to lowest temperature.

City

Temperature (8F)

Anchorage Barrow Fairbanks Juneau

15 213 210 24

2138F , 2108F; 2138F , 158F


385


Lesson 8–1

Integers

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Integers Pre-Activity Complete the activity at the top of page 294 in your textbook. Write your answers below. 1. What does a value of 26 represent? 2. Who has the most money? 3. Who owes the most money? 4. What number represents having 8 dollars in a wallet?

Reading the Lesson For Exercises 5 and 6, look at the second sentence below the activity on page 294. 5. How are the braces { and } used?

6. Within the set, two sets of ellipsis points (…) are used. What do they mean and how do they affect the content of the set?

7. In the number lines shown in this lesson, how is “continues without end” indicated?

8. How do values change as you move from left to right on a number line?

Helping You Remember 9. Antonyms are two words that have opposite meanings, such as cold and hot. Integers can be described by the antonyms negative or positive or as being above zero or below zero. Make a table of antonyms that describe situations involving negative and positive integers. Negative Integer loss


Positive Integer gain

386


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Graphs with Integers

Lowest Recorded Temperatures in Selected Cities

Statistical graphs that display temperatures, elevations, and similar data often involve negative quantities. On graphs like these, the scale usually will have a zero point and will include both positive and negative numbers.

0 –10 –20 –30 –40

San Francisco, CA

10

New York City, NY

20

New Orleans, LA

30

Cincinnati, OH

Bismarck, ND

40

Honolulu, HI

1. In which cities is the record low temperature greater than 0°F?

50

Temperature (°F)

For Exercises 1–6, use the bar graph at the right to answer each question.

60

Lesson 8–1

–50

2. In which cities is the record low temperature less than 0°F?

3. In which city is the record low temperature about 2258F? 4. Estimate the record low temperature for New York City. 5. In which cities is the record low temperature less than twenty degrees from 08F? 6. How many degrees are between the record low temperatures for Bismarck and Honolulu? 7. In the space at the right, make a bar graph for the data below. Altitudes of Some California Locations Relative to Sea Level Alameda Brawley Calexico Death Valley El Centro Salton City

Altitude (ft)

200 150

30 2112 7 2282 239 2230

100

Altitude (feet)

Location

Altitudes of Some California Locations Relative to Sea Level

50 0 –50 –100 –150 –200 –250 –300


387


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Adding Integers • The sum of two positive integers is always positive. • The sum of two negative integers is always negative. • The sum of a positive integer and a negative integer is sometimes positive, sometimes negative, and sometimes zero.

Find 23 1 (22). Method 1 Use counters. 2 2 2

Place 3 negative counters on the mat to show 23.

Method 2 Use a number line. Start at 0. Move 3 units to the left to show 23. From there, move 2 units to the left to show 22.

Place 2 negative counters on the mat to show 22.

2 2

22 23

So, 23 1 (22) 5 25.

26 25 24 23 22 21

0

1

2

3

4

5

6

Find 4 1 (21). Method 1 Use counters. 1 2 1 1 1

Method 2 Use a number line. Start at 0. Move 4 units to the right to show 14. From there, move 1 unit to the left to show 21.

Place 4 positive counters on the mat to show 14. Place 1 negative counter on the mat to show 21.

21 14

So, 4 1 (21) 5 3.

26 25 24 23 22 21

0

1

2

3

4

5

6

Add. Use counters or a number line if necessary. 1. 3 1 (26)

2. 29 1 8

3. 24 1 7

4. 6 1 (26)

5. 28 1 (22)

6. 2 1 (25)

7. 6 1 (212)

8. 26 1 (25)

9. 4 1 (23)

10. 212 1 5


11. 24 1 10

12. 23 1 (25)

388


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Adding Integers Add. Use counters or a number line if necessary. 1. 6 1 (28)

2. 9 1 (23)

3. 25 1 (24)

4. 213 1 7

5. 22 1 11

6. 10 1 (26)

7. 4 1 (24)

8. 27 1 (24) 10. 25 1 14

11. 210 1 (22)

12. 6 1 (21)

13. 23 1 4

14. 14 1 (14)

15. 22 1 (21)

16. 6 1 (23)

17. 8 1 7

18. 25 1 (26)

19. 211 1 4

20. 26 1 13

21. 212 1 6

22. 27 1 12

23. 9 1 (29)

24. 25 1 (25)

25. 3 1 (211)

26. 214 1 9

27. 15 1 (27)

28. 215 1 15

29. What is the sum of positive six and negative four? 30. What is the sum of negative five and positive five? 31. Find the result when negative eight is added to positive 4. 32. Find the sum of negative 1 and positive 7. 33. ALGEBRA Find the value of c 1 d if c 5 24 and d 5 6.


389


Lesson 8–2

9. 212 1 3

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Adding Integers 1. GAME To play a game on a game board, Drew puts his game piece on START. On his first turn, he moves his game piece ahead 7 spaces. On his second turn, Drew moves his game piece back 4 spaces. How many spaces away from START is his game piece now?

2. GAME Frita’s game piece is on square 24 of a game board. She draws a card that says, “Move back 4 spaces.” Then she draws a card that says, “Move back 2 spaces.” On which square is Frita’s game piece now?

3. WEATHER The temperature outside is 08F. If the temperature drops 148 overnight, what was the overnight low temperature?

4. WEATHER The temperature outside is 2168F. Then the temperature rises 20 degrees. What is the current outdoor temperature?

5. ANIMALS An ant crawls 14 centimeters down into an ant hole. It then crawls 6 centimeters up to the queen’s nest. Write and solve an addition sentence that gives the location of the ant.

6. ANIMALS Monarch butterflies travel an average of about 15 feet off the ground. One butterfly flies to a height of 22 feet. Tell how much higher it flies than average.

7. ANIMALS Pacific salmon swimming up the Columbia River travel 2 feet under water. Suppose one salmon darts 3 feet up and out of the water. How far out of the water did the salmon jump?

8. ANIMALS Plankton (microscopic animals) float on the top of a pond at night to feed. They drop to the bottom of the pond during the day. Express their daytime location as a negative number if the top of the pond is at sea level and the pond is 4 feet deep.


390


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Adding Integers Pre-Activity Complete the activity at the top of page 300 in your textbook. Write your answers below. 1. After Gracia’s third turn, how many spaces from the start is her game piece?

Reading the Lesson For Exercises 2 and 3, look at the cards at the top of page 300 that Gracia selected for her first three turns. 2. Suppose you were using counters to find the result. Write directions that would show the result of her first three turns.

3. Suppose you were using a number line. Write directions that would show the result of her first three turns.

25 24 23 22 21

0

1

2

3

4

5

5. Look at the Key Concept box at the bottom of page 301. It says that the sum of a positive integer and a negative integer is sometimes negative, sometimes positive and sometimes 0. How can you tell which it will be?

Helping You Remember 6. Work with a partner. Use the three rules for adding integers you have learned in this lesson to make up addition problems and sums to show each rule. Then have your partner prove your addition sum is correct by solving the problem using a number line or counters.


391


Lesson 8–2

4. Using a number line, show that a zero pair results in 0.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Speedy Addition How would you perform an addition like this? 24 1 7 1 (21) 1 4 1 (27) 1 (25) Some people add all the positive integers, add all the negative integers, then add the results. 24 1 (21) 1 (27) 1 (25) 5 217 7 1 4 5 11

→ 217 1 11 5 26

Other people find it easier to first group all the zero pairs.

}

} 0

{

24 1 4 1 7 1 (27) 1 (21) 1 (25) 1

0

1

→ 26

26

Which method do you think you would prefer? Check it out by finding each of these sums. 1. 29 1 5 1 3 1 9 1 (23) 2. 216 1 9 1 (211) 1 16 1 11 1 (212) 1 (29) 3. 10 1 (28) 1 (24) 1 (22) 4. 26 1 14 1 (211) 1 (28) 1 7 1 11 5. 215 1 6 1 (212) 1 3 1 9 1 (23) 6. 20 1 (213) 1 (25) 1 13 1 (210) 1 16 1 (25) 7. 19 1 (27) 1 (29) 1 (29) 1 15 1 (210) 1 16 8. 24 1 17 1 (28) 1 5 1 (217) 1 (213) 1 8 1 (212) 9. 16 1 (211) 1 4 1 (22) 1 11 1 (214) 1 5 1 (29) 10. 221 1 3 1 (27) 1 (24) 1 (28) 1 15 1 6 1 12 1 15 11. Which method(s) did you use in Exercises 1210? Did you choose from the methods above, or did you use a different method? Explain.


392


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Subtracting Integers To subtract an integer, add its opposite.

Find 24 2 (23). Method 1 Use counters. 2 2 2

Method 2 Use the rule. 24 2 (23) 5 24 1 3 To subtract 23, add 3.

Place 4 negative counters on the mat to show 24. Remove 3 negative counters to show subtracting 23.

2

5 21

Simplify.

So, 24 2 (23) 5 21. Find 23 2 1. Method 1 Use counters.

2 2 2

1 2

Place 3 negative counters on the mat to show 23. To subtract 11, you must remove 1 positive counter. But there are no positive counters on the mat. You must add 1 zero pair to the mat. The value of the mat does not change. Then you can remove 1 positive counter.

Method 2 Use the rule. 23 2 1 5 23 1 (21) To subtract 1, add 21.

5 24

Simplify.

The difference of 23 and 1 is 24. So, 23 21 5 24.

1. 18 2 5

2. 24 2 2

3. 7 2 (25)

4. 23 2 (25)

5. 6 2 (210)

6. 28 2 (24)

7. 21 2 4

8. 2 2 (22)

9. 25 2 (21)

10. 7 2 2

11. 29 2 (29)

12. 6 2 (22)

13. 28 2 (214)

14. 22 2 9

15. 5 2 15


393


Lesson 8–3

Subtract. Use counters if necessary.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Subtracting Integers Subtract. Use counters if necessary. 1. 9 2 4

2. 10 2 7

3. 18 2 5

4. 112 2 6

5. 23 2 (27)

6. 5 2 (29)

7. 28 2 7

8. 2 2 6

9. 216 2 (29)

10. 4 2 (215)

11. 218 2 5

12. 26 2 6

13. 7 2 4

14. 24 2 (22)

15. 28 2 10

16. 9 2 (27)

17. 3 2 12

18. 23 2 (210)

19. 213 2 7

20. 25 2 (22)

21. 6 2 6

22. 3 2 5

23. 28 2 6

24. 22 2 (22)

25. 7 2 (24)

26. 216 2 (28)

27. 12 2 (212)

28. 23 2 10

29. 21 2 (24)

30. 9 2 (26)

31. ALGEBRA Find the value of a 2 b if a 5 5 and b 5 8.

32. ALGEBRA Find the value of c 2 d if c 5 27 and d 5 22.


394


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Subtracting Integers MONEY For Exercises 1–4, use the transaction register.

A transaction register is used to record money deposits and withdrawals from a checking account. It shows how much money Mandy, a college student, had in her account as well as the 4 checks she has written so far. Date

Description of Transaction

9/04

spending money from parents

1

9/07

college bookstore — textbooks

2

9/13

graphing calculator

3

9/16

bus pass

4

9/24

Charlie’s Pizza

Payment Deposit Balance $500

$500

$291 $99 $150 $12

1. Subtract each withdrawal to find the balance after each check was written. If Mandy spends more than $500, record that amount as a negative number.

2. Which check did Mandy write that made her account overdrawn?

3. Mandy called home and asked for a loan. Her parents let her borrow $500. What is her balance now?

4. After her parents let her borrow the $500 from Exercise 3, Mandy wants to spend $300 on clothes and $150 on decorations for her dorm room. Does she have enough money in the bank? Express her balance with an integer if she buys these items.

5. WEATHER At 2 P.M., the temperature was 298F. If the temperature drops 20 degrees, what is the new temperature?

6. BASKETBALL During a high school basketball game, the home team scored 51 points and the opponents scored 62 points. What is the point differential (the difference between the number of points scored by a team and its opponent) for the home team?


395


Lesson 8–3

Check No.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Subtracting Integers Pre-Activity Complete the Mini Lab at the top of page 304 in your textbook. Write your answers below. 1. Model 8 1 (22) using a number line.

22 21

0

1

2

3

4

5

6

7

8

2. Compare this model to the model for 8 2 2. How is 8 2 2 related to 8 1 (22)? 3. Use a number line to model 23 1 (24).

28 27 26 25 24 23 22 21

0

1

2

4. Compare this model to the model for 23 2 4. How is 23 2 4 related to 23 1 (24)?

Reading the Lesson 5. What does the Mini Lab show?

6. What do the two pairs of equations near the bottom of page 304 show?

7. Look at Example 3, Method 1, on page 306. Why is it necessary to add 3 zero pairs in order to do the computation?

Helping You Remember 8. Work with a partner. Look at Your Turn toward the bottom of page 301. Change the three addition problems to subtraction problems. Solve the problems. Compare your answers with those of your partner.


396


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Windchill Temperatures When you go outside on a windy day, it usually feels much colder than the actual temperature on the thermometer. This happens because the wind causes you to lose more heat from the surface of your skin than you would lose if the air were still. The temperature you feel is called the windchill temperature. The table below lists some of the windchill temperatures that have been calculated by the National Weather Service. Windchill Temperatures (degrees Fahrenheit) Actual Temperature

Wind Speed (miles per hour)

20

15

10

5

0

25

210

215

220

5 10 15 20 25 30 35 40 45

13 9 6 4 3 1 0 21 22

7 3 0 22 24 25 27 28 29

1 24 27 29 211 212 214 215 216

25 210 213 215 217 219 221 222 223

211 216 219 222 224 226 227 229 230

216 222 226 229 231 233 234 236 237

222 228 232 235 237 239 241 243 244

228 235 239 242 244 246 248 250 251

234 241 245 248 251 253 255 257 258

Use the table above to answer each question. 1. If the wind speed is 10 miles per hour and the actual temperature is 0°F, what is the windchill temperature?

Describe the change in the windchill temperature. 3. The wind speed remains constant at 10 miles per hour, but the actual temperature rises from 258 to 208F. 4. The actual temperature remains constant at 2108F, but the wind speed increases from 5 miles per hour to 35 miles per hour. Estimate the windchill temperature in each situation. 5. The actual temperature is 88F and the wind speed is 22 miles per hour. 6. The actual temperature is 2108F and the wind speed is 55 miles per hour. © Glencoe/McGraw-Hill

397


Lesson 8–3

2. Suppose that the actual temperature is 258F and the wind speed is 15 miles per hour. How much colder than 258F does it feel?

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Multiplying Integers • The product of two integers with different signs is negative. • The product of two integers with the same sign is positive.

Multiply. 2 3 (21) 2 3 (21) 5 22

The integers have different signs. The product is negative.

24 3 3 24 3 3 5 212

The integers have different signs. The product is negative.

335 3 3 5 5 15

The integers have the same sign. The product is positive.

22 3 (24) 22 3 (24) 5 8

The integers have the same sign. The product is positive.

Multiply. 1. 3 3 (23)

2. 25 3 (22)

3. 28 3 (21)

4. 22 3 8

5. 4 3 23

6. 23 3 (22)

7. 5 3 (24)

8. 210 3 (24)

9. 23 3 6

10. 23 3 (210)


11. 6 3 (24)

12. 27 3 (27)

398


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Multiplying Integers 1. 6 3 (24)

2. 28 3 7

3. 22 3 (29)

4. 5(25)

5. 25(23)

6. 24(8)

7. 9(22)

8. 25(26)

9. 3(210)

10. 24(2)

11. 24(24)

12. 29(6)

13. 7(23)

14. 22(28)

15. 25(210)

16. 2(21)

17. 23(6)

18. 4(25)

19. 27(7)

20. 22(27)

21. 26(21)

22. 4(23)

23. 26(25)

24. 29(10)

25. 23(28)

26. 7(25)

27. 22(2)

28. 8(28)

29. 29(1)

30. 27(24)

31. 27(6)

32. 25(12)

33. 24(28)


399


Lesson 8–4

Multiply.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Multiplying Integers 1. BASKETBALL A basketball player who makes a basket scores 2 points for her team. Tanya made 9 baskets in the game. Write a number sentence to show many points she scored for her team.

2. HEALTH Jim was recovering in the shade from a walk in the hot desert. His temperature dropped 28F each hour for 2 hours. What was the total change in his temperature?

3. WEATHER The outside temperature is 238F and falling at a rate of 2 degrees per hour. What will the temperature be in 5 hours?

4. POPULATION A small town is losing residents at a rate of 24 residents per year. If this pattern continues for 5 years, what will be the change in relation to the original population?

5. SCIENCE A pebble falls into a pond. From the surface, it descends at a rate of 2 feet per second. Where is the pebble in relation to the surface of the pond after 5 seconds?

6. CONSTRUCTION A construction company is starting to excavate a hole for a new underground parking garage. If the company excavates 3 feet every hour for 4 hours, what will be the depth of the hole in relation to the surface?

7. WEATHER The outside temperature is 2208F and rising at a rate of 5 degrees per hour. How long will it be before the temperature reaches 08F?

8. SCIENCE For each kilometer above Earth’s surface, the temperature decreases 78C. If the temperature at Earth’s surface is 288, what will be the temperature 7 kilometers above the surface?


400


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Multiplying Integers Pre-Activity Complete the Mini Lab at the top of page 310 in your textbook. Write your answers below. 1. Use counters to find 4 3 (23) and 5 3 (22).

2. Make a conjecture as to the sign of the product of a positive and negative integer.

Reading the Lesson 3. How does the Mini Lab show that 3 3 2 5 16?

4. How does the Mini Lab show that 3 3 (22) 5 26?

5. In Examples 1 and 2 on page 311, how do you know that the products should be negative?

6. In Examples 3 and 4 on page 311, how do you know that the products should be positive?


Lesson 8–4

7. Look at Example 5 on page 311. Imagine that all you see is the statement of the problem. From the problem, what words indicate that the pattern will start at 0 and progress in the negative direction? How could the problem be reworded to indicate a progression in the positive direction?


401


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Integer Patterns Many number patterns involve integers. When you work with patterns like these, you need to pay special attention to the sign of each number in the pattern. Here are two examples. 1,

4,

22,

16,

28,

64,…

232,

Multiply by 22.

3 (22) 3 (22) 3 (22) 3 (22) 3 (22) 3 (22) 1,

3, 12

0, 23

2,

23

12

1,

21,

22, …

Add 2, subtract 3, add 2, and so on.

23

12

Write the next five numbers in each pattern shown above. 1. 1, 22, 4, 28, 16, 232, 64,

,

2. 1, 3, 0, 2, 21, 1, 22,

,

,

,

,

,

,

,

For each set of numbers, identify the pattern. Then write the next three numbers in the pattern. 3. 21, 3, 29, 27, 281,

,

4. 5, 21, 27, 213, 219,

, ,

5. 211, 28, 25, 22, 1,

,

,

, ,

6. 22, 210, 250, 2250, 21,250, 7. 12, 7, 8, 3, 4,

,

,

8. 215, 210, 212, 27, 29,

,

9. 7, 27, 22, 2, 7,

,

,

10. 3, 6, 22, 24, 212, 11. 24, 8, 6, 212, 214, 28, 12. CHALLENGE 1, 2, 0, 3, 21,


,

,

,

, ,

, ,

,

402


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Dividing Integers Lesson 8–5

• The quotient of two integers with different signs is negative. • The quotient of two integers with the same sign is positive.

Use counters to find 26 4 2.

There are 2 groups of 3 negative counters each.

2 2 2 2 2 2

So, 26 4 2 5 23. Divide. 10 4 (25) Since 25 3 (22) 5 10, it follows that 10 4 (25) 5 22. 212 4 (23) Since 23 3 4 5 212, it follows that 212 4 (23) 5 4.

Divide. 1. 4 4 (22)

2. 29 4 (23)

3. 28 4 2

4. 221 4 7

5. 30 4 (25)

6. 224 4 4

7. 236 4 6

8. 245 4 (25)

9. 281 4 9

10. 23 4 (23)

11. 70 4 (27)

12. 264 4 (28)

13. ALGEBRA Find the value of a 4 b if a 5 218 and b 5 6.

14. ALGEBRA For what value of p is p 4 5 = 27 true?


403


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Dividing Integers Divide. 1. 24 4 2

2. 6 4 (22)

3. 28 4 (22)

4. 3 4 (23)

5. 9 4 (13)

6. 210 4 5

7. 56 4 (27)

8. 245 4 9

9. 212 4 (26)

10. 15 4 (23)

11. 224 4 6

12. 218 4 (23)

13. 48 4 (28)

14. 240 4 8

15. 220 4 (25)

16. 36 4 (29)

17. 242 4 7

18. 254 4 (26)

19. 20 4 (210)

20. 212 4 4

21. 235 4 (25)

22. 227 4 9

23. 10 4 (22)

24. 232 4 (28)

25. 268 4 4

26. 30 4 (23)

27. 236 4 (24)

28. 216 4 (28)

29. 49 4 (27)

30. 218 4 2

31. ALGEBRA For what value of v is 42 4 v 5 6 true?

32. ALGEBRA Find the value of m 4 n if m 5 224 and n 5 24.

33. ALGEBRA For what value of b is b 4 4 5 29 true?

34. ALGEBRA Find the value of x 4 y if x 5 250 and y 5 10.


404


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. SKATING Judges in some figure skating competitions must give a mandatory 5-point deduction for each jump missed during the technical part of the competition. Marisa has participated in 5 competitions this year and has been given a total of 220 points for jumps missed. How many jumps did she miss?

2. SKATING Miranda is an excellent spinner who averages 13 points on her spins during competitions. Last year her total spin points equaled 121. About how many spins did she successfully complete?

3. WEATHER The temperature dropped 32°F in 4 hours. Suppose the temperature dropped by an equal amount each hour. What integer describes the change?

4. SKATING Dan’s scores for speed this season are 21, 23, 1, 21, 22, 0. What is his average speed score for the season? (Hint: The average is the sum of the points divided by the number of scores.)

5. FOOTBALL A football team was penalized 30 points in 3 plays. Suppose the team was penalized an equal number of yards on each play. Write an integer that gives the yards for each penalty.

6. BASKETBALL A team scored a total of 27 points for three-point field goals in the season. How many 3-point field goals did they make?

7. TRACK Anna and Sara both ran 5 laps of a race. When Anna finished, Sara was 15 meters behind Anna. Suppose Sara fell behind the same number of meters during each lap. Write an integer that describes how far Sara fell behind in each lap.

8. BAKING Maria was penalized a total of 12 points in 6 baking contests for not starting on time. Suppose she was penalized an equal number of points at each competition. Write an integer that describes the penalty during each contest.


405


Lesson 8–5

Dividing Integers

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Dividing Integers Pre-Activity Complete the Mini Lab at the top of page 316 in your textbook. Write your answers below. 1. Explain how you would model 29 4 3.

2. What would you do differently to model 8 4 2?

Reading the Lesson 3. What is the definition of division?

4. Write in words what 10 4 5 means.

5. Write in words what –10 4 2 means.

6. How do the rules for determining signs of quotients compare with the rules for determining the signs of products?

7. Look at Example 6 on page 317. Which words tell you that the answer will be a negative number?

Helping You Remember 8. Work with a partner. Make two models that show integers divided into equal groups. Give the models to your partner and have your partner write the division expression for each model.


406


NAME ________________________________________ DATE ______________ PERIOD _____

Four Negative Fours Do you think it is possible to use four negative fours to create an expression whose value is 1? Here are two ways to do it. 24 }} 1 (24) 2 (24) 5 24 5 24 1 (24) }} 5 24 1 (24)

1 1 (24) 1 4 1 28 }} or 1

Remember that the fraction bar is a symbol for division.

28

On this page, you will be challenged to work backward. Instead of finding the value of a given expression, you will be asked to find an expression for a given value. In creating these expressions, you may use addition, subtraction, multiplication, and division in any combination—just be sure to follow the order of operations. You may also use parentheses and fraction bars to group numbers. Create an expression for each value by using two negative fours. 1. 0 5

2. 1 5

3. 16 5

4. 28 5

Create an expression for each value by using three negative fours. 5. 23 5

6. 5 5

7. 2 5

8. 24 5

9. 0 5

10. 4 5

Create an expression for each value by using four negative fours. 11. 2 5

12. 0 5

13. 3 5

14. 22 5

15. 28 5

16. 25 5


407


Lesson 8–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention The Coordinate Plane A coordinate system is a grid used to locate points. The horizontal number line is the x-axis; the vertical number line is the y-axis. The x-axis and y-axis separate the coordinate system into four regions called quadrants. An ordered pair helps you locate any point on the coordinate plane. The first number is the x-coordinate. The second number is the y-coordinate. Quadrant II

Step 1 Move left on the x-axis to find the x-coordinate of point A, which is 23. Step 2 Move up the y-axis to find the y-coordinate, which is 4.

B

1 2 3 4x

O

242322

22 23 24

Point A is named by (23, 4). Graph point B at (5, 4).

Quadrant I

y 4 3 2 1

A

Identify the ordered pair that names point A.

Quadrant III

Quadrant IV

Use the coordinate plane shown above. Start at 0. The x-coordinate is 5, so move 5 units to the right. Since the y-coordinate is 4, move 4 units up. Draw a dot. Label the dot B. See grid at the top of the page.

Use the coordinate plane at the right. Write the ordered pair that names each point. 1. C 3. E

4. F 6. H

7. I

8. J

242322

O

J

2. D

5. G

G

y 4 3 2 1

A

F

C

Graph and label each point using the coordinate plane at the right. 9. A(25, 5)

10. M(2, 4)

11. G(0, 25)

12. D(3, 0)

13. N(24, 23)

14. I(2, 23)


408

H

O

I

1 2 3 4x

22 23 24

4 3 2 1 242322

B

D E

y

1 2 3 4x

22 23 24


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills The Coordinate Plane

1. (22, 4)

2. (22, 23)

Q S Y N 242322

3. (4, 4)

4. (3, 25)

5. (3, 5)

6. (4, 21)

7. (21, 3)

8. (24, 22)

T

Z L

O

y 4 3 2K 1

W

U R

1 2 3 4x

O

X

22 23 24

M

P V

Lesson 8–6

For Exercises 1–8, use the coordinate plane at the right. Identify the point for each ordered pair.

For Exercises 9–16, use the coordinate plane above. Write the ordered pair that names each point. Then identify the quadrant where each point is located. 9. K

10. L

11. M

12. N

13. O

14. P

15. Q

16. R

Graph and label each point on the coordinate plane at the right. 17. A(25, 2)

4 3 2 1

18. I(2, 1) 242322

19. J(1, 23)

20. B(25, 21)

21. C(3, 3)

22. K(21, 2)

23. L(0, 21)

24. D(2, 25)

25. E(3, 22)

26. M(24, 25)

27. N(1, 5)

28. F(22, 5)

29. G(21, 24)

30. O(5, 25)


409

y

1 2 3 4x

O

L

22 23 24

J


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems The Coordinate Plane MONEY For Exercises 1–4, use the table and the coordinate plane.

School buttons sell for $2 each. When you have completed the table and the graph, both the table and graph will show the costs of purchasing up to 5 school buttons. Number of Buttons Sold 1 2 3 4 5

Price ($)

10 9 8 7 6 5 4 3 2 1 O origin

y-axis

x-axis 1 2 3 4 5 6 7 8 9 10

1. Now complete the second column of the table by writing the cost of each number of buttons.

2. To prepare to graph the data, make a list of ordered pairs from the table.

3. Graph the ordered pairs. Label each point with its ordered pair. Describe the graph of the points.

4. Describe the coordinate plane that you have completed. How is it different from other systems you have used?

5. TRACK If it takes Trixie 8 minutes to run a mile, then 8m represents her total time where m is the number of miles she has run. List the ordered pairs (number of miles, total time) for 0, 1, 2, and 3 miles.

6. TRACK If you were to graph the ordered pairs from Exercise 5, what would their graph look like?


410


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics The Coordinate Plane Pre-Activity Complete the activity at the top of page 320 in your textbook. Write your answers below. 1. Use a letter and a number to identify where on the map Autumn Court meets Timberview Drive.

3. Write a sentence that explains how to locate a specific place on the map shown.

Reading the Lesson 4. An ordered pair is a pair that has been arranged in a certain order. In this lesson, what are the elements of an ordered pair and what do they identify?

5. In what order are the elements of an ordered pair arranged?

6. Why is it important to know the order of the numbers in an ordered pair?

7. Describe how to locate the point (–5, –3) on a coordinate grid.

8. In which quadrant is the point (–5, –3)?

Helping You Remember 9. Work with a partner. Draw a coordinate system that can be used to locate objects in your classroom. Have one person say the ordered pair of a location and the other say what object is located at that point.


411


Lesson 8–6

2. Location G2 is closest to the end of which street?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Creative Coordinates Graph each set of points on the coordinate grid below. Then use line segments to connect the points in order from left to right. 1. (22, 5); (0, 7); (22, 9); (25, 7); (25, 4); (22, 5); (1, 4); (3, 1); (27, 25);

(1, 5); (22, 5); (23, 8); (26, 6); (25, 3); (21, 2); (22, 5); (22, 23); (21, 25);

(2, 6); (21, 8); (22, 5); (25, 5); (24, 2); (0, 2); (22, 23); (21, 25); (3, 28)

(1, 7); 2. (1, 6); (21, 9); (23, 6); (24, 7); (22, 0); (22, 5); (24, 26); (23, 2); (9, 27); (1, 3); (7, 27); (0, 0); (4, 23); (25, 24); (4, 2); (2, 8);

y

y

8

8

6

6

4

4

2

2

(21, 6); (24, 5); (23, 21); (22, 28); (11, 24); (3, 27); (3, 21); (4, 5); (1, 6)

(22, 8); (24, 2); (24, 23); (7, 28); (9, 25); (4, 26); (2, 0); (3, 6);

O

26

24

2

22

4x

24

22

O

22

22

24

24

26

26

28

28

2

4

6

8

10

x

3. In the figure for Exercise 2, draw a line segment connecting each of the following pairs of points. a. (2, 2) and (5, 1) b. (22, 2) and (25, 1) c. (5, 3) and (2, 2)

d. (25, 3) and (22, 2)

e. (2, 2) and (6, 2)

f. (26, 2) and (22, 2)

4. On a sheet of graph paper, create your own figure. Then record the coordinates of the points that form the figure.


412


Chapter Chapter 99 Resource Resource Masters Masters

Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860072-3 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03







Chapter 9 Assessment Chapter 9 Test, Form 1 ..........................469–470 Chapter 9 Test, Form 2A ........................471–472 Chapter 9 Test, Form 2B ........................473–474 Chapter 9 Test, Form 2C........................475–476 Chapter 9 Test, Form 2D........................477–478 Chapter 9 Test, Form 3 ..........................479–480 Chapter 9 Extended Response Assessment .481 Chapter 9 Vocabulary Test/Review.................482 Chapter 9 Quizzes 1 & 2................................483 Chapter 9 Quizzes 3 & 4................................484 Chapter 9 Mid-Chapter Test ...........................485 Chapter 9 Cumulative Review........................486 Chapter 9 Standardized Test Practice....487–488 Unit 4 Test/Review..................................489–490 Standardized Test Practice Student Recording Sheet ..............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A31


iii



Practice: Skills






Reading to Learn Mathematics One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques.




iv


Enrichment




• Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. • A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and freeresponse questions.











v

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


Addition Property of Equality

Additive Identity

Associative [uh-SOH-shee-AY-tihv] Property

coefficient

Commutative [kuh-MYOO-tuh-tihv] Property

Distributive [dih-STRIH-byuh-tihv] Property


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____


(continued)

Found on Page


function

function rule

function table

inverse operations

Multiplicative Identity

Subtraction Property of Equality

two-step equation


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: t the day without knowing We may solve equations throughou how much more money we it. We solve equations to determine ch time we need to finish need to purchase an item or how mu to make these decisions our work. The thought process we use equations. is the same process we use to solve uations, your child will In Chapter 9, Algebra: Solving Eq n, and division to solve use addition, subtraction, multiplicatio solve two-step equations equations. Students will also learn to study of this chapter, your and how to graph functions. In the classroom assignments and child will complete a variety of daily pter project . activities and possibly produce a cha it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 9 to the real world. You math we will be learning in Chapter line Study Tools for selfmay also wish to log on to the On dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any quesother study help at www.msmath1.n t me at school. tions or comments, feel free to contac Sincerely,



ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Using Patterns Watch the news on television, consult the weather section of a newspaper, or visit a weather-related website. Then work with a family member to collect the high and low temperatures for at least nine cities. Write and solve an equation to find how much warmer the high temperature is than the low temperature.

City

1. Austin

Low Temperature

High Temperature

Equation

72°

91°

72 1 t 5 91

Solution

2.

3.

4.

5.

6.

7.

8.

9.

10.

1. The high temperature was 19° warmer.

2–10. Answers will vary © Glencoe/McGraw-Hill

x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Properties The Distributive Property To multiply a sum by a number, multiply each addend of the sum by the number outside the parentheses. 2(3 1 4) 5 2 3 3 1 2 3 4 (4 1 5)2 5 4 3 2 1 5 3 2 Commutative Properties of Addition and Multiplication The order in which numbers are added or multiplied does not change the sum or product. 2135312 4355534 Associative Properties of Addition and Multiplication The way in which numbers are grouped when added or multiplied does not change the sum or product. (2 1 3) 1 4 5 2 1 (3 1 4) (5 3 6) 3 2 5 5 3 (6 3 2) Additive Identity The sum of any number and 0 is the number. a105a 51055

Multiplicative Identity The product of any number and 1 is the number. 73157 13n5n

Find 5 3 32 mentally using the Distributive Property. 5 3 32 5 5 5 5

5(30 1 2) 5(30) 1 5(2) 150 1 10 160

Write 32 as 30 1 2. Distributive Property Multiply 5 and 30 mentally. Multiply 5 and 2 mentally. Add 150 and 10 mentally.

So, 5 3 32 5 160. Find 12 1 27 1 18 mentally. • You can add 12 and 18. So, change the order of the numbers to be added. 12 1 27 1 18 5 12 1 18 1 27 Commutative Property • Now group the numbers using the Associative Property. The parentheses tell you what to do first. 12 1 18 1 27 5 (12 1 18) 1 27 Associative Property 5 30 1 27 Add 12 and 18 mentally. 5 57 Add 30 and 27 mentally.

Find each product mentally. Use the Distributive Property. 1. 5 3 42

2. 2 3 55

3. 3 3 84

Rewrite each expression using the Distributive Property. Then evaluate the expression. 4. 2(10 1 3)

5. (30 1 4)5

6. 11(10 1 2)

Find each sum or product mentally. 7. 55 1 16 1 5 © Glencoe/McGraw-Hill

8. 17 1 21 1 13

433

9. 5 3 18 3 2 Mathematics: Applications and Concepts, Course 1

Lesson 9–1

You can use the Distributive, Commutative, and Associative Properties to make your calculations easier to do mentally.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Properties Find each product mentally. Use the Distributive Property. 1. 5 3 15

2. 7 3 12

3. 4 3 24

4. 6 3 51

5. 3 3 81

6. 2 3 72

7. 20 3 1.7

8. 11 3 2.1

9. 15 3 3.4

Rewrite each expression using the Distributive Property. Then evaluate. 10. 5(20 1 8)

11. 3(50 1 8)

12. (30 1 5)6

13. (40 1 5)6

14. 11(20 1 5)

15. 13(30 1 4)

16. (10 3 50) 1 (10 3 9)

17. (12 3 40) 1 (12 3 2)

Identify the property shown by each equation. 18. 7 3 8 5 8 3 7

19. 4 1 5 5 5 1 4

20. 14 1 27 1 16 5 14 1 16 1 27

21. 9 3 1 = 9

22. (7 3 2) 3 4 5 7 3 (2 3 4)

23. 2 3 3 3 4 5 2 3 4 3 3

24. 0 1 11 5 11

25. (6 3 4) 3 2 5 2 3 (6 3 4)

26. 15(5 1 7) 5 15 3 5 1 15 3 7

27. 5 1 (15 1 9) 5 (15 1 9) 1 5

Find each sum or product mentally. 28. 5 3 19 3 2

29. 12 1 14 1 8

30. 5 3 23 3 20

31. 15 1 17 1 15

32. 4 3 27 3 25

33. 14 1 37 1 26

34. 25 1 26 1 15

35. 25 3 6 3 2

36. 13 1 6 1 17


434


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Properties 2. COMPUTER GAMES In Carlota’s computer game, she goes up one level every time she earns 210 points. Carlota has just gone up a level for the eighth time. Use the Distributive Property to calculate mentally how many points Carlota has.

3. ENROLLMENT The sixth grade class at Parkview Middle School has 25 blondes, 18 redheads, and 25 brunettes. Use mental math to figure out how many students are in the sixth grade.

4. GYM CLASS In gym class, students were put into groups. Each group had 4 boys and 3 girls. If 7 groups were formed, how many students were in the class?

5. SPORTS CARS Every day for 11 days, Tylia saw 23 sports cars pass her bedroom window. Write a numerical expression to describe how many sports cars she saw in all. Rewrite the expression using the Distributive Property so that you can mentally calculate how many sports cars she saw.

6. MARBLES Devon has 16 blue marbles, 22 green marbles, and 14 red marbles in a bag. Write a numerical expression to describe the total number of marbles in the bag in the order given in the problem. Then rewrite the expression to make it easier to mentally calculate how many marbles are in the bag.

7. BOWLING It costs $5.75 per person for one game of bowling and $2.25 to rent one pair of shoes. What does it cost for five friends to go bowling? Write two different numerical expressions to describe the cost for five friends. Then use one to calculate the total cost for five friends.

8. GIFTS Ms. Bautista made 22 gift baskets for her students. Each basket had 5 apples and 3 oranges. How many pieces of fruit did Ms. Bautista use?


Lesson 9–1

1. HOMEWORK Jacy spends half an hour every night studying math and an hour every night studying science. Over five days, how much time does Jacy spend on his homework? Write two expressions you can use to find the answer. Then answer the question.

435


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Properties Pre-Activity Complete the Mini Lab at the top of page 333 in your textbook. Write your answers below. 1. Complete the table at the right.

multiplication expression

product

multiplication expression

a.

538

6 3 12

b.

5 3 40

6 3 200

c.

5 3 48

6 3 212

product

2. What do you notice about each set of expressions?

3. How does each product in row c compare to the sum of the products in rows a and b?

Reading the Lesson 4. Complete the table below by naming and describing the property shown by each example. Examples 5(7 1 8) 5 5 3 7 1 5 3 8 25 1 7 1 5 5 25 1 5 1 7 5 3 36 3 2 5 5 3 2 3 36 (16 1 15) 1 4 5 16 1 (15 1 4) (4 3 13) 3 3 5 4 3 (13 3 3) 12 1 0 5 12 17 3 1 5 17

Properties

Distributive Property; to multiply a sum by a number, multiply each addend of the sum by the number outside the parentheses. Commutative Property; the order in which numbers are added or multiplied does not affect the sum or product. Associative Property; the way in which numbers are grouped when added or multiplied does not affect the sum or product. Identity Property; the sum of any number and 0 is the number. The product of any number and 1 is the number.

5. In this lesson, how are the properties used?

Helping You Remember 6. Look up in a dictionary the words distribute, commute, identity, and association. Choose a meaning for each that will help you remember the meanings of Distributive Property, Addititive Identity, Multiplicative Identity, Commutative Property, and Associative Property. Write phrases or sentences or draw pictures that will help you remember.


436


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Modeling Properties Just as you can model numbers, you can also model operations. For example, here is a model of the operations in the Distributive Property.

332

1

335

5

3(2 1 5)

Write a Distributive Property statement for each model.

Lesson 9–1

1.

2.

Make a model for each statement. 3. 2 3 4 1 2 3 5 5 2(4 1 5)

4. 6(1 1 4) 5 6 3 1 1 6 3 4

Write a statement for each model using one of the properties of equality. 5.

6.

7.


437


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Solving Addition Equations Subtraction Property of Equality If you subtract the same number from each side of an equation, the two sides remain equal. 55 5 23 5 23 25 2

Solve x 1 2 5 7 using models. 1 1

5

1 1 1 1 1 1 1

x12

5

7

1 1

x1222

Model the equation.

1 1 1

5

Remove 2 counters from each side of the mat.

1 1 1 1 722

5

The counters remaining on the right side of the mat represent the solution or value of x.

1

x

5

1 1 1 1

5

5

The solution is 5. 5 1 2 5 7 ✓ 5 substituted in the original equation is correct. Solve b 1 3 5 2. b135 2 2 3 5 23 }}}}} b 1 0 5 21 b 5 21

Write the equation. Subtract 3 from each side to undo the addition of 3 on the left. Simplify.

The solution is 21. Check

b1352 21 1 3 0 2 252 ✓

Write the original equation. Replace b with 21. This sentence is true.

Solve each equation. Use models if necessary. Check your solution. 1. a 1 1 5 7

2. 3 1 b 5 8

3. c 1 7 5 4

4. 9 5 x 1 4

5. g 1 8 5 22

6. d 1 6 5 25


438


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Solving Addition Equations 1. x 1 8 5 10

2. y 1 3 5 7

3. z 1 4 5 6

4. 1 1 a 5 9

5. b 1 2 5 24

6. 5 1 c 5 21

7. g 1 5 5 2

8. 6 1 h 5 3

9. k 1 7 5 5

10. 8 5 m 1 2

11. 25 5 2 1 n

12. 4 1 s 5 1

13. 26 5 z 1 4

14. b 1 6 5 7

15. 7 1 g 5 4

16. n 1 6 5 4

17. s 1 5 5 9

18. 24 5 x 1 3

19. 5 5 1 1 k

20. 8 1 c 5 3

21. 9 1 m 5 5

22. 22 5 7 1 a

23. h 1 3 5 23

24. 25 5 y 1 4

25. Find the value of r if r 1 7 5 2.

26. If z 1 5 5 1, what is the value of z?


439


Lesson 9–2

Solve each equation. Use models if necessary. Check your solution.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Solving Addition Equations 1. BIRTHDAYS Alberto’s birthday is 7 days after Corey’s birthday. Alberto’s birthday is on the 9th. Write and solve an equation to find the day of Corey’s birthday.

2. AGE Megan and Jason are brother and sister. Jason is 4 years older than Megan. If Jason is 16 years old, write and solve an equation to find Megan’s age.

3. PAPER AIRPLANES Rebecca and Ricardo are both testing their paper airplanes. Rebecca’s plane flew 6 feet further than Ricardo’s plane. If Rebecca’s plane flew 10 feet, write and solve an equation to find how far Ricardo’s plane flew.

4. BASEBALL CARDS Ren and Chet have just started collecting baseball cards. Ren has 13 more baseball cards than Chet. Ren has 27 cards. Write and solve an equation to find how many baseball cards Chet has.

5. SKATING Susan and Ruby went skating. Ruby skated 30 minutes longer than Susan. If Ruby skated for 45 minutes, write and solve an equation to find how long Susan skated.

6. STUNT FLYER A stunt airplane is flying at 150 feet. It ascends to 325 feet. Write and solve an equation to find the change in altitude of the airplane.

7. SAVINGS Oscar is saving money to buy a jacket that costs $47. He has already saved $25. Write and solve an equation to find how much more money Oscar needs to save.

8. RECYCLING Bonnie has 27 more cans than Jackie. If she has 56 cans, write and solve an equation to find how many cans Jackie has.


440


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Solving Addition Equations Pre-Activity Read the introduction at the top of page 339 in your textbook. Write your answers below. 1. Write an expression to represent 3 more inches of rain.

2. Write an addition equation you could use to find the rainfall before the additional 3 inches.

3. You could solve the addition equation by counting back on the number line. What operation does counting back suggest?

Reading the Lesson For Exercises 4–7, look at Example 2 at the top of page 340.

5. How is the Subtraction Property of Equality used in the solution?

6. What is the additive identity (Identity Property of Addition) and how is it used in the solution?

7. What does the checkmark at the end of the example indicate?

Helping You Remember 8. In your own words, describe what inverse means. Discuss your idea with a partner. How does the concept of inverse operations compare to your understanding of inverse?


441


Lesson 9–2

4. What is the inverse operation and why is it used?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Try This Balancing Act! Do you think you can choose four of these numbers and place them on the balance scale at the right so that the two sums are equal? 32, 43, 44, 54, 55 Experiment. Put 32 and 43 on the left part of the scale. The sum is 75. Now try to pick two of the remaining numbers to make a sum of 75. Each pair of numbers you pick will total more than 75. You have to start over again. This time put 43 and 44 on the left part of the scale. The sum is 87. Put 32 and 55 on the right part of the scale. That sum is also 87. You succeeded on the second try!

43 1 44 5 87

32 1 55 5 87

Choose two numbers for the left part of the scale and two numbers for the right part so that the two sums are equal. 1. 12, 19, 36, 43

2. 42, 44, 63, 65

3. 12, 28, 51, 54, 67

4. 96, 101, 108, 112, 113

5. Balance the four parts of the scale at the right by choosing two of the numbers for each part of the scale.

12, 20 4, 28

13, 19

4, 12, 13, 15, 17, 18, 19, 20, 21, 28

15, 17


442


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Solving Subtraction Equations Addition Property of Equality If you add the same number to each side of an equation, the two sides remain equal. 55 5 13 5 13 85 8

Solve x 2 2 5 1 using models. 2 2

5

x22

5

1

2 1 2 1

5

1 1 1

x2212

5

2 1 2 1

x

1

Model the equation.

Add 2 positive counters to each side of the mat.

112

5

1 1 1

5

3

Remove the zero pairs.

The solution is 3. Solve b 2 3 5 25.

Check

Write the equation. Add 3 from each side to undo the addition of 3 on the left. Simplify.

b 2 3 5 25 22 2 3 0 25 25 5 25 ✓

Write the original equation. Replace b with 22. This sentence is true.

Solve each equation. Use models if necessary. Check your solution. 1. a 2 2 5 3

2. b 2 1 5 7

3. c 2 4 5 4

4. 22 5 x 2 4

5. z 2 6 5 23

6. g 2 3 5 24

7. 29 1 w 5 1

8. v 2 8 5 5

9. 27 5 y 2 5

10. u 2 3 5 24


11. 22 5 t 2 9

443

12. f 2 6 5 23


Lesson 9–3

b 2 3 5 22 1 3 5 13 }}}}} b 1 0 5 22 b 5 22

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Solving Subtraction Equations Solve each equation. Use models if necessary. Check your solution. 1. a 2 1 5 7

2. b 2 2 5 1

3. 3 5 c 2 1

4. x 2 3 5 21

5. 23 5 y 2 4

6. 2 5 k 2 4

7. m 2 5 5 26

8. n 2 6 5 29

9. 210 5 s 2 8

10. t 2 9 5 21

11. v 2 9 5 25

12. 26 5 v 2 7

13. 3 5 g 2 6

14. 23 5 h 2 8

15. 25 5 z 2 7

16. z 2 3 5 7

17. 5 5 f 2 1

18. 21 5 d 2 2

19. e 2 9 5 26

20. 1 5 t 2 8

21. i 2 5 5 4

22. g 2 4 5 1

23. 23 5 x 2 2

24. y 2 4 5 27

25. If r 2 7 5 27, what is the value of r?

26. Find the value of b if b 2 2 5 5.


444


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. BIRDS A house cat, Sophie, scared away 5 birds when she arrived on the porch. If 3 birds remain, write and solve an equation to find how many birds were on the porch before Sophie arrived.

2. APPLES David brought apples to school one day. After giving one to each of his 5 closest friends, David had 6 apples left. Write and solve an equation to find how many apples David brought to school.

3. BASKETBALL The basketball team is practicing after school. Four students have to leave early. If 12 basketball players remain, write and solve an equation to find how many students are on the basketball team.

4. MARBLES Virginia’s mother gave her marbles for her birthday. Virginia lost 13 of them. If she has 24 marbles left, write and solve an equation to find how many her mother gave her.

5. MONEY Claudio went for a walk. While he was walking, $1.35 fell out of his pocket. When he returned home, he counted his money and had $2.55 left. Write and solve an equation to find how much money was in Claudio’s pocket when he started his walk.

6. HANG GLIDING Aida was hang gliding. After losing 35 feet in altitude, she was gliding at 125 feet. Write and solve an equation to find her height when she started hang gliding.

7. SHARKS The average great hammerhead shark is 11.5 feet long. The average great hammerhead shark is 13.5 feet shorter than the average whale shark. Write and solve an equation to find the length of the average whale shark.

8. JOKES At a party, Tex told 17 fewer knock-knock jokes than he did riddles. If he told 23 knock-knock jokes, write and solve an equation to find how many riddles Tex told at the party.


445


Lesson 9–3

Solving Subtraction Equations

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Solving Subtraction Equations Pre-Activity Read the introduction at the top of page 344 in your textbook. Write your answers below. 1. Let h represent Lucas’ height. Write an expression for 5 inches shorter than Lucas. 2. Write an equation for 5 inches shorter than Lucas is equal to 59 inches.

3. You could find Lucas’s height by counting forward. What operation does counting forward suggest? 4. How tall is Lucas?

Reading the Lesson 5. In modeling a subtraction equation, how and why are zero pairs used?

For Exercises 6 and 7, look at Example 2 on page 345. 6. What is the inverse operation and why is it used?

7. How is the Addition Property of Equality used in the solution?

8. In the equation y 2 4 5 210, how could you get the variable alone on one side of the equation?

Helping You Remember 9. Work with a partner. Pretend your partner missed this lesson on subtraction equations. Make up a subtraction equation and solve it for your partner on a piece of paper. Show each step and explain how an inverse operation, the Addition Property of Equality, and the Additive Identity are used. © Glencoe/McGraw-Hill

446


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Clock Arithmetic Did you realize that, when you work with elapsed time, you use a special kind of arithmetic that is called clock arithmetic? In clock arithmetic, you use the symbols ! for addition and @ for subtraction. Here are two examples. 11 12 1 2 10 9 3 8

11 12 1 2 10 9 3

4 7 6

8

5

4 5

7 6

8 o’clock plus 5 hours is 1 o’clock. 8!551

4 o’clock minus 7 hours is 9 o’clock. 4@759

Add or subtract using the 12-hour clock above. 1. 11 ! 3

2. 7 ! 9

3. 3 @ 10

4. 7 @ 8

5. 2 ! 12

6. 2 @ 12

7. 4 ! 6

8. 9 @ 4

To solve “clock equations” involving the 12-hour clock, use inverse operations. d!552

j @ 4 5 10

d!5@552@5

j @ 4 ! 4 5 10 ! 4

d59

j52

9. r ! 7 5 5

10. x @ 9 5 11

11. b ! 6 5 7

12. t @ 12 5 4

13. n @ 4 5 3

14. y ! 6 5 1

Challenge In clock arithmetic, you often work with clocks that have different numbers of hours. For example, the clock shown at the right is an 8-hour clock.

7

8

1

6

Solve each equation using the 8-hour clock at the right.

2 5

4

3

15. m ! 5 5 2

16. z @ 4 5 7

17. p ! 8 5 1

18. c @ 8 5 6

19. w @ 4 5 8

20. k ! 6 5 3


447


Lesson 9–3

Solve each equation using the 12-hour clock above.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Solving Multiplication Equations In a multiplication equation, the number by which a variable is multiplied is called the coefficient. In the multiplication equation, 2x 5 8, the coefficient is 2.

Solve 2x 5 6 using models.

2x

5

1 1 1 1 1 1

5

6

5

Model the equation.

1 1 1

Divide the 6 counters equally into 2 groups. There are 3 in each group.

1 1 1

Check 2x 5 6 2(3) 0 6 656 The solution is 3.

2x 2

5

6 2

x

5

3

Write the original equation. Replace x with 3. This sentence is true. ✓

Solve 24b 5 12. 24b 5 12

Write the equation.

12 24b } } 5 }} 24 24

Divide each side by 24 to get a single positive variable by itself.

1b 5 23 b 5 23

Simplify.

Check 24b 5 12 24(23) 0 12 12 5 12 The solution is 23.

Write the original equation. Replace b with 23. This sentence is true. ✓

Solve each equation. Use models if necessary. Check your solution. 1. 5a 5 25

2. 7c 5 49

3. 24 5 6d

4. 2x 5 28

5. 18 5 29y

6. 28g 5 216

7. 18 5 23z

8. 24w 5 236

9. 56 5 7v

10. 24 5 28f © Glencoe/McGraw-Hill

11. 3u 5 227

448

12. 242 5 6t Mathematics: Applications and Concepts, Course 1

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Solving Multiplication Equations 1. 3a 5 9

2. 7b 5 14

3. 36 5 9c

4. 215 5 5x

5. 242 5 6y

6. 8z 5 216

7. 24m 5 28

8. 22n 5 8

9. 221 5 7s

10. 225 5 25r

11. 218 5 26t

12. 29p 5 218

13. 2x 5 18

14. 4w 5 24

15. 6g 5 9

16. 232 5 2v

17. 218 5 3b

18. 7h 5 235

19. 28k 5 20

20. 14 5 24d

21. 272 5 9r

22. 23z 5 27

23. 5x 5 235

24. 28 5 8y

25. Solve the equation 9y 5 81.

26. What is w if 2w 5 16?


449


Lesson 9–4

Solve each equation. Use models if necessary. Check your solution.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Solving Multiplication Equations 1. BAND SOLO Kai’s solo in the next school band performance is 4 times as long as Dena’s solo. Kai’s solo is 12 minutes long. Write and solve an equation to find the length of Dena’s solo.

2. CATS Steve’s tabby cat eats 5 times as often as his black cat. The tabby cat ate 10 times yesterday. Write and solve an equation to find how many times the black cat ate.

3. FOOTBALL In last night’s football game, the home team earned 3 times as many points as the visiting team. They won the game with 21 points. Write and solve an equation to find how many points the visiting team had.

4. MONEY Paz has 3 times as much money in her wallet as in her pocket. There is $18 in her wallet. Write and solve an equation to find how much money is in her pocket.

5. MORNINGS It takes Jun 3 times as long as it takes Kendra to get ready in the morning. It takes Jun 45 minutes to get ready. Write and solve an equation to find how long it takes Kendra.

6. FISH In his home aquarium, Enli has 12 times as many guppies as he has goldfish. Enli just counted 72 guppies. Write and solve an equation to find how many goldfish he has.

7. MUSIC Ray’s favorite song is 2 times longer than Meli’s favorite song. Write and solve an equation to find the length of Meli’s favorite song if Ray’s lasts 6 minutes.

8. TRAILS The forest trail to Round Lake is 3 times longer than the rocky trail to Round Lake. The forest trail is 15 miles long. Write and solve an equation to find the length of the rocky trail.


450


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Solving Multiplication Equations Pre-Activity Read the introduction at the top of page 350 in your textbook. Write your answers below. 1. Let x 5 the amount Kara earns each hour. Write an expression for the amount Kara earns after x hours. 2. Explain how the equation 3x = 12 represents the situation.

Reading the Lesson 3. In the equation 3x = 12, what is the coefficient?

4. In the equation 3x = 12, what is the operation? How do you know?

5. In Example 1 on page 350, why are both sides of the equation divided by 3?

6. In Example 3 on page 351, why is the equation 3.6 = 0.4,?

7. Describe what is happening in each step. 23x 5 27 27 23x }} 5 }} 23 23

1x 5 29 x 5 29

8. Work with a partner. Explain how you use division to solve a multiplication problem. Describe an example from real life where you would use division in this way.


451


Lesson 9–4


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Patterns in Equations On this page, you will explore patterns of change in equations. For each table: a. Describe how the equation changes from row to row. b. Complete the Solution column. c. Describe how the solution changes from row to row. 1.

3.

5.

Equation

Solution

2.

Equation

t1354

3x 5 6

t1353

3x 5 3

t1352

3x 5 0

t1351

3x 5 23

Equation

Solution

4.

Equation

r 2 3 5 22

m1857

r 2 3 5 21

m1757

r2350

m1657

r2351

m1557

Equation 1 }}j 5 1 }}j 5 1 }}j 5 1 }}j 5

Solution

6.

1 }}c 4 1 }}c 3 1 }}c 2 1 }}c 1

51 50 5 21 5 22


Equation

452

Solution

Solution

Solution

5 21 5 21 5 21 5 21


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Equations that have two different operations are called two-step equations. You can work backward using the reverse of the order of operations to solve a two-step equation.

Solve 2x 1 4 5 10 using models. 1 1 1 1

2x 1 4 1 1 1 1

2x 1 4 2 4

5

1 1 1 1 1 1 1 1 1 1

5

10

5

Model the equation.

1 1 1 1 1 1

Remove 4 counters from each side to get the variable by itself.

1 1 1 1 10 2 4

5

1 1 1

Divide the 6 counters equally into 2 groups. There are 3 in each group.

5 1 1 1 2x x

6 3

5 5

Solve 23z 2 4 5 8. Check your solution. 23z 2 4 5 8 14514 23z 5 12

12 23z } } 5 }} 23 23

Write the equation. Add 4 to each side. Simplify.

Check 23z 2 4 5 8 23(24) 2 4 0 8 12 2 4 0 8 858 ✓

Divide each side by 23.

Write the original equation. Replace z with 24. Multiply. Simplify.

z 5 24 Simplify. The solution is 24.

Solve each equation. Use models if necessary. 1. 4m 1 5 5 9

2. 3n 1 4 5 22

3. 3 5 2s 2 5

4. 5 5 27 1 4b

5. 6a 2 5 5 7

6. 213 1 3c 5 8

7. One more than four times a number is thirteen. What is the number? 8. Three is seven less than two times a number. What is the number? © Glencoe/McGraw-Hill

453


Lesson 9–5

Solving Two-Step Equations

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Solving Two-Step Equations Solve each equation. Use models if necessary. 1. 2a 1 4 5 6

2. 3b 1 4 5 10

3. 7 5 4c 2 5

4. 3x 2 3 5 26

5. 4y 2 2 5 214

6. 3 5 2g 1 5

7. 1 5 2f 2 7

8. 2 5 3h 1 8

9. 5z 1 1 5 16

10. 7m 2 5 5 9

11. 1 5 8n 2 7

12. 211 5 9s 1 7

13. 4t 1 7 5 25

14. 4v 1 10 5 26

15. 6 5 2x 2 10

16. 3w 1 5 5 27

17. 2r 2 5 5 3

18. 5 5 2z 2 9

19. Fourteen less than four times a number is six. What is the number?

20. Two is four more than twice a number. What is the number?

21. Nine less than three times a number is zero. What is the number?

22. Two is seventeen more than three times what number?


454


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. FIRE TRUCKS Fire Station A has one more than twice as many fire trucks as Fire Station B. If Fire Station A has three fire trucks, write and solve an equation to find how many fire trucks Fire Station B has.

2. TOY CARS Tanisha has 7 less than 4 times as many toy cars as Fernando. If Tanisha has 9 cars, write and solve an equation to find how many toy cars Fernando has.

3. ADDRESS Danielle and Erin live on the same street. Danielle lives at number 13. If Danielle’s house number is 5 less than 3 times Erin’s house number, write and solve an equation to find Erin’s house number.

4. BIRTHDAY CAKE Mrs. Zeng is slicing her son’s birthday cake. To make sure everyone will have enough, she slices the cake so that the number of slices is 6 more than twice the number of people at the party. If she slices the cake into 20 slices, write and solve an equation to find how many people are at the party.

5. DINOSAURS The largest complete dinosaur we know of was a Brachiosaurus. It reached a length of 23 meters. Its length was one less than twice its height. Write and solve an equation to find the height of the Brachiosaurus.

6. BABY-SITTING Last week, Enrique earned $30.00 baby-sitting. Enrique earned $5.00 less than 7 times what Rhea earned. Write and solve an equation to find how much money Rhea earned baby-sitting last week.

7. ELECTION Raj received 8 more than 3 times as many votes as Vinny in a school election. Raj received 44 votes. Write and solve an equation to find how many votes Vinny received.

8. JACK-O-LANTERN It took Suki 127 minutes from start to finish to carve her pumpkin. Carving the pumpkin took her 13 fewer minutes than 10 times as long as it took her to pick the pumpkin out at the pumpkin patch. Write and solve an equation to find how long it took Suki to pick out her pumpkin.


455


Lesson 9–5

Solving Two-Step Equations

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Solving Two-Step Equations Pre-Activity Read the introduction at the top of page 355 in your textbook. Write your answers below. 1. Let x 5 the cost of one book. How does the equation 2x 1 3 5 11 represent the situation?

2. Subtract 3 from each side of the equation. Write the equation that results. 3. Divide each side of the equation you wrote by 2. Write the result. What is the cost of each book?

Reading the Lesson 4. In the paragraph before Example 1 on page 355, it says that to solve a two-step equation you need to work backward using the reverse of the order of operations. What is the order of operations in the equation 2x 1 3 5 11? Tell how you would solve each of the following equations. 5. 2y 1 14 5 36

6. 225 5 22 1 3x

7. The last sentence of Example 3 on page 356 asks the question, “Is this answer reasonable?” Tell how you would find the answer to that question. Show your results.

Helping You Remember 8. Work with a partner. Think of two situations similar to the one described in Example 3 on page 356. Each of you chooses one of the situations and writes a word problem that describes the situation. Exchange word problems with your partner. Write an equation for the word problem you receive, and solve the equation.


456


NAME ________________________________________ DATE ______________ PERIOD _____

Chunking Have you ever seen an equation like 3(t 1 1) 5 18? The expression inside parentheses might make you think that solving this equation is going to be difficult. But, if you can solve 3t 5 18, you probably can solve this equation, too. The trick is to think of the expression (t 1 1) as a chunk. Here’s how. 3(t 1 1) 5 18 means the same as (t 1 1) 5 18 4 3. (t 1 1) 5 18 4 3 (t 1 1) 5 6 You know 5 1 1 5 6, so t 5 5. Solve each equation by chunking. 1. 4(a 1 3) 5 40

2. 2(m 2 5) 5 8

3. 3(c 2 2) 5 18

4. 25 5 5(z 1 4)

5. 14 5 7(k 2 4)

6. 20 5 4(x 1 1)

7. 6(1 1 x) 5 24

8. 3(12 2 r) 5 30

9. 8(9 1 t) 5 104

10. 8 5 8(b 2 5)

11. 2(6 2 q) 5 0

12. 0 5 6(10 2 a)

13. 1.3(x 1 1) 5 6.5

14. 0.4(j 2 9) 5 0.8

15. 1.5(k 2 6) 5 9

16. 0.2 5 0.05(y 1 2)

17. 0.24(d 2 5) 5 2.16

18. 0.12(e 1 2) 5 0.36


457


Lesson 9–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Functions A function rule describes the relationship between the input and output of a function. The inputs and outputs can be organized in a function table.

Complete the function table. Input (x) Output (x 2 7) 9 j 8 j 6 j The function rule is n 2 7. Subtract 7 from each input. Input 9 8 6

Output 27→ 2 27→ 1 2 7 → 22

→

Input (x) Output (x 2 7) 9 2 8 1 6 21

Find the rule for the function table. Input (x) Output (j) 23 212 1 4 2 8 Study the relationship between each input and output. Input 23 1 2

Output 3 4 → 212 34→ 4 34→ 8

The output is four times the input. So, the function rule is 4n.

Complete each function table. 1. Input (x) 21 2 4

Output (2x)

22

2. Input (x) Output (4 1 x) 23 1 4

Find the rule for each function table. 3. Input (x) 24 2 5


Output 22 4 7

4. Input (x) 24 2 6

458

Output 22 1 3


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Functions Complete each function table. 2. Input (x)

0

21

2

1

4

2

3. Input (x) Output (x 2 1)

4. Input (x)

Output (23x)

14 2

Output }1}x

25 28

21

0

4

8

5. If a function rule is 2x 2 3, what is the output for 3? 6. If a function rule is 4 2 x, what is the output for 22?

Find the rule for each function table. Write the rule in the table. 7.

9.

8.

x

x

21

24

23

212

0

23

0

29

2

21

4

25

10.

x

x

23

215

22

210

3

15


459

212

6

1

2}1}

6

23

2


Lesson 9–6

1. Input (x) Output (x 1 3)

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Functions 1. DRAGONS The Luck Dragons that live in the Enchanted Forest weigh 4x pounds when they are x years old. Write a function table that can be used to find the weights of 6-year old, 8-year old, and 10-year old Luck Dragons.

2. ROLLER COASTER Twelve people are able to ride the Serpent of Fire roller coaster at one time. Write a function table that shows the total number of people that have been on the roller coaster after 1, 2, 3, and 4 rides.

3. MOVIES At the local movie theater it costs $10.00 for 2 students to see a movie. It costs $15.00 for 3 students, and it costs $20.00 for 4 students. Let the number of students be the input. What is the function rule that relates the number of students to the cost of tickets?

4. HOMEWORK At Elmwood Middle School, sixth graders spend 1 hour every night doing homework. Seventh graders spend 2 hours, and eighth graders spend 3 hours. Let the students’ grade be the input. What is the function rule between the students’ grade and the amount of time the students spend on homework every night?

5. BEADS A bead shop sells wooden beads for $3 each and glass beads for $7 each. Write a function rule to represent the total selling price of wooden (w) and glass (g) beads.

6. Use the function rule in Exercise 5 to find the selling price of 20 wooden beads and 4 glass beads.


460


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Functions Pre-Activity Read the introduction at the top of page 362 in your textbook. Write your answers below.

2. Write an expression to represent the number of mosquitoes a brown bat can eat in 5 hours.

3. Write an expression to represent the number of mosquitoes a brown bat can eat in t hours.

Reading the Lesson 4. If you look up the word function in a dictionary, you might find a definition like the following: a quantity whose value depends on that of another quantity or quantities. In the function 600t, what does the value of 600t depend on?

5. Find the function rule for the table below. Input (x)

Output (j)

22

1

0

3

2

5

Helping You Remember 6. Work with a partner. Each of you creates a table like the one in Exercise 5 above. Decide on a function rule to use for the output quantities, but do not write the rule. Exchange tables with your partner. Identify the function rule that expresses the relationship between the input quantity and the output quantity.


461


Lesson 9–6

1. Write an expression to represent the number of mosquitoes a brown bat can eat in 2 hours.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Function Rules and Dot Patterns Function rules are often used to describe geometric patterns. In the pattern at the right, for example, do you see this relationship? 1st figure: 2nd figure: 3rd figure: 4th figure:

3 3 3 3

3 3 3 3

1 2 3 4

5 5 5 5

3 dots 6 dots 9 dots 12 dots

1st

3 dots

2nd

6 dots

3rd

9 dots

4th

12 dots

So the “nth” figure in this pattern would have 3 3 n, or 3n, dots. A function rule that describes the pattern is 3n. Write a function rule to describe each dot pattern. 1. 1st

2. 1st

3. 1st

2nd

2nd

2nd

3rd

3rd

3rd

4th

4th

4. 1st

5. 1st

6. 1st

2nd

2nd

2nd

3rd

3rd

3rd

4th

4th

4th

4th

7. CHALLENGE Create your own dot pattern. Then exchange patterns with a classmate. Try to find the function rule for each other’s patterns.


462


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Graphing Functions Make a function table for the rule y 5 x 1 2. Use input values of 22, 0, and 2. Then graph the function. Record the input and output in a function table. List the input and output as ordered pairs.

Step 2

Graph the ordered pairs on the coordinate plane.

Step 3

The points appear to lie on a line. Draw the line that contains these points. The line is the graph of y 5 x 1 2.

Input Function Rule Output Ordered Pairs (x) (x 1 2) (y) (x, y) 0 22 22 1 2 (22, 0) 0 2 (0, 2) 012 2 4 (2, 4) 212 y 4 (2, 4) 3 2 1 (0, 2)

The y-coordinates represent the output values. (22, 0) 242322

Make a function table for the graph. Then determine the function rule. Input (x) Output (y) 2 21 1 22 2 24 Input Output 21 3 (22) 2 1 3 (22) 22 2 3 (22) 24

O 22 23 24

1 2 3 4x

(1, 22) (2, 24)

22 is multiplied by each input to get the output. The function rule is y 5 22x.

2. Make a function table for the graph. Then determine the function rule. y 4 3 2 1

Output (4n)

0 242322

1

O

1 2 3 4x

(2, 21)

22 (1, 22) 23 ( 0, 23) 24

y 4 3 2 1 O

y 4 3 2 1

242322

21

242322

1 2 3 4x

(21, 2)

(x, y) (21, 2) (1, 22) (2, 24)

1. Complete the function table. Then graph the function. Input (n)

O

The x-coordinates represent the output values.

1 2 3 4x

22 23 24


463


Lesson 9–7

Step 1

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Graphing Functions Complete each function table. Then graph the function. 1.

Input (x)

Output (x 1 4)

2.

Input (x)

Output (3 2 x)

3.

Input (x)

–5

2

–3

–3

3

0

0

4

3

y 4 3 2 1 O

2625242322

y 4 3 2 1 1 2x

y 4 3 2 1 1 2 3 4x

O

242322

22 23 24

13 2

Output }1}x

242322

22 23 24

O

1 2 3 4x

22 23 24

Make a function table for each graph. Then determine the function rule. 4. (24, 2)

242322

y 4 3 2 1 (0, 0) O

1 2 3 4x

22 (2, 21) 23 24


5.

6.

y 4 3 2 1 242322

O 22 23 24

x 1 2 3 4

(4, 21) (2, 23) (1, 24)

464

y (25, 5) 5 (24, 4) 4

(22, 2) 25 242322

3 2 1 O

x 1 2 3

22 23


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Graphing Functions 2. CD RACK A CD rack fits 3 CDs across. When one shelf is full, the shelf has 3 CDs on it. When two shelves are full, it has 6 CDs, and when three shelves are full it has 9 CDs. Let the number of full shelves be the input and the number of CDs be the output. y 14 Graph the function. 12 10 8 6 4 2

1 O

1 2 3 4 5 6 7x

3. TELEPHONE Althea made a graph of how many friends call her after school. She let the number of hours that passed be the input and the number of people who called be the output. Look at her graph and determine the function rule. y 7 6 5 4 3 2 1

O

(2, 4)

O

4. DOLPHINS The more dolphins Toni uses in the dolphin show, the more people attend the show. She let the number of dolphins be the input and the number of attendees be the output, and made a graph of the function. Look at her graph and y 70 determine the 60 function rule. 50 (5, 50) 40 30 20 10

(1, 2) (0, 0) 1 2 3 4 5 6 7x

5. BOTANY Jessie planted a bean plant that was 2 inches tall. Each day it grew 1 inch. Tanya planted a bean plant that was 1 inch tall. It grew 2 inches per day. Write the function rule for each bean plant.

O

(3, 30) (1, 10) 1 2 3 4 5 6 7x

6. BOTANY Graph each function from Exercise 5 on the same coordinate plane. What does the intersection of the two graphs represent? y

O


2 4 6 8 10 12 14x

465

x


Lesson 9–7

1. LIBRARY Tia visited the library 3 times. The first time, she spent 1 hour and checked out 4 books. Then she spent 2 hours and checked out 5 books. On her last visit, she spent 3 hours and checked out 6 books. Let the number of y hours be the input 7 and the number 6 5 of books be the 4 output. Graph the 3 function. 2

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Graphing Functions Pre-Activity Read the introduction at the top of page 366 in your textbook. Write your answers below. 1. Complete the table below to find the amount you would save in 2, 3, and 6 weeks. Savings Number of Weeks

Multiply by 2.

1

231

Amount Saved $2

2 3 6 2. Graph the ordered pairs (number, amount saved). Describe how the points appear on the grid.

3. What happens to the amount saved as the number of weeks increases?

12 10 8 6 4 2

y

1 2 3 4 5 6x

Reading the Lesson 4. Example 1 on page 366 uses the term ordered pairs and lists input and output data as ordered pairs in the function table. What is an ordered pair?

5. Complete the function table. Then graph the function.

y 4 3 2 1

Input Function Rule Output Ordered Pairs (x) (x 2 2) (y) (x, y) 22

242322

0

O

1 2 3 4x

22 23 24

2

Helping You Remember 6. Draw a line on grid paper. It can be in any direction. Make a function table for the line you graphed. Then determine the function rule.


466


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

An everyday example of a function is the relationship between distance and time. You can picture this relationship in a graph like the one at the right. This particular graph pictures a situation in which a person travels at a constant rate, and so the graph is a straight line segment.

distance

Interpreting Graphs of Functions

In reality, you seldom travel at a constant rate during an entire trip. You might switch from running to walking, for example, or you might stop to rest. On this page, you will work with graphs that represent situations like these.

time

1. Patty ran for 15 minutes, then walked for 15 minutes.

2. Helmer walked for 15 minutes, then ran for 15 minutes.

3. Dale ran for 10 minutes, stopped to rest for 10 minutes, then walked for 10 minutes.

4. Josita ran for 10 minutes, stopped to rest for 10 minutes, then ran for 10 more minutes.

5. Janette ran for 10 minutes, walked for 10 minutes, then ran for 10 more minutes.

6. Ralph ran for 15 minutes, walked for 10 minutes, then ran for 5 more minutes.

time

time

time

time

distance

F distance

E distance

D

distance

C distance

B distance

A

time

time

7. CHALLENGE Assume that all the people described in Exercises 1–6 ran at the same rate, and they all walked at the same rate. Who traveled farthest in 30 minutes?


467


Lesson 9–7

Refer to the graphs below. Write the letter of the graph that best pictures each of these situations.

Chapter Chapter 10 X Resource Resource Masters Masters

Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860073-1 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03









Chapter 10 Assessment Chapter 10 Test, Form 1 ........................531–532 Chapter 10 Test, Form 2A ......................533–534 Chapter 10 Test, Form 2B ......................535–536 Chapter 10 Test, Form 2C......................537–538 Chapter 10 Test, Form 2D......................539–540 Chapter 10 Test, Form 3 ........................541–542 Chapter 10 Extended Response Assessment .................................................543 Chapter 10 Vocabulary Test/Review...............544 Chapter 10 Quizzes 1 & 2..............................545 Chapter 10 Quizzes 3 & 4..............................546 Chapter 10 Mid-Chapter Test .........................547 Chapter 10 Cumulative Review......................548 Chapter 10 Standardized Test Practice..549–550 Standardized Test Practice Student Recording Sheet ..............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A32

iii



Practice: Skills










iv


Enrichment




• Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. • A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and freeresponse questions.











v

NAME ________________________________________ DATE ______________ PERIOD _____

Reading To Learn Mathematics This is an alphabetical list of new vocabulary terms you will learn in Chapter 10. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term

Found on Page


cross products

equivalent ratios

percent

proportion

rate

ratio

scale

scale drawing

scale model

unit rate


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: ns help us to make Ratios, rates, percents, and proportio models of objects and to decisions. We can use them to make can also use them to make determine distances on a map. We ter buy at a grocery budget decisions, to determine the bet store, and to calculate sales tax. and Percent, your child In Chapter 10: Ratio, Proportion, rates as fractions, to solve will learn how to express ratios and by drawing a diagram. Your proportions, and to solve problems percents as fractions and child will also learn how to express a number. Your child will decimals and to find the percent of assignments and activities complete a variety of daily classroom . and possibly produce a chapter project it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 10 to the real world. You math we will be learning in Chapter line Study Tools for may also wish to log on to the On t Study Guide pages, and self-check quizzes, Parent and Studen et. If you have any other study help at www.msmath1.n contact me at school. questions or comments, feel free to Sincerely,

Signature of Parent or Guardian ________________________________________DATE ________


ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Cars, Trucks, and Percents Work with a family member to answer the following questions. Ask ten family members or friends what kind of cars they drive: sports utility, truck, sedan, van, convertible, or other. Record the results in the space below. 1. a. What percent of these people drive sports utility vehicles?

b. Express the percent as a decimal.

2. a. What percent of these people drive trucks?


3. a. What percent of these people drive sedans?


4. a. What percent of these people drive vans?



x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Ratios A ratio is a comparison of two numbers by division. A common way to express a ratio is as a fraction in simplest form. Ratios can also be written in other ways. For example, the ratio }2} can be written as 3 2 to 3, 2 out of 3, or 2:3.

Refer to the diagram at the right. Write the ratio that compares the number of circles to the number of triangles. circles triangles

➝ }4} The GCF of 4 and 5 is 1. ➝ 5

So, the ratio of circles to triangles is }4}, 4 to 5, or 4:5. 5 For every 4 circles, there are 5 triangles. Write the ratio that compares the number of circles to the total number of figures.

N

➝ }4} 5 }2} The GCF of 4 and 10 is 2. ➝ 10 N 5 42

The ratio of circles to the total number of figures is }2}, 2 to 5, or 2:5. 5 For every two circles, there are five total figures. A rate is a ratio of two measurements having different kinds of units. When a rate is simplified so that it has a denominator of 1, it is called a unit rate.

Write the ratio 20 students to 5 computers as a unit rate. 45

N

20 students }} 5 computers

4 students }} 1 computer

Divide the numerator and the denominator by 5 to get a denominator of 1.

N

45

The ratio written as a unit rate is 4 students to 1 computer.

Write each ratio as a fraction in simplest form. 1. 2 guppies out of 6 fish

2. 12 puppies to 15 kittens

3. 5 boys out of 10 students

Write each ratio as a unit rate. 4. 6 eggs for 3 people


5. $12 for 4 pounds

491

6. 40 pages in 8 days


Lesson 10–1

42

circles total figures

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Ratios Write each ratio as a fraction in simplest form. 1. 3 sailboats to 6 motorboats

2. 4 tulips to 9 daffodils

3. 5 baseballs to 25 softballs

4. 2 days out of 8 days

5. 6 poodles out of 18 dogs

6. 10 yellow eggs out of 12 colored eggs

7. 12 sheets of paper out of 28

8. 18 hours out of 24 hours

9. 16 elms out of 20 trees

10. 15 trumpets to 9 trombones

11. 5 ducks to 30 geese

12. 14 lions to 10 tigers

13. 6 sodas out of 16 drinks

14. 20 blue jays out of 35 birds

Write each ratio as a unit rate. 15. 14 hours in 2 weeks

16. 36 pieces of candy for 6 children

17. 8 teaspoons for 4 cups

18. 8 tomatoes for $2

19. $28 for 4 hours

20. 150 miles in 3 hours

21. $18 for 3 CDs

22. 48 logs on 6 trucks

23. Write the ratio 21 wins to 9 losses as a fraction in simplest form.

24. Write the ratio $12 dollars for 3 tickets as a unit rate.


492


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Ratios 1. FOOTBALL In the NFL 2001–2002 season, the Miami Dolphins won 11 games and the Oakland Raiders won 10 games. What is the ratio of wins for the Dolphins to wins for the Raiders?

2. GARDENING Rod has 10 rosebushes, 2 of which produce yellow roses. Write the ratio 2 yellow rosebushes out of 10 rosebushes in simplest form.

3. TENNIS Nancy and Lisa played 20 sets of tennis. Nancy won 12 of them. Write the ratio of Nancy’s wins to the total number of sets in simplest form.

4. AGES Oscar is 16 years old and his sister Julia is 12 years old. What will be the ratio of Oscar’s age to Julia’s age in 2 years? Write as a fraction in simplest form.

9 }} 7

5. MOVIES Four friends paid a total of $32 for movie tickets. What is the ratio $32 for 4 people written as a unit rate?

6. WORKING At a warehouse, the employees can unload 18 trucks in 6 hours. What is the unit rate for unloading trucks?

7. ANIMALS A reindeer can run 96 miles in 3 hours. At this rate, how far can a reindeer run in 1 hour? Explain.

8. SHOPPING Jenny wants to buy cereal that comes in large and small boxes. The 32-ounce box costs $4.16, and the 14-ounce box costs $2.38. Which box is less expensive per ounce? Explain.


493


Lesson 10–1

1 }} 5

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Ratios Pre-Activity Read the introduction at the top of page 380 in your textbook. Write your answers below. 1. Write a sentence that compares the number of navy socks to the number of white socks. Use the word less in your sentence.

2. Write a sentence that compares the number of black socks to the number of white socks. Use the word half in your sentence.

3. Write a sentence comparing the number of white socks to the total number of socks. Use a fraction in your sentence.

Reading the Lesson 4. A ratio compares amounts of two different things by division. Tell what different things are compared in the examples in your textbook. Example 1 Example 2 5. Write the ratio of 2 pens out of a total of 3 pens 4 different ways.

6. What is the denominator in a unit rate?

Helping You Remember 7. Go to your local grocery store and make a list of unit rates that are used to price items in the store. Also, compare prices for different brands of a certain product. How can you find out which brand provides the best value? Does the store help you to make the comparison? If so, how?


494


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Ratios and Rectangles 1. Use a centimeter ruler to measure the width and the length of each rectangle. Then express the ratio of the width to the length as a fraction in simplest form.

B A

Lesson 10–1

C

E D

2. Similar figures have the same shape, but not necessarily the same size. Two rectangles are similar if the ratio of the width to the length is the same for each. Which rectangles in Exercise 1 are similar? 3. For centuries artists and architects have used a shape called the golden rectangle because people seem to find it most pleasant to look at. In a golden rectangle, the ratio of the width to the length is a little less than 5 }}. Which rectangle in Exercise 1 is most nearly a golden rectangle? 8


495


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Solving Proportions A proportion is an equation stating that two ratios are equivalent. For example, the ratios }1} and }3} are 2

6

equivalent, so the equation }1} 5 }3} is a proportion. In order for two ratios to form a proportion, their 2

6

cross products must be equal. 1 3 5 2 6

1 3 6 is one cross product

2 3 3 is the other cross product

1365233 656 The cross products are equal

When one value in a proportion is unknown, you can use cross products to solve the proportion.

Solve }2} 5 }4}. 5

Solve }3} 5 }b}. 4

n

2 3 n 5 5 3 4 Cross products 2n 5 20 Multiply. 2n 20 } } 5 }} 2 2

3 3 12 5 4 3 b 36 5 4b 36 4b }} 5 } } 4 4


n 5 10 The solution is 10.

12

Cross products Multiply. Divide each side by 4.

95b The solution is 9.

Determine whether each pair of ratios form a proportion. Explain your reasoning. 1. }3}, }6}

2. }2}, }4}

5 10

9 16

Solve each proportion. 3. }2} 5 }8}

12 4. }3} 5 } }

5. }2} 5 }y}

6. }3} 5 }b}

c 1.2 7. } } 5 }}

8. }d} 5 }3}

3

5

4

n

15

1.5 9. }x} 5 } } 2.6

1.3


4

x

1.5

9

16

10. }2} 5 }6} y

8

8

0.1 0.5 11. } } 5 }}

9

2.6

496

z


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Solving Proportions Solve each proportion. 1. }2} 5 }8}

2. }2} 5 }4}

3. }3} 5 }b}

4. }2} 5 }c} 36

5. }4} 5 }d}

20 10 6. } } 5 }}

28 7. }g} 5 } } 14

10 8. }2} 5 } } 25

9. }4} 5 }h}

10 2 10. } } 5 }}

11. }t} 5 }3} 6

12. }2} 5 }6}

13. }9} 5 }s}

14. }n} 5 }2} 6

12 15. }4} 5 } }

16. }5} 5 }m} 12

17. }d} 5 }4} 9

15 18. }5} 5 } }

15 5 19. } } 5 }} k

20 20. }4} 5 } } 30

24 21. }b} 5 } }

22. }z} 5 }4} 7

24 23. }6} 5 } } 28

24. }6} 5 }x}

14 b 25. } } 5 }}

24 26. }8} 5 } }

t 16 27. } } 5 }}

1.2 2.4 28. } } 5 }}

s 0.5 29. } } 5 }}

8 1.6 30. } } 5 }}

9

2

30

2

6

27

35

16

2.4

7

x

5

x

18

r

6

36

27

x

c

8

r

1.8

n

5

y

30

4

25

3

3

u

8

3

8

27

36

9

w

f

18

m

21

q

9

24

9

16

31. What is the solution of }3} 5 }2}? Round to the nearest tenth. 5

k

4.3 n 32. Find the solution of } } 5 }} to the nearest tenth. 3


2.2

497


Lesson 10–2

5

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Solving Proportions 1. SCHOOL The ratio of boys to girls in history class is 4 to 5. How many girls are in the class if there are 12 boys in the class? Explain.

2. FACTORIES A factory produces 6 motorcycles in 9 hours. Write a proportion and solve it to find how many hours it takes to produce 16 motorcycles.

6 16 }} 5 }}; 24 h x 9

3. READING James read 4 pages in a book in 6 minutes. How long would you expect him to take to read 6 pages?

4. COOKING A recipe that will make 3 pies calls for 7 cups of flour. Write a proportion and solve it to find how many pies can be made with 28 cups of flour.

p 3 }} 5 }}; 12 pies 28 7

5. TYPING Sara can type 90 words in 4 minutes. About how many words would you expect her to type in 10 minutes?

6. BASKETBALL The Lakewood Wildcats won 5 of their first 7 games this year. There are 28 games in the season. About how many games would you expect the Wildcats to win this season? Explain your reasoning.

20 games; Sample answer: If

the season, }5} 5 }x}. 7

7. FOOD Two slices of Dan’s Famous Pizza have 230 Calories. How many Calories would you expect to be in 5 slices of the same pizza?

28

8. SHOPPING Andy paid $1.40 for 4 grapefruits. Write a proportion and solve it to find how many grapefruits he can purchase for $2.10.

$1.40 $2.10 }} 5 }}; 6 grapefruits 4 x


498


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Solving Proportions Pre-Activity Complete the Mini Lab at the top of page 386 in your textbook. Write your answers below. 1. Complete each ratio so that the ratios comparing the areas are equivalent. a. b.

5

5

?

?

2. How did you find which figure made the ratios equivalent?

3. Suppose a green block equals 2, a blue block equals 4, a yellow block equals 6, and a red block equals 3. Write a pair of equivalent ratios.

Reading the Lesson 5. Look at the arithmetic example in the Key Concept box on page 386. What is the significance of the two instances of 3 3?

6. If two ratios are equivalent, and therefore form a proportion, what do you know about the cross products? 7. Look at the final sentence in Example 3 on page 387—‘‘So, 375 students can be expected to prefer gel toothpaste.’’ Why is it important to use can be expected in this answer?

Helping You Remember 8. Work with a partner. Study Example 1 on page 387. Write a proportion that needs to be solved for an unknown value. Exchange proportions and solve for the unknown value. Explain how you arrived at your solution.


499


Lesson 10–2

4. What relationship exists in these equivalent ratios?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Ada Did you know that a woman wrote the first description of a computer programming language? She was the daughter of a famous English lord and was born in 1815. She had a deep understanding of mathematics and was fascinated by calculating machines. Her interests led her to create the first algorithm. In 1843, she translated a French version of a lecture by Charles Babbage. In her notes to the translation, she outlined the fundamental concepts of computer programming. She died in 1852. In 1979, the U.S. Department of Defense named the computer language Ada after her. To find out this woman’s full name, solve the proportion for each letter. 28 1. }7} 5 } } 40

2. }5} 5 }B}

3. }1} 5 }C}

35 4. }5} 5 } }

5. }2} 5 }E}

6. }2} 5 }L}

12 7. }6} 5 } }

8. }9} 5 }O}

9. }2} 5 }R}

A

D

N

4

63

5

25 10. }5} 5 } } V

20

11

14

3

36

18

44

8

15

27

4

11. }7} 5 }Y}

30

4

28

Now look for each solution below. Write the corresponding letter on the line above the solution. If you have calculated correctly, the letters will spell her name.

}} }} }} 10

9

10

}}

}}

}}

3

36

6

}} }} }} }} }} }} 8


45

49

}}

}} }} }}

3

10

1

5

36

7

8

500


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Scale Drawings and Models Scale drawings and scale models are used to represent objects that are too large or too small to be drawn or built at actual size. The scale gives the ratio that compares the measurements on the drawing or model to the measurements of the real object. The measurements on a drawing or model are proportional to the measurements of the actual object. RACE CARS A model of a race car has a width of 3.5 inches. The scale

is 1 inch 5 2 feet. Find the actual width of the race car. Let w represent the actual width. Scale

Race Car 3.5 ➝ model width ➝ }1} 5 } } 2 w ➝ actual width ➝

model width actual width

1 3 w 5 2 3 3.5 w57

Find the cross products. Multiply.

The actual width of the race car is 7 feet. HIKING On a map, the distance between Round Lake and June Lake is 6 inches. The scale on the map is 3 inches 5 5 miles. Find the actual distance between the two lakes.

Let d represent the actual distance. Map Scale

Actual Distance

➝ }3} 5 }6} ➝ map distance d ➝ actual distance ➝ 5 3 3 d 5 5 3 6 Find the cross products. 3d 5 30 Multiply.

map distance actual distance

3d 30 } } 5 }} 3 3

Divide.

The distance between the two lakes is 10 miles.

DRAFTING For Exercises 1–4, use the following information.

On a set of drawings, the scale is 2 inch 5 4 feet. Find the actual measurements. 1. 2. 3. 4.

Object door wall tree computer

Drawing Actual Size 4 inches 6 inches 12 inches 1 inch


5. MAPS A map has a scale of 2 inches 5 7 miles. The distance between Pirate’s Cove and Midnight Lagoon on the map is 12 inches. What is the actual distance between the two places?

501


Lesson 10–3

d 5 10

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Scale Drawings and Models DRAFTING On a set of drawings, the scale is 2 inches 5 3 feet. Find the actual measurements.

1. 2. 3. 4. 5. 6.

Object table wall road door computer lamp

Drawing 4 inches 10 inches 18 inches 5 inches 1 inch 0.5 inch

Actual Size

LIZARDS Models of lizards were made using the given scales. Find the actual measurements.

Scale: 1 inch 5 }1} inch 2

7. 8.

Whiptail Lizard body length tail length

Model 6 inches 12 inches

Actual Size

Model 9 inches 18 inches

Actual Size

Model 3.6 inches 2 inches

Actual Size

Scale: 2 inches 5 3 inches 9. 10.

Desert Iguana body length tail length

Scale: 4 inches 5 5 inches 11. 12.

Ground Gecko body length tail length

MAPS A map has a scale of 3 inches 5 7 miles. Find the actual distance between the cities with the map distances given.

13. 8.4 inches between Fall City and Summit

14. 2 inches between Potter and Green River


502


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Scale Drawings and Models 1. MAPS On a map with a scale of 1 inch 5 9 miles, the distance between two towns is 3 inches. What is the actual distance between the two towns?

2. BLUEPRINTS On an architect’s blueprint, the front of a building measures 27 inches. The scale of the blueprint is 1 inch 5 2 feet. How wide will the front of the actual building be?

3. MODELS The model of an airplane has a wingspan of 20 inches. The model has a scale of 1 inch 5 4 feet. What is the wingspan of the actual airplane?

4. ARCHITECTURE The drawing for a building has a scale of 1 inch 5 3 feet. The building in the drawing has a height of 14 inches. How tall will the actual building be?

5. ROCKETS A model of the Saturn V rocket has a scale of 1 inch 5 12 feet. If the model rocket is 30 inches tall, how tall was the actual Saturn V rocket?

6. CARS Ron took a photograph of his car and then measured the length of the car in the photograph. The length was

7. MODELS A model of a 4-cylinder gasoline engine is built on a scale of 1 inch 5 6 inches. If the length of the model engine is 9 inches, how long is the actual engine?

8. PHOTOGRAPHY A photo lab technician is going to reduce a photograph that is 9 inches wide using a scale of


4}1} inches. If the scale of the 2

1 inch 5 }2} inch. How wide will the 3

reduced photo be?

503

6 in.


Lesson 10–3

photograph is 1 inch 5 4 feet, how long is Ron’s actual car?

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Scale Drawings and Models Pre-Activity Read the introduction at the top of page 391 in your textbook. Write your answers below. 1. Explain how you would use a ruler to find the number of miles between any two cities on the map.

2. Use the method you described in Exercise 1 to find the actual distance between Haletown and Jasper. 3. What is the actual distance between Kimball and Signal Mountain?

Reading the Lesson 4. Look up the word scale in a dictionary. Write the meaning that matches the way the word is used in this lesson.

5. Look at Example 1 at the bottom of page 391. Then tell what is happening at each step of the process below. 1 23 }} 5 }} 8 h

1 3 h 5 8 3 23 h 5 184 6. Look at Example 2 at the top of page 392. What do you need to know in order to solve for d, the actual distance?

7. Bring a map or set of maps to school (for example, maps of the world as found in an almanac). Using the scale on the map, practice measuring distances between objects on the map.

Helping You Remember 8. Make a scale drawing of some object with which you are familiar. Take the actual measurements of the object. Decide on a scale. Create the drawing. Be sure to put the scale somewhere on your drawing so a reader will be able to tell the size of the actual object. © Glencoe/McGraw-Hill

504


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Planning a Room Before moving furniture into a room, many people plan an arrangement by making a scale drawing. This makes it possible to find the best arrangement for the room without actually moving heavy furniture. For each piece of furniture, actual measurements are given. Compute scale measurements using the scale }1} inch 5 1 foot. 2

1. bed: 6}1} feet long, 3 feet wide 2

2. bedside table: 1}1} feet long, 1}1} feet wide 2

2

3. bookcase: 3}1} feet long, 1 foot wide 2

4. desk: 42 inches long, 18 inches wide 5. chest of drawers: 39 inches long, 18 inches wide 6. Use your answers from Exercises 1–5. Show how the furniture might be arranged in the bedroom shown below.

Lesson 10–3

WINDOW

Scale:

1 inch = 1 foot 2

DOOR


505


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Modeling Percents Ratios like 41 out of 100, 25 out of 100, or 2 out of 100 can be written as percents. A percent (%) is a ratio that compares a number to 100. Since the word percent means out of one hundred, you can use a 10 3 10 grid to model percents.

Model 10%. 10% means 10 out of 100. So, shade 10 of the 100 squares.

Model 78%. 78% means 78 out of 100. So, shade 78 of the 100 squares.

You can use what you know about decimal models and percents to identify the percent of a model that is shaded.

Identify each percent that is modeled.

There are 30 out of 100 squares shaded. So, the model shows 30%.

There are 43 out of 100 squares shaded. So, the model shows 43%.

Model each percent. 1. 20%

2. 55%

3. 12%

Identify each percent that is modeled. 4.


5.

6.

506


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Modeling Percents Model each percent. 1. 15%

2. 50%

3. 75%

4. 80%

5. 21%

6. 48%

7.

8.

9.

10.

11.

12.

13.

14.

15.


507


Lesson 10–4

Identify each percent that is modeled.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Modeling Percents 1. FOOTBALL In the 2001–2002 season, the Dallas Cowboys football team won 45% of their games. Make a model to show 45%.

2. LANDSCAPING Jacob is making a 10 foot by 10 foot patio in his backyard using paving stones that are 1 foot square. The shaded area of the model indicates the finished part of the patio. What percent of the patio has Jacob finished?

55%

3. ART Lydia is making a collage using 100 photographs arranged in a square pattern. The shaded area in the model indicates the part of the collage already covered by photos. What percent of the collage is finished?

4. ENERGY In the year 2000, nuclear energy accounted for 8% of the energy used in the U.S. Make a model to show 8%.

5. GAMES The figure shows the starting position for a game played on a 10 by 10 board. The shaded squares contain game pieces. What percent of the squares on the board contain game pieces?

6. MUSIC In the school chorus, 52% of the girls sing soprano and 44% sing alto. Which of these two sections of the chorus has more girls? Explain using models.

Sample answer: There are more


508


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Modeling Percents Pre-Activity Read the introduction at the top of page 395 in your textbook. Write your answers below. 1. What ratio compares the number of students who prefer grape flavored lollipops to the total number of students?

2. What decimal represents this ratio? 3. Use a decimal model to represent this ratio.

Reading the Lesson 4. Explain why a 10 3 10 grid is a good way to model percents.

5. Complete the table. 75% 37 out of 100 6. Look at the model in Example 3 on page 396. What is another way to model 25%?

7. Look at the nutrition facts on any food label. Which item contains the highest percent of daily value per serving? Make a model to represent that amount. Label the model to indicate what the model shows.


509


Lesson 10–4


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment We the People

Population of the United States, 2000 American Indian, Eskimo, and Aleut 1%

Who are the people of the United States? The graphs at the right show just a small part of the data gathered in the 2000 Census of the Population. Using the data shown on these graphs, decide whether each statement is true or false.

Black 12% White 75%

1. About 12% of all the people counted in the census responded that they are black.

Asian and Pacific Islander 4% Other Races 8%

Total Population: 281,421,906

2. About 5% of all the people counted in the census identified their national origin as Cuban.

Hispanic or Latino Americans: National Origin, 2000 Puerto Rico 10% Cuba 4%

3. About 58% of the Hispanic Americans counted in the census identified their national origin as Mexican.

Mexico 58%

4. The number of people who identified themselves as white is about 120 million.

5. How well can you picture data? In the space at the right, sketch a circle graph to show the data below.

Other 28%

Total Population: 35,305,818

, Americans Region of Residence, 2000

Americans’ Region of Residence, 2000 Northeast Midwest South West


19% 23% 35% 23%

510


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention To write a percent as a fraction, write it as a fraction with a denominator of 100. Then simplify.

Write 15% as a fraction in simplest form. 15% means 15 out of 100. 15 15% 5 } } 3

Write the percent as a fraction with a denominator of 100.

20


100

@ 15 5} or }3} 20 100 @

Write 180% as a fraction in simplest form. 180% means 180 out of 100. 180 180% 5 } }

Write the percent as a fraction with a denominator of 100.

100 4

@ 180 5} or 1}4} 5 100 @

Simplify.

5

You can also write fractions as percents. To write a fraction as a percent, write a proportion and solve.

Write }2} as a percent.

Write }9} as a percent.

5

2 n }} 5 }} 5 100

2 3 100 5 5 3 n 200 5 5n 200 5n } } 5 }} 5 5

8

p 9 }} 5 }} 8 100

Set up a proportion.

Set up a proportion.

9 3 100 5 8 3 p 900 5 8p

Write the cross products. Multiply.

Write the cross products. Multiply.

8p 900 }} 5 }} 8 8


40 5 n


112.5 5 p

So, }2} is equivalent to 40%.

So, }9} is equivalent to 112.5%.

5

8

Write each percent as a fraction in simplest form. 1. 20%

2. 35%

3. 70%

4. 60%

5. 150%

6. 225%

Write each fraction as a percent. 7. }3} 10

10. }1} 5


8. }2}

9. }8}

100

5

10 11. } }

13 12. } }

8

100

511


Lesson 10–5

Percents and Fractions

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Percents and Fractions Write each percent as a fraction in simplest form. 1. 40%

2. 30%

3. 55%

4. 75%

5. 140%

6. 175%

7. 24%

8. 68%

9. 44%

10. 92%

11. 110%

12. 155%

13. 18%

14. 74%

15. 43%

Write each fraction as a percent. 16. }4}

17. }3}

18. }7}

19. }3}

20. }3}

21. }5}

22. }6}

23. }9}

13 24. } }

17 25. } }

26. }9}

11 27. } }

19 28. } }

13 29. } }

21 30. } }

5

5

5

20

20


20

10

2

4

20

20

5

10

10

100

512


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. TOYS The Titanic Toy Company has a 4% return rate on its products. Write this percent as a fraction in simplest form.

2. MUSIC There are 4 trombones out of 25 instruments in the Landers town band. What percent of the instruments are trombones?

3. SHOPPING Alicia’s favorite clothing store is having a 30% off sale. What fraction represents the 30% off sale?

4. FOOD At Ben’s Burger Palace, 45% of the customers order large soft drinks. What fraction of the customers order large soft drinks?

9 }} 20

5. BASKETBALL In the 2001–2002 NBA season, Shaquille O’Neal of the Los Angeles Lakers made 60% of his field goals. What fraction of his field goals did Shaquille make?

6. SCHOOL In Janie’s class, 7 out of 25 students have blue eyes. What percent of the class has blue eyes?

17 7. TESTS Michael answered } } questions

8. RESTAURANTS On Saturday afternoon,

20

41 }} telephone calls taken at The 50

correctly on his test. What percent of the questions did Michael answer correctly?


Overlook restaurant were for dinner reservations. What percent of the telephone calls were for dinner reservations?

513


Lesson 10–5

Percents and Fractions

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Percents and Fractions Pre-Activity Read the introduction at the top of page 400 in your textbook. Write your answers below. 1. What was the second most popular reason? 2. What percent represents this section of the graph?

3. Based on the meaning of 22%, make a conjecture as to how you would write this percent as a fraction.

Reading the Lesson 4. Write the two steps to use to write a percent as a fraction.

5. Look at the graphic at the top of page 400. What is the sum of the percents? Look at the table at the top of page 401. What is the sum of the percents? Why is this important?

6. Look at Example 2 on page 400. Why is 125% written a mixed number?

Helping You Remember 7. Write a fraction as a percent using the steps shown in Examples 4 and 5 on page 401. Choose any fraction you like different from those in the Examples. Step

Equation(s)

Set up a proportion. Write the cross products. Multiply. Divide. Conclusion. © Glencoe/McGraw-Hill

So, ___________ is equivalent to ____________.

514


NAME ________________________________________ DATE ______________ PERIOD _____

Percent and the Hundred Chart The chart at the right shows all the whole numbers from 1 through 100.

1

This page challenges you to connect percents to what you know about number theory—factors, multiples, divisibility, and so on. Whenever you can, use a pattern in the chart to make your work easier.

2

3

4

5

6

7

8

9

10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

For example, the multiples of 5 make up two columns of the chart—the fifth column and the tenth. So, 20 out of 100 numbers, or 20% of the numbers, are multiples of 5.

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Use the hundred chart above. Find the percent of the numbers that: 1. are even numbers.

2. are odd numbers.

3. are multiples of 9.

4. are multiples of 11.

5. are divisible by 5.

6. are divisible by 3.

7. are divisible by 2 and divisible by 5.

8. are divisible by 2 and divisible by 3.

9. contain only even digits.

10. contain only odd digits.

11. have digits whose sum is 10.

12. have digits whose sum is 5.

13. contain the digit 0.

14. contain the digit 5.

15. are factors of 100.

16. are factors of 101.

17. are prime.

18. are composite.


515


Lesson 10–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Percents and Decimals To write a percent as a decimal, first rewrite the percent as a fraction with a denominator of 100. Then write the fraction as a decimal.

Write 23% as a decimal. 23 23% 5 } }

Rewrite the percent as a fraction with a denominator of 100.

100

5 0.23

Write the fraction as a decimal.

Write 127% as a decimal. 127 127% 5 } }

Rewrite the percent as a fraction with a denominator of 100.

100

5 1.27


Write 0.8% as a decimal. 0.8 0.8% 5 } }

100 1 10 @ 0.8 5} 3 } 10 100 @

Rewrite the percent as a fraction with a denominator of 100. 10 Multiply by } } to eliminate the decimal in the numerator. 10

10

5 0.008


To write a decimal as a percent, first write the decimal as a fraction with a denominator of 100. Then write the fraction as a percent.

Write 0.441 as a percent. 441 0.441 5 } }

1,000 441 4 10 5} } 1,000 4 10 44.1 5} } or 44.1% 100

Write the decimal as a fraction. Divide by 10 to get a denominator of 100. Write the fraction as a percent.

Write each percent as a decimal. 1. 39%

2. 57%

3. 82%

4. 135%

5. 112%

6. 0.4%

Write each decimal as a percent. 7. 0.86 10. 0.2


8. 0.36

9. 0.65

11. 0.148

12. 0.217

516


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Percents and Decimals 1. 5%

2. 8%

3. 37%

4. 12%

5. 29%

6. 54%

7. 48%

8. 79%

9. 0.1%

10. 0.6%

11. 0.2%

12. 0.5%

13. 123%

14. 102%

15. 135%

16. 310%

Write each decimal as a percent. 17. 0.3

18. 0.7

19. 0.19

20. 0.74

21. 0.66

22. 0.52

23. 0.21

24. 0.81

25. 0.13

26. 0.362

27. 0.528

28. 0.245

29. 0.194

30. 0.334

31. 0.426

32. 0.059


517


Lesson 10–6

Write each percent as a decimal.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Percents and Decimals 1. COMMUTING According to the 2000 U.S. census, 76% of U.S. workers commute to work by driving alone. Write 76% as a decimal.

2. BASEBALL Barry Bonds’s batting average for the 2002 season was 0.370. Write 0.370 as a percent.

3. ELECTIONS In the 2002 U.S. midterm elections, 39% of eligible adults voted. What is 39% written as a decimal?

4. BASKETBALL In the 2001–2002 season, Jason Kidd of the New Jersey Nets had a field goal average of 0.391. What is 0.391 written as a percent?

5. SPORTS When asked to choose their favorite sport, 27% of U.S. adults who follow sports selected professional football. What decimal is equivalent to 27%?

6. AGE Lawrence is 18 years old and his brother Luther is 12 years old. This means that Lawrence is 1.5 times older than Luther. What percent is equivalent to 1.5?

7. WATER About 5% of the surface area of the U.S. is water. What decimal represents the amount of the U.S. surface area taken up by water?

8. POPULATION China accounts for 0.207 of the world’s population. What percent of the world’s population lives in China?


518


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Percents and Decimals Pre-Activity Read the introduction at the top of page 404 in your textbook. Write your answers below. 1. What percent does the circle graph represent?

Lesson 10–6

2. What fraction represents the section of the graph labeled rent?

3. Write the fraction from Exercise 2 as a decimal.

Reading the Lesson Complete each of the following sentences. 4. To rewrite a fraction with a denominator of 100 as a decimal, move the decimal point of the numerator __________ places to the __________.

5. To rewrite a fraction with a denominator of __________ as a decimal, move the decimal point of the numerator 3 places to the left.

6. Look at Example 3 on page 404. Why does the denominator change from 100 to 1,000?

Helping You Remember 7. Look at Example 5 on page 405. Explain why the first fraction has a denominator of 1,000. Then explain what happens at the next step.


519


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Percent and Per Mill A percent is a ratio that compares a number to 100. 83 }} 5 83 percent 5 83% 5 0.83 100

A ratio that compares a number to 1,000 is called a per mill. Just like percent, the ratio per mill has a special symbol, ‰. 83 }} 5 83 per mill 5 83‰ 5 0.083 1,000

Throughout the world, the ratio that is used most commonly is percent. However, in some countries, you will find both ratios in use. Express per mill as a decimal. 1. 325‰

2. 71‰

3. 6‰

4. 900‰

5. 20‰

6. 100‰

Express each per mill as a fraction in simplest form. 7. 47‰

8. 400‰

10. 25‰

11. 150‰

9. 100‰

12. 30‰

Express each fraction as a per mill. 729 13. } }

8 14. }5}

15. }7}

16. }1}

17. }3}

18 }5}

19. }4}

17 20. } }

21. }1}

1,000

2

5

100

10

4

8

20

3

22. CHALLENGE In the United States, you will sometimes find the mill used as a monetary unit. What amount of money do you think is represented by 1 mill? © Glencoe/McGraw-Hill

520


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Percent of a Number One way to find the percent of a number is to write the percent as a fraction and then multiply. Another way is to write the percent as a decimal and then multiply.

Find 70% of 40. Method 1 Write the percent as a fraction.

Method 2 Write the percent as a decimal.

70 7 70% 5 } } or }}

70 70% 5 } } or 0.7

7 7 }} of 40 5 }} 3 40 or 28 10 10

0.7 of 40 5 0.7 3 40 or 28

100

10

100

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0

4

8

12

16

20

24

28

32

36

40

The model comfirms that 70% of 40 is 28.

Find 120% of 25. Method 1 Write the percent as a fraction.

Method 2 Write the percent as a decimal.

120 6 120% 5 } } or }} 100 5 6 6 }} of 25 5 }} 3 25 or 30 5 5

120 120% 5 } } or 1.2 100

1.2 of 25 5 1.2 3 25 or 30

So, 120% of 25 is 30.

Find the percent of each number. 1. 10% of 120

2. 60% of 25

3. 75% of 24

4. 90% of 40

5. 120% of 20

6. 150% of 2

7. 15% of 40

8. 30% of 70

9. 150% of 6

10. 165% of 20


11. 8% of 15

12. 6% of 6

521


Lesson 10–7

So, 70% of 40 is 28. Use a model to check the answer.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Percent of a Number Find the percent of each number. 1. 25% of 16

2. 50% of 70

3. 10% of 30

4. 60% of 40

5. 75% of 20

6. 20% of 90

7. 30% of 110

8. 50% of 140

9. 25% of 80

10. 4% of 100

11. 75% of 36

12. 90% of 120

13. 125% of 40

14. 8% of 25

15. 150% of 22

16. 110% of 50

17. 125% of 60

18. 0.4% of 5

19. 6.5% of 40

20. 0.5% of 14

21. 0.1% of 29

22. 130% of 80

23. 4.5% of 60

24. 0.5% of 34

25. 14.5% of 60

26. 14% of 30

27. 24% of 15

28. 140% of 30

29. 6% of 55

30. 160% of 22


522


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Percent of a Number 2. AGE Theresa is 60% as old as her sister Mala, who is 20 years old. How old is Theresa?

3. TIPPING Charlie wants to leave a 15% tip for a meal that costs $40. How much should Charlie leave for a tip?

4. SALES TAX Charmaine wants to buy a shirt for $15. If the sales tax is 4% of $15, how much will she pay in sales tax?

5. FOOTBALL In the 2001–2002 regular season, the Green Bay Packers won 75% of their games. There were 16 regular season games. How many games did Green Bay win?

6. BASEBALL During the 2002 World Series, Rich Aurilia of the San Francisco Giants had a batting average of 250 or 25%. He was at bat 32 times. How many hits did he get?

7. RUNNING Thomas finished the race in 120 minutes. James took 95.5% as long as Thomas to finish the race. How long did it take James to finish the race?

8. SHOPPING A DVD player that normally costs $160 is on sale for 70% of its normal price. What is the sale price of the DVD player?

Lesson 10–7

1. SCHOOL There are 520 students at Northridge High School. 80% of these students take the bus. How many students take the bus?


523


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Percent of a Number Pre-Activity Read the introduction at the top of page 409 in your textbook. Write your answers below. 1. What percent of the cars were traveling 20 miles per hour over the speed limit?

2. Write a multiplication sentence that involves a percent that could be used to find the number of cars out of 300 that were traveling 20 miles an hour over the speed limit.

Reading the Lesson 3. What are two different methods you can use to find the percent of a number?

4. Complete the statement: 12% of 48 has the same meaning as 12% 48.

Helping You Remember 5. Work with a partner. Make up a problem in which you can find the percent of a number as in Examples 1 and 2. One person uses Method 1, writing the percent as a fraction. The other person uses Method 2, writing the percent as a decimal. Compare your results. Make up another problem and have each person use the other method. Again, compare your results. Do you prefer one method over the other? Explain.


524


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Estimating Sales Tax Many states charge a sales tax on purchases. To be sure that you have enough money, you should be able to estimate the amount of sales tax and the total cost of an item. For example, this is how you can estimate the total cost of the purchase shown at the right. First, round the price and the rate. $10.95 ➝ $11 6.75% ➝ 7%

5 0.9 1 $ sales tax rate: 6.75%

Multiply the rounded numbers. 11 dollars 3 7¢ per dollar }} 77¢ < 80¢

7% means 7¢ per 100¢, or 7¢ per dollar.

Estimate the total cost of each purchase. 1.

2.

$6

3.

$1

.9 8

sales tax rate: 5%

1 .9

$1 7

sales tax rate: 5.75%

4.

9 .9

6.

$7 5

sales tax rate: 6}1}%

9 .0

$1 0

sales tax rate: 8}1}%

2

8


5.

$2

9 .8

17

.9 9


4

Will $50 be enough money to make such purchase? 7.

8.

$4

8 .9

9.

$4 5

sales tax rate: 3%

6 .9

$4 9


6 .9

9

sales tax rate: 8}1}% 4

10. CHALLENGE The price marked on a cassette tape is $8.99. With the sales tax, the total cost of the tape is $9.37. Estimate the sales tax rate.


525


Lesson 10–7

So, the total cost is close to $11 1 80¢, or $11.80.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Estimating with Percents The table below shows some commonly used percents and their fraction equivalents.

Percent-Fraction Equivalents 20% 5 }1}

5 30% 5 }3} 10 40% 5 }2} 5

50% 5 }1}

2 60% 5 }3} 5 70% 5 }7} 10

80% 5 }4}

5 90% 5 }9} 10

25% 5 }1}

33}1}% 5 }1}

4 75% 5 }3} 4

3

3

66}2}% 5 }2} 3

3

100% 5 1

Estimate each percent. 20% of 58

76% of 25.

20% is }1}.

76% is close to 75% or }3}.

5

4

Round 58 to 60 since it is divisible by 5.

Round 25 to 24 since it is divisible by 4.

12

6

1 1 60 @ }} 3 60 5 } 3 } 5 @ 5 1

3 }} 4

5 12 So, 20% of 58 is about 12.

5 18 So, 76% of 25 is about 18.

1

3 24 @ 3 24 5 } 3 } 4 @ 1 1

Estimate the percent of the figure that is shaded. 2 out of 9 circles are shaded. 2 3 1 }} is about }} or }} 9 9 3 1 1 }} 5 33}}% 3 3 So, about 33}1}% of the figure is shaded. 3

Estimate each percent. 1. 49% of 8

2. 62% of 20

3. 40% of 51

4. 24% of 27

5. 81% of 32

6. 19% of 46

Estimate the percent that is shaded in each figure. 7.


8.

9.

526


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Estimating with Percents 1. 58% of 5

2. 41% of 10

3. 75% of 17

4. 50% of 39

5. 24% of 13

6. 82% of 24

7. 19% of 31

8. 73% of 61

9. 62% of 34

10. 49% of 71

11. 38% of 42

12. 27% of 81

13. 79% of 16

14. 52% of 118

15. 19% of 94

16. 33% of 61

17. 91% of 82

18. 67% of 241

Estimate the percent of the figure that is shaded. 19.


20.

21.

527


Lesson 10–8

Estimate each percent.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Estimating with Percents 1. SCHOOL At Westside High School, 24% of the 225 sixth grade students walk to school. About how many of the sixth grade students walk to school?

2. BASKETBALL In the 2002 regular season the WNBA Cleveland Rockers won 31.25% of their games. They had 32 games in their regular season. About how many games did they win?

3 }} 3 30 5 9 games 10

3. SALES TAX The sales tax rate in Lacon is 9%. About how much tax would you pay on an item that costs $61?

4. SPORTS The concession stand at a football game served 178 customers. Of those, about 52% bought a hot dog. About how many customers bought a hot dog?

1 }} 3 180 5 90 customers 2

5. READING Max has completed 39% of his reading assignment. If there are 303 pages in the assignment, about how many pages has Max read?

6. SHOPPING A store is having a 20% sale. That means the customer pays 80% of the regular price. About how much would you pay for an item that regularly sells for $44.99?

answer: }4} 3 45 5 $36 5

7. SLEEP A recent study shows that people spend about 31% of their time asleep. About how much time will a person spend asleep during an average 78 year lifetime?


8. BIOLOGY The human body is 72% water, on average. About how much water will be in a person that weighs 138 pounds?

528

7 }} 3 140 5 98 lb water 10


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Estimating with Percents Pre-Activity Read the introduction at the top of page 415 in your textbook. Write your answers below. 1. What would be the cost of the notebook at 10% off? 2. What would be the cost of the pencils at 25% off? Round to the nearest cent. 3. Explain how you might estimate the cost of the notebook at 10% off and the cost of the pencils at 25% off.

Reading the Lesson 4. Write the fraction for each percent. 40% 5

1 4

25% 5 }}

1 3

60% 5

1 2

50% 5 }}

80% 5

3 4

75% 5 }}

100% 5 1

Lesson 10–8

20% 5

2 3

33}1}% 5 }} 66}2}% 5 }} 3

3

5. Complete the sentence. When you estimate with percents, you round to numbers that are _______________.

Helping You Remember 6. Work with a partner. Using the fractions and percents in the table you completed for Exercise 4, take turns saying either a fraction or percent. If you say a fraction, your partner writes the corresponding percent. If you say a percent, your partner writes the corresponding fraction. Make sure your partner cannot see the table above. Continue with your practice until you can remember all the fractions and percents.


529


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Using 100%, 10%, and 1% Many people think of 100%, 10%, and 1% as key percents. 100% is the whole.

100% of 24 5 1 3 24, or 24.

10% is one tenth of the whole.

10% of 24 5 0.1 3 24, or 2.4.

1% is one hundredth of the whole.

1% of 24 5 0.01 3 24, or 0.24.

Find the percent of each number. 1. 100% of 8,000

2. 10% of 8,000

3. 1% of 8,000

4. 10% of 640

5. 100% of 720

6. 1% of 290

7. 1% of 50

8. 100% of 33

9. 10% of 14 11. 1% of 9

10. 100% of 2 12. 10% of 7

This is how you can use the key percents to make some computations easier. 3% of 610 5 ? . 5% of 24 5 ? . 1% of 610 5 6.1,

10% of 24 5 2.4,

so 3% of 610 5 3 3 6.1, or 18.3.

so 5% of 24 5 }1} of 2.4, or 1.2. 2

Find the percent of each number. 13. 2% of 140

14. 8% of 2,100

15. 4% of 9

16. 20% of 233

17. 70% of 90

18. 30% of 4,110

19. 5% of 160

20. 5% of 38

21. 50% of 612

22. 25% of 168

23. 2.5% of 320

24. 2.5% of 28


530


Chapter Chapter 11 11 Resource Resource Masters Masters

Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5



Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge; and be used solely in conjunction with Glencoe Mathematics: Applications and Concepts, Course 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240

ISBN: 0-07-860074-X 1 2 3 4 5 6 7 8 9 10

024

Mathematics: Applications and Concepts, Course 1 Chapter 11 Resource Masters 12 11 10 09 08 07 06 05 04 03




Lesson 11-4


Chapter 11 Assessment Chapter 11 Test, Form 1 ........................577–578 Chapter 11 Test, Form 2A ......................579–580 Chapter 11 Test, Form 2B ......................581–582 Chapter 11 Test, Form 2C......................583–584 Chapter 11 Test, Form 2D......................585–586 Chapter 11 Test, Form 3 ........................587–588 Chapter 11 Extended Response Assessment ...............................................589 Chapter 11 Vocabulary Test/Review...............590 Chapter 11 Quizzes 1 & 2..............................591 Chapter 11 Quizzes 3 & 4..............................592 Chapter 11 Mid-Chapter Test .........................593 Chapter 11 Cumulative Review......................594 Chapter 11 Standardized Test Practice..595–596 Unit 5 Test/Review..................................597–598 Standardized Test Practice Student Recording Sheet ..............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A26


iii



Practice: Skills










iv

Enrichment






Assessment Options












v

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


complementary events

event

independent events

outcomes

population

random


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


sample

sample space

survey [sir-vay]

theoretical probability [THEE-uh-REHT-uh-kuhl] [prah-buh-BILL-uh-tee]

tree diagram


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Family Letter

ermine how likely We can use probability to help us det we know that when we something is to occur. For example, l land faceup is toss a coin, the probability that it wil 1 bability and analyze likely }}. Knowing how to calculate pro 2 rmed decisions. outcomes will help us make more info ld will learn how to find In Chapter 11, Probability, your chi nt, to predict actions of a and interpret the probability of an eve find outcomes using lists, larger group using a sample, and to the study of this chapter, tree diagrams, and combinations. In daily classroom your child will complete a variety of ly produce a chapter assignments and activities and possib project . it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 11 to the real world. math we will be learning in Chapter Online Study Tools for You may also wish to log on to the t Study Guide pages, self-check quizzes, Parent and Studen 1.net. If you have any and other study help at www.msmath contact me at school. questions or comments, feel free to Sincerely,



ix


Family Letter


NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity What’s Your Preference? Work with a family member to answer the following questions. 1. Determine the number of parents, siblings, grandparents, aunts, uncles, and close friends you have. Record the number below.

2. Write the name of each family member or friend on a separate piece of paper. Place all of the papers in a hat. Without looking, select five pieces of paper. Record the names of those family members or friends selected in the space below.

3. Ask those five family members or friends what color they prefer. Record the results in the space below.

4. What fraction of your family members or friends selected in Exercise 2 prefers red? blue? yellow? green?

5. Based on your sample, predict how many of your family members and friends listed in Exercise 1 prefer blue.

6. Based on your sample, predict how many of your family members and friends listed in Exercise 1 prefer yellow.

7. Based on your sample, predict how many of your family members and friends listed in Exercise 1 prefer red.


x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Theoretical Probability When tossing a coin, there are two possible outcomes, heads and tails. Suppose you are looking for heads. If the coin lands on heads, this would be a favorable outcome or event. The chance that some event will happen (in this case, getting heads) is called theoretical probability. You can use a ratio to find probability. The probability of an event is a number from 0 to 1, including 0 and 1. The closer a probability is to 1, the more likely it is to happen. equally likely to occur

certain to occur

0

1 or 0.25 4

1 or 0.50 2

3 or 0.75 4

1

0%

25%

50%

75%

100%

There are four equally likely outcomes on the spinner. Find the probability of spinning green or blue.

red

blue

green

yellow

number of favorable outcomes P(green or blue) 5 }}}} number of possible outcomes 5 }2} or }1} 4 2

The probability of landing on green or blue is }1}, 0.50, or 50%. 2

Complementary events are two events in which either one or the other must happen, but both cannot happen at the same time. The sum of the probabilities of complementary events is 1.

There is a 25% chance that Sam will win a prize. What is the probability that Sam will not win a prize? P(win) 1 P(not win) 5 1 0.25 1 P(not win) 5 1 – 0.25 5 –0.25 }}}}}}}}}}}}} P(not win) 5 0.75

Replace P(win) with 0.25. Subtract 0.25 from each side.

So, the probability that Sam won’t win a prize is 0.75, 75%, or }3}. 4

1. There is a 90% chance that it will rain. What is the probability that it will not rain?

One pen is chosen without looking from a bag that has 3 blue pens, 6 red, and 3 green. Find the probability of each event. Write each answer as a fraction, a decimal, and a percent. 2. P(green)


3. P(blue or red)

551

4. P(yellow)


Lesson 11–1

impossible to occur

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Theoretical Probability A card is randomly chosen. Find each probability. Write each answer as a fraction, a decimal, and a percent. 1. P(B)

B

A

S

Q

K

E O

2. P(Q or R)

R

3. P(vowel)

4. P(consonant or vowel)

5. P(consonant or A)

6. P(T) The spinner shown is spun once. Write a sentence explaining how likely it is for each event to occur.

dog

dog

7. P(dog) cat

hamster

8. P(hamster)

dog

cat

9. P(dog or cat)

10. P(bird)

11. P(mammal)

WEATHER The weather reporter says that there is a 12% chance that it

will be moderately windy tomorrow. 12. What is the probability that it will not be windy?

13. Will tomorrow be a good day to fly a kite? Explain.


552


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Theoretical Probability Write each answer as a fraction, a decimal, and a percent. PARTY For Exercises 1 and 2, the spinner shown is spun once.

The spinner shows the prizes a person can win at a party.

yo-yo whistle

cap

cap

cap

yo-yo

1. What is the probability that a person will spin a cap? a whistle? a cap or yo-yo?

2. What is the probability that a person will spin a stuffed animal? Explain. What is the probability that a person will win a prize?

3. WEATHER The weather report says there is an 85% chance it will be very hot tomorrow. Should you get ready to use the air conditioner? Explain.

4. EATING HABITS 7% of Americans are vegetarians. If you ask a random person whether he or she is a vegetarian, what is the probability that the person is not a vegetarian? Explain.

5. SCHOOL Theresa is taking a multiplechoice test and does not know an answer. She can guess answer A, B, C, D, or E. What is the probability that Theresa will guess correctly? incorrectly?

6. NUMBER CUBE You roll a number cube. How likely is it that you will roll a number less than 1? less than 7? Explain.

7. FOOD Mrs. Phillips has 10 identical cans without labels. She knows that she had 1 can of peas, 5 cans of corn, 1 can of carrots, and 3 cans of beets. She opens one can. What is the probability it is carrots? corn or beets?

8. In Exercise 7, how likely is it Mrs. Phillips will open a can of corn? a can of peas? Explain.


553


Lesson 11–1

key cap ring

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Theoretical Probability Pre-Activity Read the introduction at the top of page 428 in your textbook. Write your answers below. 1. Write a ratio that compares the number of cards numbered 3 to the total number of cards. 2. What percent of the cards are numbered 3? 3. Does Morgan have a good chance of winning? Explain.

4. What would happen to her chances of winning if cards 1, 4, 7, 9, and 10 were added to the cards shown?

5. What happens to her chances if only cards 3 and 8 are facedown on the table?

Reading the Lesson For Exercises 6–8, see the Key Concept box at the bottom of page 428. 6. In the equation, how is P(event) read? In terms of the game at the top of the page, what is the event?

7. In terms of the game, what are the favorable outcomes? 8. In terms of the game, what are the possible outcomes? 9. In Example 3 at the bottom of page 429, how do you read the equation P(snow) 1 P(not snowing) 5 1? What are “snowing” 1 “not snowing” called?

Helping You Remember 10. A deck of cards contains 52 cards divided equally into four suits—spades, hearts, diamonds, clubs. What is the probability that a player will draw a spade from a facedown deck? Write an equation using the symbols from this lesson.


554


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Working Backward with Probabilities Suppose that you are given this information about rolling a number cube. P (1) 5 }1}

P (3) 5 }1}

2

?

P (5) 5 }1}

3

6

?

?

Can you tell what numbers are marked on the faces of the cube? Work backward. Since a cube has six faces, express each probability as a fraction whose denominator is 6. P (1) 5 }3}

P (3) 5 }2}

6

P (5) 5 }1}

6

6

So, the cube must have three faces marked with the number 1, two faces marked 3, and one face marked 5.

1. P(2) 5 }1}

2. P(1) 5 }1}

3 P (4) 5 }1} 3 P (6) 5 }1} 3

3. P(1 or 2) 5 }5}

6 P(4) 5 }1} 6

6 P(2 or 3) 5 }2} 3

P(factor of 4) 5 1

P(1, 2, or 3) 5 1

Each set of probabilities is associated with the spinner shown at the right. How many sections of each color are there? 4. P(red) 5 }1}

5. P(yellow or purple) 5 }5}

2

P (blue) 5 }1}

8 P(purple or white) 5 }3} 4

P (green) 5 }1}

P(green or blue) 5 0

4

8 P (black) 5 }1} 8

Lesson 11–1

Each set of probabilities is associated with rolling a number cube. What numbers are marked on the faces of each cube?

?

?

?

?

?

? ?

?

P(yellow, purple, or white) 5 1

6. Suppose that you are given this information about pulling a marble out of a bag. P(green) 5 }1}

P(blue) 5 }1}

P(red) 5 }3}

P(yellow) 5 }1} 24

P(white) 5 }1} 24

P(black) 5 }1}

4

6

8

8

If the bag contains 48 marbles, how many marbles of each color are there?


555


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Outcomes The set of all possible outcomes is called the sample space. A tree diagram is a diagram used to show the total number of possible outcomes. It can be used to show the sample space. When you make a tree diagram, you have an organized list of outcomes. When you know the number of outcomes, you can easily find the probability that an event will occur.

How many sandwiches are possible from a choice of turkey or ham with jack cheese or Swiss cheese? Draw a tree diagram. Sandwich

Outcome

Cheese jack (J)

TJ

Swiss (S)

TS

jack (J)

HJ

Swiss (S)

HS

turkey (T)

ham (H)

There are four possible sandwiches. Use the tree diagram from Example 1. Find the probability of choosing a ham with jack cheese sandwich. The outcome column of the tree diagram shows there is one possible outcome for ham with jack cheese. There are 4 possible outcomes. So, P(ham, jack) 5 }1}, 0.25, or 25%. 4

Draw a tree diagram to show the sample space for each situation. Then tell how many outcomes are possible and find the probability. 1. buy a can or a bottle of grape or orange soda Find P(bottle, grape).

2. toss a coin and roll a number cube Find P(4, tails).

3. wear jeans or shorts with a blue, white, black, or red T-shirt. Find P(jeans, white T-shirt).


556


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Outcomes 1. In how many ways can 2 coins be chosen from a set of 1 penny, 1 nickel, 1 dime, and 1 quarter? Make a list to show the sample space. Draw a tree diagram to show the sample space for each situation. Then tell how many outcomes are possible and find the given probability. 2. Each spinner is spun once. How many outcomes are possible? Find P(pink, Z).

X pink green

Y

Z

Lesson 11–2

3. chocolate, vanilla, strawberry, or mint ice cream with sugar or waffle cone How many outcomes are possible? Find P(vanilla, waffle).

4. paint room cream, violet, or blue with red, white or gold trim How many outcomes are possible? Find P(blue, red).


557


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Outcomes 1. OUTINGS Olivia and Candace are deciding between Italian or Chinese food and then whether to go to a movie, walk in the park, or go for a bike ride. Draw a tree diagram to show the sample space. How many choices do they have?

2. PETS Terence is going to get a parrot. He can choose among a yellow, green, or multi-colored female or male parrot. Draw a tree diagram showing all the ways Terence can choose. What is the probability he will choose a yellow female?

Outcome IM IW IB CM CW CB

3. CAKE Julia is ordering a birthday cake. She can have a circular or rectangular chocolate or vanilla cake with chocolate, vanilla, or maple frosting. Draw a tree diagram showing all the possible ways Julia can order her cake. How many options does she have?

4. GAMES Todd plays a game in which you toss a coin and roll a number cube. Draw a tree diagram to find all possible outcomes. What is P(heads, odd number)?

5. SCHOOL Melissa can choose two classes. Her choices are wood shop, painting, chorus, and auto shop. List all the ways two classes can be chosen.

6. SHOPPING Kaya has enough allowance to purchase two new baseball caps from the five he likes. How many ways can he choose?


558


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Outcomes Pre-Activity Read the introduction at the top of page 433 in your textbook. Write your answers below. 1. List the possible ways to choose a soft drink, a popcorn, and a candy.

2. How many different ways are possible?

3. Braces { } are used beside the number cube and spinner on page 433. What do these braces indicate? What is each set called?

4. In the tree diagram in Example 1 on page 433, which part of the diagram shows the sample space? 5. In the tree diagram at the right, find the sample space.

C A

6. In Example 3 on page 434, why are there three ways to choose two of the puppies and not six ways?

D E C

B

D E

Helping You Remember 7. Work with a partner. Think up a situation for which you could make a tree diagram to show all possible outcomes. Make the diagram. Then choose one or more desired outcomes and show how to determine the P(desired outcome). © Glencoe/McGraw-Hill

559


Lesson 11–2

Reading the Lesson

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Listing Outcomes in a Table Suppose that you spin the two spinners below. What is the probability that the sum of the numbers you spin is 5? 2

1

2

1

4

3

6

3 4 5

Second Spinner

To find this probability, you first need to count the outcomes. One way to do this is to use a table of sums like the one at the right. From the table, it is easy to see that there are 24 outcomes. It is also easy to see that, in 4 of these outcomes, the sum of the numbers is 5. So, the probability that the sum of the numbers is 5 is }4}, or }1}. 24

First Spinner

1

1

2

3

4

1

2

3

4

5

2

3

4

5

6

3

4

5

6

7

4

5

6

7

8

5

6

7

8

9

6

7

8

9

10

6

Use the spinners and the table above. Find each probability. 1. P(sum is 8)

2. P(sum is 12)

3. P(sum is greater than 6)

4. P(sum is less than or equal to 10)

Suppose you roll two number cubes. Each cube is marked with 1, 2, 3, 4, 5, and 6 on its faces. Find each probability. (Hint: On a separate sheet of paper, make a chart like the one above.) 5. P(sum is 9)

6. P(sum is 3)

7. P(sum is an even number)

8. P(sum is a multiple of 3)

9. P(sum is a prime number) 11. P(sum is greater than 12)

10. P(sum is a factor of 12) 12. P(sum is less than 6)

13. CHALLENGE Here is a set of probabilities associated with two spinners. P(sum is 4) 5 }1} 6

P(sum is 6) 5 }1}

P(sum is 8) 5 }1}

P(sum is 10) 5 }1}

3

3

6

In the space at the right, sketch the two spinners.


560


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Making Predictions A survey is a method of collecting information. The group being surveyed is the population. To save time and money, part of the group, called a sample, is surveyed. A good sample is:

• selected at random, or without preference, • representative of the population, and • large enough to provide accurate data. Every sixth student who walked into the school was asked how he or she got to school. Determine whether the sample is a good sample. This sample is good because it is random (every sixth student), representative of the population (students coming to school), and large enough to provide accurate information.

Using the information from Example 1, what is the probability that a student at the school rode a bike to school? number of students that rode a bike P(ride bike) 5 }}}}}

number of students surveyed 10 1 1 5} } or }} So, P(ride bike) 5 }}, 0.25, or 25%. 40 4 4

School Transportation Method Students walk 10 ride bike 10 ride bus 15 get ride 5

There are 360 students at the school. Predict how many bike to school.

Determine whether the following sample is a good sample. Explain. 1. 300 people at the opera were surveyed to find their favorite type of music.

SCHOOL Use the following information and the table Favorite Subject shown. Every tenth student entering the school was asked Subject Students which one of the four subjects was his or her favorite. Language Arts 10 Math 10 2. Find the probability that any student attending school Science 15 prefers science. Social Studies 5

3. There are 400 students at the school. Predict how many students would prefer science. © Glencoe/McGraw-Hill

561


Lesson 11–3

Write a proportion. Let s 5 number of students who will ride a bike. s 10 }} 5 } } 360 40 You can solve the proportion to find that of the 360 students, 90 will ride a bike to school.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Making Predictions Determine whether each sample is a good sample. Explain. 1. 250 people at the beach in the summer are asked to name their favorite vacation spot.

2. Every fourth shopper at a grocery store is asked whether or not he or she owns a pet.

For Exercise 3–6, use the table and the following information. A survey of students’ favorite sports was taken from a random sample of students in a school. The results are shown in the table. 3. What is the size of the sample?

Students’ Favorite Sports Soccer 8 Baseball /Softball 3 Volleyball 5 Track & Field 4

4. What is the probability that a student will prefer soccer?

5. What is the probability that a student will prefer volleyball?

6. There are 550 students in the school. Predict how many students at the school prefer track and field.

For Exercises 7–10, use the table and the following information. A random sample of 40 flower shop customers was surveyed to find customers’ favorite flowers. The table shows the results. The shop expects to sell 50 bunches of flowers on Sunday. How many bunches of each flower should the shop order?

Favorite Flower Type Shoppers Daisy 8 Gardenia 4 Mum 8 Rose 20

7. daisy 8. rose 9. mum 10. gardenia


562


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Making Predictions MOVIES For Exercises 1–3, use

SLEEP For Exercises 4–7, use the table

the table of results of Jeremy’s survey of favorite kinds of movies.

of results of the Better Sleep Council’s survey of Americans to find the most important factors for good sleep.

Favorite Movie Type Type People Drama 12 Foreign 3 Comedy 20 Action 15

Most Important Factors for Good Sleep Good Mattress 32 Daily Exercise 20 Good Pillows 8 Healthy Diet 11 Other Factors 29

1. MOVIES How many people did Jeremy use for his sample?

2. If Jeremy were to ask any person to name his or her favorite type of movie, what is the probability that it would be comedy?

3. If Jeremy were to survey 250 people, how many would you predict would name comedy?

4. SLEEP Predict how many people out of 400 would say that a good mattress is the most important factor.

5. What is the probability that any person chosen at random would not say that a healthy diet is the most important factor?

6. Suppose 250 people were chosen at random. Predict the number of people that would say good pillows are the most important factor.

7. What is the probability that any person chosen at random would say that daily exercise is the most important factor for a good night sleep?

8. ICE CREAM Claudia went to an ice cream shop to conduct a survey. She asked every tenth person who entered the shop to name his or her favorite dessert. Did Claudia select a good sample? Explain.


563


Lesson 11–3

2 }}, 0.4, or 40% 5

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Making Predictions Pre-Activity Complete the Mini Lab at the top of page 438 in your textbook. Write your answers below. 1. When working in a group, how did your group predict the number of left-handed and right-handed students in your school?

2. Compare your group’s prediction with the class prediction. Which do you think is more accurate? Explain.

Reading the Lesson 3. Write the three characteristics of a good sample.

4. Using the characteristics listed in the table above, do you think that a classroom is a good sample of an entire school? Explain.

5. If the question of the survey is, “What is your favorite television program?” would you change the sample in any way? If so, how would you change it?

6. In Examples 2 and 3 on page 439, how is the prediction used?

Helping You Remember 7. Work with a partner. Find the results of a survey that is of interest to you. For example, to find surveys on favorite TV programs, go to a search engine on the Internet and enter “survey TV programs.” Choose one survey. Do you think the survey is a good survey? If so, why? If not, why not and how would you change it? © Glencoe/McGraw-Hill

564


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Odds People who play games of chance often talk about odds. You can find the odds in favor of an event by using this formula. number of ways an event can occur odds in favor 5 }}}}} number of ways the event cannot occur

With the spinner shown at the right, for example, this is how you would find the odds in favor of the event prime number. There are four prime numbers (2, 3, 5, 7). Six numbers are not prime (1, 4, 6, 8, 9, 10).

→ 4 2 }} 5 }} → 6 3

2 3 4 1 5 6 10 9 8 7

The odds in favor of the event prime number are }2} or 2 to 3. 3

Suppose that you spin the spinner shown above. Find the odds in favor of each event. 1. number greater than 3

2. number less than or equal to 6

3. even number

4. odd number

5. multiple of 3

6. factor of 10

To find the odds against an event, you use this formula. number of ways an event cannot occur odds against 5 }}}}} number of ways the event can occur

7. number less than 5

9. even number

11. number divisible by 3

8. number greater than or equal to 2

10. odd number

12. factor of 12

13. CHALLENGE The probability of an event is }2}. What are the odds in favor 3

of the event? the odds against the event?


565


Lesson 11–3

Suppose that you roll a number cube with 1, 2, 3, 4, 5, and 6 marked on its faces. Find the odds against each event.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Probability and Area Probability can be expressed as the ratio of areas. The probability of landing in a specific region of a target is the ratio of the area of the specific region to the area of the target. area of specific region P(specific region) 5 }}} area of the target

Find the probability that a randomly thrown dart will land in the shaded region of the dartboard. Assume it is equally likely for a dart to land anywhere in the rectangle.

15 in. 50 in.

35 in. 100 in.

area of shaded region P(shaded region) 5 }}} area of the target

Area of shaded region

Area of dartboard

, 3 w 5 15 3 100 5 1,500 sq in.

, 3 w 5 50 3 100 5 5,000 sq in.

3 1,500 P(shaded region) 5 } } or }} 5,000

10

So, the probability that a randomly thrown dart will land in the shaded region is }3} , 0.30, or 30%. 10

Predict how many times a dart will land in the shaded area above if 30 darts are randomly thrown. Write a proportion that compares the number of darts landing in the shaded region to the number of darts thrown. Let n 5 the number of darts landing in the shaded region. n 3 } } 5 }} 30 10

→ →

n 3 10 5 30 3 3 10n 5 90 10n 90 } } 5 }} 10 10

n 59

darts landing in the shaded region darts thrown Write the cross products. Multiply. Divide each side by 10.

So, if 30 darts are randomly thrown, 9 darts will land in the shaded region.

Use the dartboard from Example 1. 1. What is the probability that a randomly thrown dart will land in the region that is not shaded? 2. Predict the number of darts that will land in the region that is not shaded if 40 darts are randomly thrown.


566


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Probability and Area Find the probability that a randomly thrown dart will land in the shaded region of each dartboard. 1.

2.

3.

Suppose you randomly throw 10 darts at each dartboard below. How many darts would you expect to land in each shaded area? 4.

10 ft

5.

6.

10 yd

6m

8 yd

2 ft 3 ft

3m 5 yd

10 yd

2m

Use the dartboard at the right. 7. What is the probability of a randomly thrown dart landing on a consonant?

10 m

V Q W O E Z I X

8. If 40 darts are randomly thrown, how many would you predict to land on a consonant?

9. What is the probability that a randomly thrown dart would land on a

10. If 200 darts are randomly thrown, how many would you predict to land on a vowel?


567


Lesson 11–4

vowel?

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Probability and Area GAMES For Exercises 1–5, use the following information and the game boards below. Game Board 1 is for a beanbag toss game in which you are blindfolded and toss a beanbag at the board. The game board shows a bird’s head with eyes, beak, and a hole for a mouth. Game Board 2 is for a dart game in which you randomly throw a dart at the board. Game Board 1 Game Board 2 12 in. 30 in. 18 in. 30 in.

1. Refer to Game Board 1. The shaded region represents the mouth hole. Dawn will randomly throw a beanbag at the board. What is the probability that the beanbag will go into the mouth hole? What is the probability that the beanbag will not go into the mouth hole?

2. Use your answer from Exercise 1. Predict how many beanbags will go into the mouth hole if Dawn throws 20 beanbags. Explain.

1 }} for one bag, and the ratio must 5

be the same for 20 bags, or 4 }}. So, 4 out of the 20 beanbags 20

will go into the mouth. 3. Use your answer from Exercise 1. Predict how many beanbags will not go into the mouth hole if Dawn throws 40 beanbags.

4. Refer to Game Board 2. Pam will randomly throw a dart at the dartboard. What is the probability that her dart will land in the shaded region? Explain.

2 }}, 0.4, or 40%; Sample answer: 5

Since the shaded region is whole is }2}. 5

5. Use your answer from Exercise 4. Predict the number of darts that will land in the shaded area if Pam randomly throws 60 darts.

6. SKYDIVING A skydiver is dropped from a plane above a field that is 35 yards by 16 yards. In the center is a region of sand that is 7 yards by 7 yards. What is the probability that the skydiver will land in the sandy region?

7 }}, 0.0875, or 8.75% 80


568


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Probability and Area Pre-Activity Complete the Mini Lab at the top of page 444 in your textbook. Write your answers below. 1. Find P(a piece of rice lands in blue region).

area of blue region 2. How does this ratio compare to the ratio }}} ? Explain. area of target

Reading the Lesson 3. Is experimental or theoretical probability used in Examples 1 and 2? How do you know?

4. Find P(black region) and P(gray region).

Helping You Remember 6. Use grid paper to make two models to illustrate probability and area— one model with a large shaded area and one with a small shaded area. Find the percent probabilities for each model.


569


Lesson 11–4

5. Explain how you used area when you found the answers to Exercise 4 above.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Spinners and More Spinners When you spin a spinner, it is not necessarily true that all outcomes are equally likely. With the spinner shown at the right, for example, you can see it is most likely that the pointer will stop in region A. To find probabilities on a spinner like this, you need to consider what fraction of a complete turn of the pointer is associated with each region. In the spinner at the right, region

B A

C D

A involves about }1} of a complete turn, so P(A) is about }1}. Using the 2

2

same reasoning, P(B) is about }1}, P(C) is about }1}, and P(D) is about }1}. 4

8

8

Estimate each probability. 1.

2. A D

C

3. D

A B D

B C

C

P(A):

P(A):

P(A):

P(B):

P(B):

P(B):

P(C):

P(C):

P(C):

P(D):

P(D):

P(D):

A B

Sketch a spinner that satisfies the given conditions. 4. P(A) 5 }1}

2 P(B) 5 }1} 3 P(C) 5 }1} 12 P(D) 5 }1} 12

5. P(A) 5 }1}

6. P(A) 5 }1}

4 P(B) 5 }1} 4 1 P(C) 5 }} 3 P(D) 5 }1} 6

8 P(B) 5 }5} 8 P(C) 5 }3} 16 P(D) 5 }1} 16

7. CHALLENGE Use the spinner at the right. Estimate each probability. P(A):

P(B):

P(C):

P(D):


570

A

B

C

D


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention If the outcome of one event does not affect the outcome of a second event, the two events are independent events. The probability of two independent events is found by multiplying the probability of the first event by the probability of the second event.

A spinner is spun and a number card is chosen at random. What is the probability that red is spun and a 4 is chosen?

red

blue

4

2

1

3

4

4

P(red) 5 }1} 2

P(4) 5 }3} or }1} 6 2 1 1 1 P(red and 4) 5 }} 3 }} 5 }} 2 2 4 So, the probability is }1}, 0.25, or 25%. 4

A spinner is spun and a number card is chosen at random. Find the probability of each event. R

1

3

4

3

6

3

M

E

A R

1. P(M and 3)

2. P(R and 3)

3. P(consonant and odd)

4. P(consonant and 3)

5. P(vowel and less than 7)

6. P(vowel and even)

A coin is tossed and a number cube is rolled. Find the probability of each event. 7. P(tails and even)

8. P(heads and less than 4)

9. P(heads and greater than 2)


571


Lesson 11–5

Probability of Independent Events

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Probability of Independent Events The two spinners shown are spun. Find the probability of each event.

blue

1

red 2

red blue

3 white

red

1. P(1 and white)

2. P(3 and red)

3. P(2 and blue)

4. P(odd and red)

5. P(4 and white)

6. P(even and any color other than white)

Suppose you select a card from the pile shown and then roll a number cube. Find the probability of each event.

P

B B

E

T

7. P(B and 4)

8. P(B and even)

9. P(consonant and 5)

10. P(vowel and odd)

11. P(E and number less than 7)

12. P(5 and odd)

13. NATURE The table lists the autumn leaves each girl collected. Each girl reaches into her own bag and randomly selects a leaf. Find the probability that Jane chooses a maple and Mary chooses an aspen leaf. Name

Maple

Cottonwood

Aspen

Jane

14

8

6

Mary

8

10

2


572


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems GAMES For Exercises 1–3, use the spinner and the letter cards and the

following information. Brad is playing a game with his little sister in which you spin the spinner and randomly choose a letter card. The spinner tells how many words you must name that begin with the letter on the letter card you choose.

5

4

4

6

K

M

1. What is the probability of spinning an even number and choosing a vowel?

E K

U

L

2. What is the probability of spinning an even number and a consonant? Explain.

1 }}, 0.5, or 50%; Sample answer: 2

There are 3 out of 4 chances to

3. Find P(even and M). What are the possible numbers of words beginning with M that Brad or his sister will have to name?

4. WEATHER The probability of snow on Monday is 0.2. The probability of snow on Tuesday is 0.4. What is the probability that it will snow on both days?

2 }}, 0.08, or 8% 25

5. GAMES Stephen is playing a game with two coins. In order to score points, both coins must land on heads or both must land on tails. What is the probability that Stephen will score points on one toss?

6. FOOD A bakery sells muffins and beverages. The beverages are coffee, tea, orange juice, and milk. There are five kinds of muffins. If a customer chose a beverage and a muffin at random, what is the probability the customer would choose a milk and a blueberry muffin?

1 }}, 0.05, or 5% 20


573


Lesson 11–5

Probability of Independent Events

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Probability of Independent Events Pre-Activity Complete the Mini Lab at the top of page 450 in your textbook. Write your answers below. 1. How many outcomes are in the sample space?

2. What is the probability of rolling a 5 on the number cube?

3. Find the probability of selecting a yellow marble.

4. Use the tree diagram to find P(5 and yellow).

5. Describe the relationship between P(5), P(yellow), and P(5 and yellow).

Reading the Lesson 6. Why are rolling a number cube and choosing a marble considered to be independent events?

7. Complete the equation: P(first event and second event) 5 ____________. 8. Look at Example 2 on page 451. What is the relationship between red and not yellow?

Helping You Remember 9. Look at Example 1 on page 450. Explain each equation. P(heads) 5 }1} 2

P(3) 5 }1} 4

P(heads and 3) 5 }1} 3 }1} or }1} 2


4

8

574


NAME ________________________________________ DATE ______________ PERIOD _____

Dependent Events If the result of one event affects the result of a second event, the events are called dependent. For example, suppose you draw one card from the set of cards shown at the right, but do not replace it. Then you draw a second card. What is the probability that you will draw the T, then an L?

A

R R

First find the probability of drawing the T. → There is 1 card marked T. P(T) 5 }1} → There are 10 cards in all. 10

R

Then find the probability of drawing an L after drawing the T. → There are 3 cards marked L. P(L after T) 5 }3} → There are 9 cards left. 9

R

L

L L

Now multiply. P(T, then L) 5 P(T) 3 P(L after T) 5 }1} 3 }3}

9 10 3 5 }} or }1} 90 30

T

The probability of drawing the T, then an L, is }1}. 30

M

A card is drawn from the set of cards above, and it is not replaced. Then a second card is drawn. Find each probability. 1. P(A, then M)

2. P(T, then R)

3. P(L, then R)

4. P(R, then L)

5. P(L, then L)

6. P(M, then M)

A bag contains two red marbles and four blue marbles. Three marbles are pulled from the bag, one at a time, and they are not replaced. Find each probability. 7. P(blue, then red, then blue) 9. P(three blue marbles)

8. P(red, then blue, then red) 10. P(three red marbles)

11. CHALLENGE Refer to the cards at the top of the page. Suppose you draw two cards at once. What do you think is the probability that you draw an R and an L?


575


Lesson 11–5

Enrichment


Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860075-8 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03







Chapter 12 Assessment Chapter 12 Test, Form 1 ........................629–630 Chapter 12 Test, Form 2A ......................631–632 Chapter 12 Test, Form 2B ......................633–634 Chapter 12 Test, Form 2C......................635–636 Chapter 12 Test, Form 2D......................637–638 Chapter 12 Test, Form 3 ........................639–640 Chapter 12 Extended Response Assessment ...............................................641 Chapter 12 Vocabulary Test/Review...............642 Chapter 12 Quizzes 1 & 2..............................643 Chapter 12 Quizzes 3 & 4..............................644 Chapter 12 Mid-Chapter Test .........................645 Chapter 12 Cumulative Review......................646 Chapter 12 Standardized Test Practice..647–648 Standardized Test Practice Student Recording Sheet ..............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A27

iii



Practice: Skills










iv

Enrichment






Assessment Options












v

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


centimeter

cup

fluid ounce

foot

gallon

gram

hour

inch

kilogram

kilometer

liter

meter


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


metric system

mile

milligram

milliliter

millimeter

minute

ounce

pint

pound

quart

second

ton

yard


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: ly lives, from estimating the We use measurement skills in our dai to actually calculating its length, weight, or capacity of an object ents of multiple objects. measurements or comparing measurem are feet can be ny squ For example, understanding how ma y be helpful when deciding painted using one gallon of paint ma ded to paint a wall that is how many gallons of paint will be nee often helpful to be able to 12 feet long by 9 feet wide. It is also to another. convert from one measurement unit child will learn the various In Chapter 12, Measurement, your t, and capacity in both the measurement units for length, weigh dents will also learn how customary and the metric systems. Stu tem, estimate the metric to change units within the metric sys tract measures of time. In measure of objects, and add and sub will complete a variety of the study of this chapter, your child ivities and possibly produce daily classroom assignments and act a chapter project . with your child, you agree By signing this letter and returning it olved. Enclosed is an to encourage your child by getting inv ld that also relates the activity that you can do with your chi 12 to the real world. You math we will be learning in Chapter Study Tools for may also wish to log on to the Online dy Guide pages, and t Stu self-check quizzes, Parent and Studen et. If you have any questions other study help at www.msmath1.n at school. or comments, feel free to contact me Sincerely,



ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Travel Times Work with a family member to answer the following questions. 1. How long does it take you to travel from your home to your school? Record the time you leave home and the time you arrive at school in the space below. Calculate how many minutes it takes to get from your home to school.

2. How long does it take you to travel from your school to your grocery store? Record the time you leave school and the time you arrive at the grocery store in the space below. Calculate how many minutes it takes to get from your school to the grocery store.

3. How long does it take you to travel from your home to a movie theater? Record the time you leave home and the time you arrive at the theater in the space below. Calculate how many minutes it takes to get from your home to a movie theater.

4. How long does it take you to travel from the movie theater to a favorite restaurant? Record the time you leave the theater and the time you arrive at the restaurant in the space below. Calculate how many minutes it takes to get from the movie theater to a favorite restaurant.

5. Using your answers from above, how many minutes would it take you to travel from home to school to the grocery store?

6. Using your answers from above, how many minutes would it take you to travel from home to the movie theater to a favorite restaurant?


x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Length in the Customary System The most commonly used customary units of length are shown below. Customary Units Of Length Unit

Model

1 inch (in.)

width of a quarter

1 foot (ft) 5 12 in.

length of a large adult foot

1 yard (yd) 5 3 ft

length from nose to fingertip

1 mile (mi) 5 1,760 yd

10 city blocks

• To change from larger units of length to smaller units, multiply. • To change from smaller units of length to larger units, divide.

Complete. ?

ft

24 in. 5

Since 1 yard 5 3 feet, multiply by 3. 33359 So, 3 yards 5 9 feet.

?

ft

Since 1 foot 5 12 inches, divide by 12. 24 4 12 5 2 So, 24 inches 5 2 feet.

Lesson 12–1

3 yd 5

Most rulers are divided into eighths of an inch, so you can measure to the nearest eighth inch.

Draw a line segment

Measure the length of the nail to the

measuring 1}5} inches.

nearest half, fourth, or eighth inch.

8

in.

1

2

Draw a line segment from 0 to 1}5}.

in.

2

1

3

8

The nail is between 2}7} inches and 3 inches. 8

It is closer to 2}7} inches. 8

The length of the nail is about 2}7} inches. 8

Complete. 1. 3 ft 5

?

in.

2. 15 ft 5

?

yd

3. 2 mi 5

?

yd

4. Draw a line segment that is }3} in. long. 4

5. Measure the length of the object to the nearest half, fourth, or eighth inch. © Glencoe/McGraw-Hill

599


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Length in the Customary System Complete. 1. 2 ft 5

?

4. 60 in. 5

7. 3 yd 5

in.

?

?

2. 5 yd 5

ft

?

ft

5. 3,520 yd 5

?

8. 3}1} yd 5

in.

2

?

3. 18 ft 5

mi

ft

?

6. 36 in. 5

9. 2 mi 5

yd

?

?

yd

ft

Draw a line segment of each length. 10. 3}1} in.

11. 1}3} in.

12. 2}1} in.

13. 1}7} in.

14. 2}1} in.

15. }5} in.

2

4

8

8

4

8

For Exercises 16–18, find the length of each line segment or object to the nearest half, fourth, or eighth inch. 16.

17.

?

18.

19. Which is greater: 2}1} feet or 26 inches? Explain. 4

20. Which is greater: 3}1} yards or 12 feet? Explain. 3


600


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Length in the Customary System toolbox with length 2 feet, width 1}1} feet, 2 and height 3 feet. What are the dimensions of Anthony’s box in inches?

3. WEATHER Raquel and her family are moving from Portland, Oregon, to Seattle, Washington. She is comparing annual rainfall to prepare for her move.

2. TRIATHLON Julie is training for a small triathlon where she will run 3 miles, bike 10 miles, and swim 150 yards. How many yards will Julie run? How many feet will she swim?

4. SEWING Abe needs 13.5 feet of fabric to make a bedspread. How many yards does he need?

4}1} yd

Portland’s annual rainfall is 3}1} feet.

2

12

Seattle’s annual rainfall is 37 inches. Which city gets more rain?

5. TRAVEL On her trip to New York City, Celia read that the famous Woolworth building was built in 1913 and stands 792 feet tall. How high is the building in yards?

6. FOOTBALL The length of a football field is 100 yards. How many feet is that? How many inches?

7. SCHOOL Krista lives }1} mile from school.

8. CRAFTS David is making a pattern for the mouth of a puppet. The mouth will be a rectangle of red felt fabric. The

2

Desiree lives 872 yards away from school. Who lives closer? Explain.

rectangle will be }3} inch wide and

8 1 2}} inches long. Draw a pattern for 4

David.


601


Lesson 12–1

1. WOODWORKING Anthony is building a

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Length in the Customary System Pre-Activity Complete the Mini Lab at the top of page 465 in your textbook. Write your answers below. 1. Compare your nonstandard and standard measures with the measures of other groups. Are they similar? Explain.

2. Explain the advantages and the disadvantages of using nonstandard measurement and standard measurement.

Reading the Lesson 3. In the Mini Lab, four units of length are used. What are the units?

4. If someone told you that something was 3.5 units long, what else would you need to know in order to determine the length?

5. Explain in your own words what the word customary means.

6. If a mile is 1,760 yards, how many feet are in a mile? Explain.

Helping You Remember 7. Work with a partner. Using a customary ruler or measuring tape, provide the lengths of each object. Once you have one actual measure for an object, you can use multiplication or division to find the other units of measure for that same object. a. your arm’s length in inches _________ b. your classroom’s width in yards _________ c. your arm’s length in feet _________

d. your classroom’s length in yards _________

e. your foot’s length in inches _________

f. your classroom’s length in feet _________

g. your foot’s length in feet _________

h. your classroom’s length in inches _________


602


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Estimating Lengths Many people estimate lengths using rules of thumb like those you see at the right.

An inch is about the width of a quarter. A foot is about the length of a sheet of notebook paper. A yard is about the distance from the floor to a doorknob. A mile is about the length of ten city blocks.

1. length of a bus

40 in.

40 ft

40 yd

2. length of a baseball bat

15 in.

1 ft

1 yd

3. height of a flagpole

30 in.

3 ft

5 yd

4. height of a table

36 in.

10 ft

2 yd

5. distance across a street

20 ft

200 yd

1 mi

6. length of one city block

30 ft

180 yd

1 }} mi 2

7. width of a door

15 in.

15 ft

1 yd

8. height of the world’s tallest building

50 ft

100 yd

1 }} mi 4

9. Estimate the length of the path from A to B. Then measure. How close was your estimate?

A


B

603


Lesson 12–1

Use the rules of thumb to estimate. Circle the most reasonable measure.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Capacity and Weight in the Customary System The most commonly used customary units of capacity are shown below. Customary Units Of Capacity Unit

Model

1 fluid ounce (fl oz)

2 tablespoons of water

1 cup (c) 5 8 fl oz

coffee cup

1 pint (pt) 5 2 c

small ice cream container

1 quart (qt) 5 2 pt

large measuring cup

1 gallon (gal) 5 4 qt

large plastic jug of milk

• To change from larger units of length to smaller units, multiply. • To change from smaller units of length to larger units, divide.

Complete. 2 gal 5

?

qt

THINK 1 gallon = 4 quarts

23458 Multiply to change a larger unit to a smaller unit. So, 2 gallons 5 8 quarts. The most commonly used customary units of weight are shown below. Customary Units Of Weight Unit

Model

1 ounce (oz)

pencil

1 pound (lb) 5 16 oz

package of notebook paper

1 ton (T) 5 2,000 lb

small passenger car

FOOD A box of cereal weighs 32 ounces. How many pounds is this?

32 oz 5

?

lb

THINK 16 ounces = 1 pound

32 4 16 5 2

Divide to change ounces to pounds.

So, 32 ounces 5 2 pounds.

Complete. 1. 2 pt 5

?

4. 16 qt 5 7. 16 c 5

c ?

?

2. 32 fl oz 5 gal

qt


?

c

3. 3 lb 5

?

oz

?

lb

5. 1}1} qt 5

?

pt

6. 3 T 5

8. 2 gal 5

?

pt

9. 64 oz 5

2

604

?

lb


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Capacity and Weight in the Customary System Complete. ?

oz

2. 3 gal =

4. 32 oz =

?

lb

5. 4 pt =

7. 2}1} pt =

?

c

8. 6 c =

10. 44 qt =

?

gal

2

13. 10,000 lb =

16. 3}1} c = 2

?

?

?

?

?

11. 3}3} pt =

T

14. 2 T =

T

qt

?

3. 40 fl oz =

c

6. 16 pt =

?

qt

pt

9. 1}1} T =

?

lb

12. 3 gal =

?

pt

15. 1}1} qt =

?

c

2

c

oz

2

17. 96 oz =

?

lb

18. 64 fl oz =

20. 2}1} lb =

?

oz

21. 11 qt =

2

?

c

?

4

fl oz

19. 32,000 oz =

?

?

?

c

gal

Choose the better estimate for each measure. 22. the weight of a bag of potatoes: 5 tons or 5 pounds

23. the amount of water in a sports bottle: 16 fluid ounces or 4 pints

24. the weight of an apple: }1} pound or 32 ounces 2


605


Lesson 12–2

1. 2 lb =

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Capacity and Weight in the Customary System 1. COOKING Sylvia is making a pot of stew that needs 1 quart of beef broth. How many cups of beef broth does she need?

2. CANDY Wade works at the candy shop. He wrapped 56 pieces of fudge to sell. How many total pounds of fudge did he wrap if each piece weighed 1 ounce?

3}1} lb 2

3. TRUCKS Shauna’s truck can handle up to 4. GIFTS Jason made 34 bottles of flavored 2 tons of weight. She wants to haul olive oil to give to his class. How many 3,500 pounds of wood. How many tons of pints of flavored olive oil did Jason make wood is that? Can she haul all of it at if each bottle holds 8 fluid ounces? once?

5. CIDER Mary bought five gallons of apple cider for her birthday party. She expects 20 guests. How many cups of cider will each guest get?

6. PETS Pam has a 4-pound bag of dry cat food. Every day she puts out 4 ounces of dry cat food for her cat. For how many days will the bag of cat food be enough to feed her cat? Explain.

7. LUNCH Suzie fills a 1-pint thermos with milk each day for lunch. How many times will she be able to fill her thermos

8. COOKING James is making a quart of won ton soup using canned chicken broth. A can of chicken broth holds 14 fluid ounces. How many cans will James need to buy? Explain how you found your answer.

with }1} gallon of milk? Explain how you 2

found your answer.

Sample answer: 1 qt 5 4 c, 4 c 5


606


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Capacity and Weight in the Customary System Pre-Activity Complete the Mini Lab at the top of page 470 in your textbook. Write your answers below. Complete. 1. 1 quart 5

pints

2. 2 quarts 5

pints

3. 1 gallon 5

quarts

4. 1 gallon 5

pints

5. What fractional part of 1 gallon would fit in 1 pint?

6. How many gallons are equal to 12 quarts? Explain.

Reading the Lesson

For Exercises 8 and 9, write a word in the blank to make the sentence true. 8. To change a larger unit of capacity to a smaller unit of capacity, you

.

9. To change a smaller unit of capacity to a larger unit of capacity, you

.

10. What are the three most commonly used units of weight in the customary system?

Helping You Remember 11. What measuring devices do you have in your home that you can use to determine the capacity or weight of an object? Using each device, complete a table like the following. Find measures for several objects. Object Capacity Capacity Capacity Capacity

Measuring Device

Measure

or Weight or Weight or Weight or Weight


607


Lesson 12–2

7. Describe how you could determine the liquid capacity of a waterproof container.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Relating Customary and Metric Units Both customary and metric measurements are used in the United States. Therefore, it is a good idea to develop some sense of the relationships between the two systems. Here are some rules of thumb that are commonly used. An inch is about equal to 2.5 centimeters. A yard is a little less than a meter. A mile is a little more than 1.5 kilometers. A kilogram is a little more than 2 pounds. A liter is a little more than 1 quart. Use the relationships given above. Tell whether each statement is true or false. 1. A length of 4 meters is longer than 4 yards.

2. A weight of 10 pounds is more than 5 kilograms.

3. A capacity of 1 gallon is more than 4 liters.

4. A length of 1 foot is about the same as 30 centimeters.

5. A kilometer is more than half a mile.

6. A pound is a little more than half a kilogram.

7. On a road in Canada, the posted speed limit is 45 kilometers per hour. Aimée is driving at a speed of 40 miles per hour. Is this above or below the speed limit?

9. The posted load limit for a bridge is 5 tons. The mass of Darryl’s truck is 1,500 kilograms, and it is holding cargo that weighs a half ton. Can Darryl drive his truck across the bridge? © Glencoe/McGraw-Hill

8. Sean has a recipe that calls for 0.25 L of milk. He has a one-cup container of milk in the refrigerator. Is this enough milk for the recipe?

10. Leah is pouring paint from a 5-gallon can into some jars. She has twelve jars that each hold 1 liter and six jars that each hold 1.25 liters. Does she have enough jars for all the paint?

608


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Length in the Metric System The meter is the basic unit of length in the metric system. The most commonly used metric units of length are shown below.

Metric Units of Length Unit

Model

Benchmark

1 millimeter (mm)

thickness of a dime

25 mm < 1 inch

1 centimeter (cm)

half the width of a penny

2.5 cm < 1 inch

1 meter (m)

width of a doorway

1 kilometer (km)

six city blocks

1 m < 1.1 yard 1.6 km < 1 mile

Write the metric unit of length that you would use to measure each of the following. height of a box of popcorn The height of a box of popcorn is more than the width of a penny, but less than the width of a doorway. So, the centimeter is an appropriate unit of measure. length of a car Since the length of a car is greater than the width of a doorway, but less than six city blocks, the meter is an appropriate unit of measure. 5 cm

Measure the length of the line segment in centimeters.

cm

1

2

3

4

5

Write the metric unit of length that you would use to measure each of the following. 1. height of a mountain

2. thickness of a dried bean

3. length of a pen

4. height of a table

Measure each line segment in centimeters and millimeters. 5.

6.

7.

8.


609


Lesson 12–3

The line segment is 5 cm.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Length in the Metric System Write the metric unit of length you would use to measure each of the following. 1. depth of an ocean

2. length of an eyelash

3. length of your bedroom

4. length of the Panama Canal

5. height of a can of soup

6. depth of a swimming pool

7. length of the eye of a needle

8. height of a washing machine

9. length of a pencil

10. width of a pencil

Measure each line segment or side of each figure in centimeters and millimeters. 11.

14.


12.

13.

15.

16.

610


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Length in the Metric System TRAVEL For Exercises 1 and 2, use the figures below.

To

pa oth

ste ?

1. Gabe is going on a trip to San Diego. He is taking a tube of toothpaste and a toothbrush holder. How long is the tube of toothpaste in centimeters and in millimeters?

2. How long is the toothbrush holder in centimeters and in millimeters?

3. SWIMMING Harry takes diving lessons at the community pool. He is trying to estimate the depth of the deepest part of the pool. Which is the most likely estimate: 3.5 centimeters, 3.5 meters, or 3.5 kilometers? Explain.

4. INSECTS Michaela is an entomologist, a scientist who studies insects. When she measures the length of the leg of a fly, what metric unit of measure does she most likely use?

5. SCHOOL Roshawn rides his bike

6. BRIDGES Paula noticed an error in the following statement, “The Golden Gate Bridge in San Francisco, California, is the second longest suspension bridge in North America spanning 1,260 kilometers.” What is the error Paula found? Explain.

2}1} miles to and from school. What type 2 of measurement would he use if he were to convert the distance to metric units? Explain.


611


Lesson 12–3

?

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Length in the Metric System Pre-Activity Read the introduction at the top of page 476 in your textbook. Write your answers below. 1. What unit of measure is used?

2. What is the depth of the deepest point?

3. Use the Internet or another source to find the meaning of meter. Then write a sentence explaining how a meter compares to a yard.

Reading the Lesson 4. Look up the word decimeter in a dictionary. How long is a decimeter?

5. Complete the following table. Unit

Abbreviation Number of Meters Number of Units in a Meter km

meter

millimeter

m dm cm mm

1,000 1

0.001 1 10

0.1

0.01 0.001

100

1,000

6. Using information in the table above, explain what it means to say that the metric system is a decimal system.

Helping You Remember 7. Work with a partner. Kilo-, deci-, centi-, and milli- are combining forms. They are found combined with other words. In a dictionary, look up the meanings for kilo-, deci-, centi-, and milli-. Then explain the meanings of kilometer, decimeter, centimeter, and millimeter.


612


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment A Metric Crossword Puzzle Here is a crossword puzzle with a “twist.” To locate the first letter of each word, you have to measure from the upper left corner of the puzzle. Each square of the puzzle measures 1 cm on each side. The first word has been entered for you, to help you get started. Good luck! Across • 2.5 cm across, 25 mm down Ask • 6.5 cm across, 35 mm down Compact disc (abbreviation)

Down

• 3.5 cm across, 15 mm down Light Red

• 65 mm across, 3.5 cm down Young person

• 4.5 cm across, 65 mm down Customary unit of length

• 35 mm across, 0.5 cm down Opposite of closed

• 6.5 cm across, 5 mm down Opposite of P.M.

• 75 mm across, 3.5 cm down Ten cents

• 5.5 cm across, 55 mm down Boy’s name

• 15 mm across, 3.5 cm down Wave in Spanish

• 3.5 cm across, 35 mm down New Hampshire (abbreviation)

• 65 mm across, 0.5 cm down Alaska (abbreviation)

• 0.5 cm across, 5 mm down Yellow, egg-shaped fruit

• 25 mm across, 4.5 cm down Belonging to me

• 6.5 cm across, 45 mm down Greeting

• 45 mm across, 0.5 cm down Opposite of day

• 0.5 cm across, 35 mm down Face- ? -face

• 55 mm across, 5.5 cm down Type of metal

• 0.5 cm across, 45 mm down Kind of tree

• 5 mm across, 0.5 cm down Pay attention

• 0.5 cm across, 75 mm down Saturday and Sunday

• 45 mm across, 6.5 cm down Maine (abbreviation)


613


Lesson 12–3

• 0.5 cm across, 55 mm down Thin, pointed piece of metal

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Mass and Capacity in the Metric System In the metric system, the most commonly used units of mass are the milligram (mg), gram (g), and kilogram (kg). One milligram is 0.001 gram and 1 kilogram is 1,000 grams. Metric Units of Mass Unit

Model

Benchmark

1 milligram (mg)

grain of salt

1 mg < 0.00004 oz

1 gram (g)

small paper clip

1 g < 0.04 oz

1 kilogram (kg)

six medium apples

1 kg < 2 lb

Write the metric unit of mass that you would use to measure a portable radio. Then estimate the mass. A portable radio has a mass greater than six apples. So, the kilogram is the appropriate unit. Estimate Since a portable radio is about three times heavier than six apples, the mass of a portable radio is about 3 kilograms. The basic unit of capacity in the metric system is the liter (L). One milliliter (mL) is 0.001 liter. Metric Units of Capacity Unit

Model

Benchmark

1 milliliter (mL)

eyedropper

1 mL < 0.03 fl oz

1 liter (L)

small pitcher

1 L < 1 qt

Write the metric unit of capacity that you would use to measure a mug of soup. Then estimate the capacity. A mug of soup is greater than an eyedropper and less than a small pitcher. So, the milliliter is the appropriate unit. Estimate There are 1,000 milliliters in a liter. A small pitcher can fill about 4 mugs. So, a mug of soup is about 1,000 ÷ 4 or about 250 milliliters.

Write the metric unit of mass or capacity that you would use to measure each of the following. Then estimate the mass or capacity. 1. peanut

2. serving of salad dressing

3. eyelash

4. large soda bottle

5. bottle of milk

6. house cat

7. screw

8. pencil


614


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Mass and Capacity in the Metric System Write the metric unit of mass or capacity that you would use to measure each of the following. Then estimate the mass or capacity. 1. leaf

2. large cup of hot chocolate

3. home aquarium

4. feather

5. crayon

6. water in a plastic wading pool

7. mosquito

8. penny

10. bowling ball

11. liquid in a thermometer

12. teaspoon of vanilla extract

13. rectangular eraser

14. grain of sand

15. wheat bread sandwich

16. banana

17. pot of tea

18. calculator

19. house cat

20. car key

21. small glass of juice

22. pair of skis

23. water in a washing machine for large load

24. piano

25. tube of oil paint

26. small bucket of soapy water

27. feather pillow

28. hammer

29. surfboard

30. can of soup


615


Lesson 12–4

9. spaghetti sauce in a saucepan

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Mass and Capacity in the Metric System 1. ANTS Earl has an ant farm. What metric unit of mass would Earl use to measure one of his ants?

2. MEDICINE Garry is taking a tablespoonful of cough syrup for his cold. What is the metric unit of measure most likely used for his recommended dosage? Estimate the amount.

3. WEIGHTLIFTING Amy does three sets of squats with 85 pounds at the gym. What metric unit of measure would Amy use to measure the weight she lifts?

4. FISHING Which is the most likely unit of measure Jacob finds on his fishing weights: milligram, gram, or kilogram?

5. DOGS What metric unit of mass would Toni most likely use to measure the mass of her dog?

6. AQUARIUMS Sage is making a fish tank out of an old 5-gallon glass water bottle. What unit of metric measure should she use to decide how much water the bottle will hold? Estimate the amount.

7. PETS Carla’s dog eats 321 grams of beef chow and 410 grams of chicken chow each day. Meda’s dog eats 1 kilogram of mixed chow each day. Whose dog eats more chow each day? Explain your reasoning.

8. SHOPPING Liquid detergent comes in 1.62-liter bottles and 1,500-milliliter bottles. Which bottle contains more detergent? Explain your reasoning.


616


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Mass and Capacity in the Metric System Pre-Activity Complete the Mini Lab at the top of page 484 in your textbook. Write your answers below. 1. How does the number of paper clips needed to balance the roll of breath mints compare to the mass of the roll in grams? 2. Estimate the mass of one paper clip. 3. How many paper clips were needed to balance 2 pencils? 4. What is the mass of 1 pencil in grams?

Reading the Lesson 5. In your own words, describe the difference between mass and capacity.

6. Complete the following table. Unit

Abbreviation Number of Grams kg

gram

g mg

1,000 1

Number of Units in a Gram

0.001 1 1,000

0.001

7. Tell which of the following are units of mass and which are units of capacity—gram, liter, milliliter, milligram, kilogram.

8. Look at the labels on various products you have in your home. List three items that have a mass greater than 1 kilogram, three items that have a mass between 1 gram and 1 kilogram, and three items that have a mass less than 1 gram. Identify each item by name and list its actual metric mass as given on the label. Do the same for capacity, listing three items that are 1 liter or greater, and three that are less than 1 liter.


617


Lesson 12–4


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Length, Mass, or Capacity? When you encounter a problem about measurement, you won’t necessarily see or hear one of the words length, mass, or capacity. Often you need to decide what type of measurement is involved, then choose the best unit of measure. Tell whether each question most likely involves length, mass, or capacity. 1. Do I have enough milk to make this recipe?

2. Do I have enough string to tie around this package?

3. Will this punch bowl fit inside that box?

4. Will this amount of punch fit inside that bowl?

5. Is that tunnel high enough for this truck to drive through it?

6. Is that bridge strong enough for this truck to drive over it?

Circle the most reasonable measure for each object. 7. height of a doorway 2g

2 kg

2L

2 mL

2m

2 cm

1,000 L

1,000 mL

1,000 m

1,000 cm

15 mL

1.5 m

150 cm

4L

0.4 m

400 cm

8. load limit of an elevator 1,000 g

1,000 kg

9. amount of water in a bathtub 150 g

1.5 kg

150 L

10. amount of cereal in a cereal box 400 g

4 kg

4,000 mL

Name an item that you think has the given measure. 11. about 2 kg

12. about 250 mL

13. about 30 cm

14. about 25 g


618


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention To change from one unit to another within the metric system, you can either multiply or divide by powers of ten.

thousandths

hundredths centi

Each place value is 10 times the place value to its right.

milli

tenths

0.01 0.001

deci

ones

0.1

basic unit

1

tens

hundreds hecto

10

deka

thousands kilo

1,000 100

• To change from larger units to smaller units, multiply. • To change from smaller units to larger units, divide. 3 1,000

Multiply larger unit

km 4 1,000

3 100 m

3 10

cm 4 100

mm 4 10

smaller unit Divide

Complete. 650 cm =

?

m

?

Since 1 meter 5 100 centimeters, divide by 100. 650 4 100 5 6.5 So, 650 cm 5 6.5 m. 9,100 g =

?

mL = 3.2 L

Since 1 liter 5 1,000 milliliters, multiply by 1,000. 3.2 3 1,000 5 3,200 So, 3,200 mL 5 3.2 L.

kg

CHECK Since a kilogram is a larger unit than a gram, Since 1 kilogram 5 1,000 grams, divide by 1,000. 9,100 4 1,000 5 9.1 the number of kilograms should be less than So, 9,100 g 5 9.1 kg. the of grams. The answer seems reasonable.

Complete. 1. 2.5 L 5 4. 25 cm 5 7.

?

?

mL

?

mm

m 5 5.6 km

10. 6.21 L 5

?


mL

2. 400 mm 5

?

5. 4,100 cm 5

cm

3. 8.4 g 5

m

6. 3.2 m 5

?

mm

9. 0.6 kg 5

?

g

?

8. 1,900 g 5

?

kg

11. 900 mg 5

?

g

619

12.

?

?

mg

km 5 500 m


Lesson 12–5

Changing Metric Units

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Changing Metric Units Complete. ?

1. 530 mm =

cm

3. 1,500 mL =

?

L

2. 23 kg =

4.

?

?

g

m = 340 cm

5. 13 cm =

?

mm

6. 16 g =

7. 3.72 L =

?

mL

8.

?

cm = 9.75 m

m

10.

?

m = 524 cm

9. 149 cm =

11.

?

g = 0.56 kg

13. 1.5 km =

15.

?

?

?

12. 3 mm =

m

?

19. 2 kg =

?

21. 0.89 m =

16. 2.5 L =

cm

mg

?

mg

?

cm

14. 4,200 mm =

L = 650 mL

17. 13.2 m =

?

18.

?

?

?

m

mL

mm = 8.3 m

20. 6,000,000 mm =

cm

22. 0.085 g =

?

?

mg

23.

?

m = 4,600 mm

24.

?

kg = 7,124 g

25.

?

cm = 40 mm

26.

?

m = 7 km

27.

?

mL = 0.0817 L

28. 480 mL =

29. 5,000 mg =

?


kg

30. 4.8 km =

620

?

?

km

L

cm


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems 1. MEDICINE Stephanos got a travel pack of 4 aspirin, each 500 milligrams. How many total grams are in the pack?

2. SNAILS While doing a report on snails, Kay learned that the average snail moves about 0.013 meter per second. How many centimeters per second does a snail move?

3. SPORTS The Wildcats’ water cooler holds 15.3 liters of sports drink. How many milliliters is that?

4. BAKING A box of specialty baking flour holds 1.8 kilograms. How many angel food cakes can be made with a recipe that calls for 100 grams of flour?

5. WRESTLING As a Sumo wrestler, Ishi must weigh a minimum of 70 kilograms. How many grams is that?

6. SOCCER Joey walks 4.2 kilometers to soccer practice. How many meters does he walk?

7. MILK Each week Mrs. Lopez has six 946-milliliter bottles of milk delivered to her home. How many liters is each bottle?

8. EARTH Beth’s class is studying earthquakes. They learned that the Pacific plate, a huge section of the Earth’s crust, moves 45 millimeters per year. How many centimeters per year is that?


621


Lesson 12–5

Changing Metric Units

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Changing Metric Units Pre-Activity Complete the Mini Lab at the top of page 490 in your textbook. Write your answers below. 1. How many cans did it take to fill the 2-liter bottle? 2. If the capacity of a soda can is 355 milliliters, how would you find the number of milliliters in the 2-liter bottle? 3. How many milliliters are in 2 liters? 4. Based on this information, how could you find the number of milliliters in one liter? 5. How many milliliters are in one liter?

Reading the Lesson Write the name for each of the following amounts. 6. one thousand grams

7. one thousandth of a gram

8. one hundred meters

9. one hundredth of a meter

10. ten liters

11. one tenth of a liter

12. Look at the illustration at the bottom of page 490. Explain each operation.

13. Circle the underlined word that makes the sentence true. To divide by 100, move the decimal point two places to the (left, right).

Helping You Remember 14. Make a copy of the place-value chart on page 490. Using numerals, explain to someone else how to use the diagram to indicate various metric units of measure.


622


NAME ________________________________________ DATE ______________ PERIOD _____

Other Metric Units Meters, millimeters, centimeters, and kilometers are the most commonly used metric units of length. But did you know that there are other units, like decimeters, dekameters, and hectometers? This table shows how all these units are related to the meter. Unit

Number of Meters

kilometer (km)

1,000 m

hectometer (hm)

100 m

dekameter (dam)

10 m

meter (m)

1m

decimeter (dm)

0.1 m

centimeter (cm)

0.01 m

millimeter (mm)

0.001 m

Each unit in the table is ten times as large as the unit below it. So, 1 km 5 10 hm, and 1 hm 5 10 dam. It follows that 1 km 5 (10 3 10) dam, or 1 km 5 100 dam.

Use the table to complete each statement. 1. 1 dm 5

cm

4. 12 km 5

dam

7. 1 m 5

dm 5

8. 1 km 5

hm 5

2. 1 dm 5

mm

5. 8.5 km 5 cm 5

3. 5 hm 5

hm

dam

6. 3.2 dam 5

dm

mm

dam 5

m

Complete each table, modeling it on the table above. 9. Unit

Number of Grams

kilogram (kg)

1,000 g

gram (g)

1g

milligram (mg)

0.001 g


10.

623

Unit

Number of Liters

liter (L)

1L


Lesson 12–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Measures of Time Units of Time Unit

Model

1 second (s)

time needed to say 1,001

1 minute (min) 5 60 seconds

time for 2 average TV commercials

1 hour (h) 5 60 minutes

time for 2 weekly TV sitcoms

To add or subtract measures of time, first add or subtract the seconds, next add or subtract the minutes, and then add or subtract the hours. Rename if necessary in each step.

Find the sum of 3 h 14 min 12 s and 4 h 48 min 3 s.

Find the difference of 5 h 7 min 20 s and 2 h 25 min 12 s.

Estimate 3 h 14 min 12 s is about 3 h, and 4 h 48 min 3 s is about 5 h. 3 h 1 5 h 5 8 h.

Estimate 5 h 7 min 20 s is about 5 h, and 2 h 25 min 12 s is about 2 h. 5 h 2 2 h 5 3 h.

3 h 14 min 12 s Add seconds first, then 14 h 48 min 3 s minutes, and finally hours. 7 h 62 min 15 s 62 minutes equals

5 h 7 min 20 s Since you cannot subtract 22 h 25 min 12 s 25 minutes from 7 minutes, you must rename 5 hours 7 minutes as 4 hours 67 minutes.

1 hour 2 minutes.

So, the sum is 8 h 2 min 15 s. Compare the answer to the estimate.

5 h 7 min 20 s 22 h 25 min 12 s

4 h 67 min 20 s → 22 h 25 min 12 s 2 h 42 min 8 s Compare the answer to the estimate.

Gloria practiced on her flute from 11:40 A.M. until 1:52 P.M. How long did she practice? You need to find how much time has elapsed. Gloria’s practice time is 20 minutes 1 1 hour 52 minutes or 1 hour 72 minutes. Now rename 72 minutes as 1 hour 12 minutes. 1 h 1 1 h 12 min 5 2 h 12 min. Gloria practiced for 2 hours 12 minutes.

11:40 A.M. to 12:00 noon is 20 minutes.

12:00 noon to 1:52 P.M. is 1 hour 52 minutes.

Add or subtract. 1.

4 h 18 min 11 s 23 h 15 min 4 s

2.

6 h 7 min 42 s 12 h 12 min 38 s

3.

5 h 18 min 12 s 22 h 6 min 41 s

Find each elapsed time. 4. 4:25 P.M. to 11:55 P.M. © Glencoe/McGraw-Hill

5. 9:20 A.M. to 5:05 P.M.

624

6. 10:30 A.M. to 1:43 P.M.


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Measures of Time 1.

23 min 16 s 112 min 34 s

2.

9 h 42 min 23 h 18 min

3.

6 h 38 min 15 h 22 min

4.

6 min 15 s 22 min 32 s

5.

4 h 43 min 111 h 27 min

6.

12 min 43 s 1 9 min 58 s

7.

21 min 54 s 126 min 19 s

8.

14 h 2 9 h 43 min

9.

2 h 13 min 28 s 18 h 20 min 15 s

10.

12 h 20 min 38 s 2 7 h 13 min 20 s

11.

2 h 15 min 2 s 14 h 48 min 9 s

12.

11 h 14 min 27 s 2 2 h 13 min 45 s

13.

11 h 23 min 6 s 2 5 h 36 min 29 s

14.

6 h 10 min 47 s 12 h 51 min 28 s

15.

20 h 2 8 h 33 min 18 s

Find each elapsed time. 16. 6:35 A.M. to 9:55 A.M.

17. 12:20 P.M. to 3:05 P.M.

18. 11:05 A.M. to 4:37 P.M.

19. 10:45 A.M. to 5:25 P.M.

20. 9:18 P.M. to 1:33 A.M.

21. 9:52 A.M. to 5:20 P.M.


625


Lesson 12–6

Add or subtract.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Measures of Time 1. BUS RIDES Cheryl rides the city bus to and from ballet practice. Her ride to the dance studio takes 48 minutes. Her ride home takes 1 hour 7 minutes. What is the total time Cheryl rides the bus?

2. ECLIPSES Heather has seen two solar eclipses; one on June 21, 2001, which took 4 min 57 s and the other on August 11, 1999, which took 2 min 23 s. How much longer did the Sun take to complete the eclipse in 2001?

3. TRAVEL The Rosenberg family is taking a road trip. First they will drive 9 hours 53 minutes to camp in the Red Rock Canyons. Then they will drive 8 hours 21 minutes to ski near Salt Lake City. What will be their total driving time?

4. RUNNING The Boston Marathon course record holder in the Women’s Open is Margaret Okayo. She ran the course in 2 hours, 20 minutes, and 43 seconds. Jean Driscoll is the record holder in the Women’s Wheelchair division with a time of 1 hour 34 minutes 22 seconds. How much longer did it take Okayo to finish the course?

5. BEACH Toni left at 6:45 A.M. to go surfing. She got home 7 hours and 26 minutes later. What time did she get home?

6. HOMEWORK James started doing his homework at 10:35 A.M. and stopped at 1:17 P.M. What was the total time he spent on homework?

7. TRAVEL Kevin is flying from San Francisco, California, to Hartford, Connecticut, with a layover in New York. His flight from California to New York will take 5 hours and 22 minutes. His flight from New York to Connecticut will take 53 minutes. What is his total flying time?

8. PAINTING Geri worked on her painting this morning from 10:15 A.M. to 12:32 P.M., then again in the afternoon from 4:45 P.M. to 6:30 P.M. How much time did she spend total working on her painting?


626


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Measures of Time Pre-Activity Read the introduction at the top of page 494 in your textbook. Write your answers below. 1. How long did Bethany take to wash the car? 2. How long did Bethany take to fold laundry?

4. What is the sum of the hours? 5. How long did it take to wash the car and fold the laundry?

Reading the Lesson 6. In Example 1 on page 494, why is it necessary to rename?

7. In Example 2 on page 495, why is it necessary to rename?

8. Write each of the following in simplest form. Remember to rename as needed. 1 hr 67 min 12 s 3 hr 59 min 78 s 4 hr 47 min 13 s

9. Look at Example 3 on page 495. What if the plane left Boston at 9 A.M. and the flight took the same length of time? What time would the plane land in Miami?

Helping You Remember 10. Work with a partner. One partner finds the sum of 3 h 15 min 37 s and 1 h 50 min 45 s. The other partner finds the difference. Show all computation and explain each step to your partner.


627


Lesson 12–6

3. What is the sum of the minutes?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Fractions of Time Denise organized information about some of her activities into the chart you see at the right. Then she decided to estimate what fraction of the school day she spends studying. This is how she did it. 4:00 P.M.–5:15 P.M.

→

1 h 15 min

7:00 P.M.–8:00 P.M.

→

1h

Total

2 h 15 min

Then she rounded 2 h 15 min to 2 h. Denise estimated that she spends about }2}, or 24 1 }}, of her day studying. 12

breakfast

7:15 A.M. – 7:30 A.M.

classes

8:05 A.M. – 11:30 A.M.

lunch

11:30 A.M. – 12:20 P.M.

classes

12:20 P.M. – 2:15 P.M.

swimming

2:25 P.M. – 3:30 P.M.

studying

4:00 P.M. – 5:15 P.M.

dinner

5:30 P.M. – 6:30 P.M.

studying

7:00 P.M. – 8:00 P.M.

watching TV

8:00 P.M. – 9:55 P.M.

sleeping

10:30 P.M. – 6:45 A.M.

Use the chart above. Estimate what fraction of a school day Denise spends on each activity. 1. swimming

2. watching TV

3. classes

4. eating

5. sleeping

6. at school (classes and lunch)

7. Denise sleeps from 11:30 P.M. until 8:30 P.M. on Saturday and Sunday. About what fraction of the seven-day week does she spend sleeping?

8. Denise studies about 4 hours on Saturday and about 2 hours on Sunday. About what fraction of the seven-day week does she spend studying?

9. Denise goes to school 180 days of the year. About what fraction of the 365-day year does she spend in classes?


10. Denise tries to swim every day at the same time, Monday through Friday, all through the year. About what fraction of the year does she spend swimming?

628



Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860076-6 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03







Chapter 13 Assessment Chapter 13 Test, Form 1 ........................679–680 Chapter 13 Test, Form 2A ......................681–682 Chapter 13 Test, Form 2B ......................683–684 Chapter 13 Test, Form 2C......................685–686 Chapter 13 Test, Form 2D......................687–688 Chapter 13 Test, Form 3 ........................689–690 Chapter 13 Extended Response Assessment ...............................................691 Chapter 13 Vocabulary Test/Review...............692 Chapter 13 Quizzes 1 & 2..............................693 Chapter 13 Quizzes 3 & 4..............................694 Chapter 13 Mid-Chapter Test .........................695 Chapter 13 Cumulative Review......................696 Chapter 13 Standardized Test Practice..697–698 Standardized Test Practice Student Recording Sheet ..............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A27

iii



Practice: Skills










iv

Enrichment






Assessment Options












v

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics This is an alphabetical list of new vocabulary terms you will learn in Chapter 13. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term

Found on Page


acute [uh-KYOOT] angle angle bisect [BYE-sehkt] complementary congruent [kuhn-GROO-uhnt] congruent figures corresponding parts degree [dih-GREE] equilateral [e-kwuh-LA-tuh-rul] triangle heptagon [HEP-tuh-GAHN] hexagon [HEK-suh-GAHN] isosceles [eye-SAH-suh-LEEZ] triangle line of symmetry [SIH-muh-tree] line symmetry obtuse [ahb-TOOS] angle © Glencoe/McGraw-Hill

vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


octagon parallelogram pentagon perpendicular [PUHRpuhn-DIH-kyuh-luhr] polygon quadrilateral [KWAHdruh-LA-tuh-ruhl] rectangle regular polygon rhombus [RAHM-buhs] right angle rotational symmetry scalene [SKAY-LEEN] triangle side similar figures square straight angle supplementary triangle vertex


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: the geometric principle of Every time we look in a mirror we see asures, lines of symmetry, reflection at work. We use angle me to see our reflection from and reflection when hanging a mirror ror of a car to check other head to toe, when using the side mir traffic, and when building a telescope. and Polygons, your child In Chapter 13, Geometry: Angles re angles, construct will learn how to classify and measu symmetry, congruency, and segments and angles, and determine r, your child will complete a similarity. In the study of this chapte and activities and variety of daily classroom assignments possibly produce a chapter project . it with your child, you agree By signing this letter and returning olved. Enclosed is an to encourage your child by getting inv t also relates the math activity you can do with your child tha the real world. You may we will be learning in Chapter 13 to dy Tools for self-check also wish to log on to the Online Stu ide pages, and other quizzes, Parent and Student Study Gu you have any questions or study help at www.msmath1.net. If school. comments, feel free to contact me at Sincerely,

Signature of Parent or Guardian ________________________________________DATE ________


ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Lines of Symmetry Have a family member name four letters of the alphabet. Write each capital letter below. Then draw all lines of symmetry. Check the symmetry lines with your family member. 1.

2.

3.

4.

Have a family member draw a picture or trace a small object on either side of each line. Then draw the reflection of each figure. Check the reflections together. 5.

6.

7.

8.


x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Angles Angles have two sides that share a common endpoint called the vertex. Angles are measured in degrees. One degree is equal to }1}th of a circle. 360

Angles can be classified according to their measure. right angle symbol Obtuse angles measure between 90˚and 180˚.

sides

vertex

Straight angles measure 180˚. Acute angles measure between 0˚ and 90˚.

Right angles measure 90˚.

90

100 80

110 70

12 0 60

30˚

13 50 0 40

15

0

0 15 30

20 160

160 20

10 170

170 10

0˚

The angle measures 308. It is an acute angle. Two angles are complementary if the sum of their measures is 908.

Align the center of the protractor. This angle measures 30˚.

Two angles are supplementary if the sum of their measures is 1808. ALGEBRA Angles A and B are complementary. If m/A 5 258, what is

the measure of /B? m/A 1 m/B 5 908 258 1 m/B 5 908 258 1 m/B 2 258 5 908 2 258 m/B 5 658

Complementary angles Replace m/A with 258. Subtract 258 from each side.

So, m/B 5 658.

Since 258 1 658 5 908, the answer is reasonable.

Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or straight. 1.

2.

3.

4. ALGEBRA Angles K and L are supplementary. If m/L 5 808, what is m/K? 5. ALGEBRA If m/C 5 408 and /C and /D are complementary, what is m/D? © Glencoe/McGraw-Hill

649


Lesson 13–1

80 100

0

30

50 0 13

70 11 0 60 0 12

14

To measure an angle, place the center of a protractor on the vertex of the angle. Place the zero mark of the scale along one side of the angle. Then read the angle measure where the other side of the angle crosses the scale.

40 14 0

Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Angles Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or straight. 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13. ALGEBRA If m/K 5 608 and /J and /K are complementary, what is m/J?

14. ALGEBRA Angles A and B are supplementary. What is m/B if m/A 5 1208?


650


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Angles SHOPPING For Exercises 1–3, use the

circle graph that shows preferred shopping days of United States shoppers.

Preferred Shopping Days for United States Shoppers 4% Monday 5% Tuesday 13% no preference 7% Sunday

29% Saturday

12% Wednesday 13% Thursday

1. Find the approximate measure of each angle formed by the sections of the circle graph.

2. Find the sum of the measures of the angles of the circle graph.

3. If the shoppers with no preference could be persuaded to shop on Wednesdays, what would be the new angle measure of the Wednesday section of the graph?

4. CARPENTRY Jorge is building a standard bookshelf. For the books to sit squarely on the shelves, will he be using obtuse, right, or acute angles when placing the shelves in the bookcase?

5. TILING Fatima is tiling her bathroom floor. She cut a square tile along one of the diagonals. What is the angle measure created by the diagonal and a side of the tile?

6. PIZZA Cody has half a pizza to share with two of his friends. What angle measure should Cody use to cut half of the pizza into three equal pieces?


651


Lesson 13–1

17% Friday

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Angles Pre-Activity Read the introduction at the top of page 506 in your textbook. Write your answers below. 1. Mai-Lin planted the most of which food? Explain how you came to this conclusion. 2. Of which did she plant the least? 3. The percents 30%, 25%, 20%, 15%, and 10% correspond to the sections in the graph. Explain how you would match each percent with its corresponding section.

Reading the Lesson 4. Complete the following table. Tell how each expression is read. Expression

How the Expression is Read

m/C 08 908 , m/C , 1808 5. Complete the following table. Type of Angle

Number of Degrees

Example

acute right obtuse straight 6. Tell which pair of angles is complementary and which is supplementary. a. 458 and 458 b. 458 and 1358

Helping You Remember 7. Work with a partner. Have each person fold a piece of paper several times to form different sizes of angles. Mark each angle and give it a letter designation. Exchange papers with your partner. Measure each marked angle and identify its type. © Glencoe/McGraw-Hill

652


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Clock Watching You probably don’t have to look far to find an everyday model for an angle. Just look at a clock like the one at the right, and think of the hour and minute hands as the sides of an angle. Here’s how you can find the measure of the angle at 1:00.

11

12

1 2

10 9

There are 3608 in a circle.

3 4

8 7

There are 12 evenly spaced hours on the clock face.

6

5

3608 4 12 5 308 So the measure of the angle at 1:00 is 308.

1. 2:00

2. 5:00

3. 8:00

4. 11:00

5. 3:00

6. 9:00

7. List all the hours when the hands of the clock form an obtuse angle.

8. How many hours are there when the hands of the clock form an acute angle?

9. A straight angle measures 1808. At what hour do the hands of the clock form a straight angle?

10. What is the measure of the angle formed by the hands of the clock at 12:00?

11. How many times between 1:00 and 2:00 do the hands of the clock form a right angle?

12. CHALLENGE How many times each day do the hands of the clock form a right angle? © Glencoe/McGraw-Hill

653


Lesson 13–1

Find the measure of the angle formed by the hands of the clock at each hour.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Using Angle Measures To estimate the measure of an angle, compare it to an angle whose measure you know.

45˚

You can use the measures of these angles to estimate measures of other angles.

90˚

135˚

A protractor and a straightedge can be used to draw angles.

Estimate the measure of the angle shown. Compare the given angle to the angles shown above. The angle is a little greater than 458, so a reasonable estimate is about 458. Draw a 140° angle. Step 2 Place the center point of the protractor on the vertex. Align the mark labeled 0 on the protractor with the line. Find 1408 and make a pencil mark. 70 1 10 60 0 12

80 100

90

100 80

1 10 70

12 0 60

13 50 0 40

0 0 15 30

30 15 0

50 0 13

Step 3 Use the straightedge to draw the side that connects the vertex and the pencil mark.

14

40 14 0

Step 1 Draw one side. Mark the vertex and draw an arrow.

20 16 0

160 20

10 170

170 10

Estimate the measure of each angle. 1.

2.

3.

Use a protractor and a straightedge to draw angles having the following measurements. 4. 358


5. 1108

6. 158

654


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Using Angle Measures Estimate the measure of each angle. 1.

2.

3.

4.

5.

6.

7. 1058

8. 408

9. 808

10. 648

11. 1238

12. 1678

13. 938

14. 268

15. 1428


655


Lesson 13–2

Use a protractor and straightedge to draw angles having the following measurements.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Using Angle Measures 1. TIME Marissa started working on her homework at noon. Since then the minute hand has moved 1808. What time is it now?

2. BICYCLING Scott went for a bike ride. After heading east for a while he turned left 578. Draw an angle showing Scott’s route.

3. PIZZA Rene cut a pizza into eight equal slices. Draw a picture showing how Rene cut the pizza. What is the angle measure of each slice?

4. PIZZA Refer to Exercise 3. What would the angle measure be of three pieces side by side? Draw the angle.

5. CLOCKS Give examples of times when the hour hand and minute hand make a 308 angle, a 608 angle, and a 1508 angle. Draw three clocks showing these times.

6. TILING Stasia has 4 pieces of tile. One angle on each piece measures 388, 228, 688, and 518. Which two pieces should she use side by side to make a right angle?


656


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Using Angle Measures Pre-Activity Complete the Mini Lab at the top of page 510 in your textbook. Write your answers below. 1. Use the wedges to estimate the measure of each angle shown.

2. How did the wedges help you to estimate each angle?

3. Explain how the 908 and 458 wedges can be used to estimate the angle at the right. What is a reasonable estimate for the angle?

Reading the Lesson 5. In this lesson, how do you estimate the measure of an angle?

6. What is one type of a straightedge?

7. Step 2 of Example 2 on page 511 says to find 748 on the correct scale and make a pencil mark. Why does it specify the “correct scale”?

Helping You Remember 8. Work with a partner. Study Example 2 in your textbook. Practice using the steps to draw angles on your own. Then demonstrate to your partner how to draw an angle. Explain what you are doing at each step.


657


Lesson 13–2

4. How would you estimate the measure of any angle without using the wedges?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Compass Directions When a plane is in flight, its direction is expressed as an angle measure. One method of doing this is to give the measure of the angle formed by the plane’s flight path and one of the directions of the compass—north, east, south, or west. For example, this is how you express the two flight paths shown in the figure at the right.

N

plane A 38˚ W

E

plane B

plane A: west 388 north, or W 388 N

72˚

plane B: south 728 west, or S 728 W

S

Write an expression for the direction of each flight path. (You will need to measure the angle with your protractor.) 1.

2.

N

W

E

3.

N

W

S

E

N

W

E

S

S

Use your protractor to draw each flight path. 4. E 708 S

5. E 518 N N

W

N

E

S

6. W 758 N

W

N

E

W

E

S

S

7. CHALLENGE The bearing of a plane is the measure of the angle between its flight path and due north, measured in a clockwise direction. For example, in the figure at the top of the page, the bearing of plane B is 908 1 908 1 728 5 2528. Give the bearing for each flight path in Exercises 1–6. © Glencoe/McGraw-Hill

658


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Bisectors To bisect something means to separate it into two equal parts. You can use a straightedge and a compass to bisect line segments and angles.

Use a straightedge and compass to bisect B wC w.

B

C

Draw w BC w. X

Place the compass at point B. Set the compass greater than wC w. Draw two arcs as shown. Use the same half the length of B setting to place the compass point at C and draw another pair of arcs. Label the intersections X and Y.

B

C Y

X B M

Use a straightedge to align the intersections and draw a segment that intersects B wC w. Label the intersection point M.

C

Y

X wY w bisects w BC w. Use a straightedge and compass to bisect /ABC.

A

A X

Draw /ABC. Place the compass at point B and draw an arc that intersects B both sides of the angle. Label the intersections X and Y.

Use a straightedge to draw w BZ w. w BZ w bisects /ABC.

A X Z B

Y C

B A X Z

YC

B

Y C

Draw each line segment or angle having the given measurement. Then use a straightedge and a compass to bisect the line segment or angle. 1. 2 in.

2. 458

3. 4 cm

4. 1508


659


Lesson 13–3

With the compass at point X, draw an arc as shown. Use the same setting to place the compass point at Y and draw another arc. Label the intersection Z.

C

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Bisectors Draw each line segment or angle having the given measurement. Then use a straightedge and a compass to bisect the line segment or angle. 1. 808

2. 1 in.

3. 1208

4. 408

5. 2 cm

6. 908

7. 3 cm

8. 788

9. 1.25 in.

11. 1658

12. 2.25 in.

10. 258


660


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Bisectors KITES For Exercises 1–6, use the design shown. It shows the kite

B

design Steve is using to build a kite. A

E

C

1. For which line segment should Steve use B wD w as a perpendicular bisector when making his kite?

2. Should Steve use C wA w as a perpendicular bisector for w DB w? Why or why not?

3. Which angles, if any, does B wD w bisect?

4. Should Steve use A wE w as a bisector for /BAD? Why or why not?

5. Use a compass and a straightedge to show where the perpendicular bisector for w BD w would be. Use a dashed line and label it X wY w.

6. Use a compass and a straightedge to bisect /BAD. Use a dashed line and label the bisector w AZ w.


661


Lesson 13–3

D

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Bisectors Pre-Activity Read the introduction at the top of page 515 in your textbook. Write your answers below. 1. Use the Internet or a dictionary to find the meaning of each word.

2. What do the meanings have in common? 3. What does the prefix bi- mean? 4. Make a conjecture about what it means to bisect something.

Reading the Lesson 5. How do you read each of the following? Expression

Read as

NX w w>w NY w /JKM > /MKL 6. When you bisect a line segment, what setting should you use for the compass? Why is it important to set the compass this way?

7. In what other way is the bisector of a line segment related to the line segment?

Helping You Remember 8. Work with a partner. Have one partner study Example 1 and demonstrate how to bisect a line segment. Have the other partner study Example 2 and demonstrate how to bisect an angle.


662


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Creative Constructions The compass and straightedge are very simple tools, yet they can be used to create some very complex and beautiful designs. It might surprise you to know that the designs on this page involve nothing more complicated than bisecting segments and angles! For instance, the outline of the design at the right was created in just four steps.

Step 1

Step 2

Step 3

Step 4

Construct a copy of each design in the empty circle. 2.

Lesson 13–3

1.

Construct a copy of each design on a separate sheet of paper. 3.


4.

5.

663


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Two-Dimensional Figures A polygon is a simple, closed, two-dimensional figure with three or more sides. The number of sides determines a polygon’s name.

triangle (3 sides)

hexagon (6 sides)

quadrilateral (4 sides)

pentagon (5 sides)

heptagon (7 sides)

octagon (8 sides)

When all of the sides and angles of a polygon are congruent, the polygon is a regular polygon.

Identify the polygon. Then tell if it is a regular polygon. The polygon has 7 sides. So, it is a heptagon. Since the sides and angles are not congruent, it is not a regular polygon.

Identify each polygon. Then tell if it is a regular polygon. 1.

2.

3.

4. Draw a quadrilateral with four equal sides and four equal angles. Identify this quadrilateral.


664


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Two-Dimensional Figures Identify each polygon. Then tell if it is a regular polygon. 1.

2.

3.

4.

5.

6.

7.

8.

9.

Draw an example of each polygon. 10. pentagon

Lesson 13–4

11. a scalene triangle

12. a quadrilateral that is not a rectangle


665


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Two-Dimensional Figures STAINED GLASS For Exercises 1–6,

use the design for a stained glass window shown.

A

B

C

O

N

D

P

T M

E

F Q

S

L

K

R

J

I

G

H

1. Find and name two triangles in the design.

2. Is there a regular quadrilateral in the design? If so, where is it?

3. Find and name an octagon in the design.

4. Can you find a parallelogram in the design? Identify it.

5. Is the pentagon CQRST a regular pentagon? Explain.

6. If the perimeter of the window is 8 feet, what is the length of each side? How do you know?

COMMON OBJECTS For Exercises 7 and 8, use the list of polygons you see on a

regular basis. door

stop sign

textbook cover

vinyl album cover

computer screen

CD case

7. Which object on the list is not a quadrilateral? What type of polygon is it?


8. Are there any objects on the list that are regular? If so, what are they? Explain.

666


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Two-Dimensional Figures Pre-Activity Complete the Mini Lab at the top of page 522 in your textbook. Write your answers below. 1. What is true about the angles and sides of a square?

2. Using two more straws, what changes need to be made to the square to form a rectangle that is not a square?

3. How are rectangles and squares alike? How do they differ?

4. Push on one vertex of the rectangle so it is no longer a rectangle. What is true about the opposite sides?

Reading the Lesson 5. For each polygon, write the number of sides. a. hexagon

sides

d. heptagon

b. triangle

sides

e. octagon

c. pentagon

sides

sides sides

f. quadrilateral

sides

6. What do tick marks through the sides of a figure indicate? What do the arcs in the angles of a figure indicate?


Identify the Figure


Congruent Sides

Parallel Sides

Angles

opposite

all

opposites are congruent

all

all

opposites are congruent

opposite

all

all are right angles

all

all

all are right angles

667


Lesson 13–4

7. Quadrilaterals can be classified by their sides and their angles. Complete the following table and study it until you can identify quadrilaterals easily.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Making Conjectures A conjecture is an educated guess or an opinion. Mathematicians and scientists often make conjectures when they observe patterns in a collection of data. On this page, you will be asked to make a conjecture about polygons. Use a protractor to measure the angles of each polygon. Then find the sum of the measures. (Use the quadrilateral at the right as an example.) 1.

2.

3.

4.

5.

6.

107˚

121˚

89˚

43˚

89˚ 1 107˚ 1 121˚ 1 43˚ 5 360˚

7. Make a conjecture. How is the sum of the angle measures of a polygon related to the number of sides?

8. Test your conjecture. On a clean sheet of paper, use a straightedge to draw a hexagon. What do you guess is the sum of the angle measures? Measure each angle and find the sum. Was your conjecture true?


668


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention If a figure can be folded in half so that the two halves match exactly, the figure has line symmetry. The line that separates the figure into two matching halves is a line of symmetry. If a figure can be rotated less than 360° and look exactly as it did before being turned, the figure has rotational symmetry.

Draw all lines of symmetry for each figure. a

b

one line of symmetry

c

four lines of symmetry

no lines of symmetry

Tell whether each figure has rotational symmetry. a

The figure appears as it did before being rotated after being rotated 180°. So, the figure has rotational symmetry. 0˚

90˚

180˚

270˚

360˚

b

The figure looks the same only when rotated 360°. So, the figure does not have rotational symmetry. 0˚

90˚

180˚

270˚

360˚

Draw all lines of symmetry for each figure. 1.

2.

3.

Tell whether each figure has rotational symmetry. Write yes or no. 4.


5.

6.

669


Lesson 13–5

Lines of Symmetry

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Lines of Symmetry Draw all lines of symmetry for each figure. 1.

2.

3.

4.

5.

6.

7.

8.

9.

Tell whether each figure has rotational symmetry. Write yes or no. 10.


11.

12.

670


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems GAMES For Exercises 1–4, use the following information. Katie and

Natalie designed a symmetry game for a math assignment. The strategy of the game is for Katie and Natalie to sit on opposite sides of the board and see the exact same thing on the board. 1. The board they designed is shown below. If Katie and Natalie sit where the K and N are placed, will they see the same thing? In other words, does the board have rotational symmetry?

2. The number 1991 is written in each oval of the board. Do Katie and Natalie see the same thing? Explain.

K N

3. Suppose the number 1961 is written instead. Do Katie and Natalie see the same thing? Explain.

4. What are three more numbers that can be used in this game?

5. NUMBERS Frank and Cassandra drew lines of symmetry for the numbers 1 through 6. Frank says that five numbers do not have any lines of symmetry. Cassandra says that only four do not have any lines of symmetry. Who is correct? Explain.

6. NUMBERS Refer to Exercise 5. Are there any numbers with more than 1 line of symmetry? If so, which one(s)? Explain.


671


Lesson 13–5

Lines of Symmetry

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Lines of Symmetry Pre-Activity Complete the Mini Lab at the top of page 528 in your textbook. Write your answers below. 1. Compare the left side of the figure to the right side.

2. Draw another figure that has the same characteristic as a butterfly, a dragonfly, and a lobster.

Reading the Lesson 3. Look up the word symmetry in a dictionary. Write the meaning of the word as it is used in this lesson.

4. Can a figure have a line of symmetry if the figure does not have line symmetry? Explain.

Helping You Remember 5. Find an object that has rotational symmetry and an object that does not have rotational symmetry. Demonstrate to your class how each object either has or does not have rotational symmetry, and explain why.


672


NAME ________________________________________ DATE ______________ PERIOD _____

African Weaving For the people of Africa, weaving is a form of art. They have woven intricate and beautiful designs into fabric for many centuries. As with so many other art forms, the beauty of their designs is based on geometric principles. The designs on this page were created more than one hundred years ago in the region of Africa that today is Zaire. They are examples of strip patterns, which were repetitive patterns used as decorative borders on clothing. In the exercises below, you will take a closer look at the geometry of these patterns. In a strip pattern, the pattern unit is the basic design that is repeated along the strip. For each of these patterns: a. Identify the pattern unit and make a sketch of it in the space at the right. b. Name the type or types of symmetry that the pattern unit has. 1.

2.

3.

4.


673


Lesson 13–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Similar and Congruent Figures Figures that have the same size and shape are congruent figures. Figures that have the same shape but not necessarily the same size are similar figures.

Tell whether each pair of figures is similar, congruent, or neither. a

b

The parallelograms have the same shape but not the same size, so they are similar.

c

The triangles have the same shape and size, so they are congruent.

The rectangles are neither the same size nor the same shape, so they are neither congruent nor similar.

Tell whether each pair of figures is congruent, similar, or neither. 1.

2.

3.

4.

5.

6.


674


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Similar and Congruent Figures 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.


675


Lesson 13–6

Tell whether each pair of figures is similar, congruent, or neither.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Similar and Congruent Figures TILING For Exercises 1–6, use the following

A

information. Amy is using the design at the right to tile a hexagon-shaped floor. Before deciding which colors to use, she wants to identify all similar and congruent shapes.

G

F

H

I

B

J

E

K

L

M

N

C

D

1. Suppose Amy cut a red tile the size of nACE. What other triangle in the design would that tile fit? In other words, what triangle is congruent to nACE?

2. Amy is looking for congruent quadrilaterals that are neither squares nor rectangles. Can you identify them?

3. Find a triangle that is similar to but not congruent to nBCK.

4. Amy’s friend suggested that she cut four congruent white triangular tiles and place them in the design so that they are not overlapping and do not share common sides. Is that possible? If so, name the four triangles.

5. Can you help Amy find a shape that is either similar or congruent to AKDJ?

6. Is the hexagon GIKNLJ similar to ABCDEF? How do you know?


676


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Similar and Congruent Figures Pre-Activity Read the introduction at the top of page 534 in your textbook. Write your answers below. 1. How many different-sized triangles are in the pattern?

Reading the Lesson 3. Tell whether each characteristic is true for congruent and similar figures. Write congruent, similar, or both. a. have the same shape b. may or may not have the same size c. must have the same size

4. If the perimeters of the four arms of the windmill in Examples 3 and 4 on page 535 are added together, what is the total perimeter?

Helping You Remember 5. Complete the following table. Draw an original figure in the box on the left. Then, for the original figure, draw a figure that is similar, a figure that is congruent, and a figure that is neither similar or congruent. Original Figure


Similar

Congruent

677

Neither


Lesson 13–6

2. Compare the size and shape of these triangles.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Rep-Tiles The word rep-tiles stands for repeating tiles. A geometric figure is a rep-tile if it can be divided into smaller parts according to these rules. 1. All the smaller parts must be congruent to each other. 2. All the smaller parts must be similar to the original tile. Here are two examples of figures that are rep-tiles.

Divide each rep-tile into four congruent parts. 1.

2.

3.

4.

5.

6.

7. CHALLENGE Show how to use four figures like the one at the right to make a rep-tile.


678



Course 11 Course


0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5




ISBN: 0-07-860077-4 1 2 3 4 5 6 7 8 9 10

024

12 11 10 09 08 07 06 05 04 03







Chapter 14 Assessment Chapter 14 Test, Form 1 ........................729–730 Chapter 14 Test, Form 2A ......................731–732 Chapter 14 Test, Form 2B ......................733–734 Chapter 14 Test, Form 2C......................735–736 Chapter 14 Test, Form 2D......................737–738 Chapter 14 Test, Form 3 ........................739–740 Chapter 14 Extended Response Assessment ...............................................741 Chapter 14 Vocabulary Test/Review...............742 Chapter 14 Quizzes 1 & 2..............................743 Chapter 14 Quizzes 3 & 4..............................744 Chapter 14 Mid-Chapter Test .........................745 Chapter 14 Cumulative Review......................746 Chapter 14 Standardized Test Practice..747–748 Unit 6 Test/Review..................................749–750 Second Semester Test ...........................751–753 Final Test ................................................755–760 Standardized Test Practice Student Recording Sheet ..............................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A33

iii



Practice: Skills










iv

Enrichment






Assessment Options












v

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics This is an alphabetical list of new vocabulary terms you will learn in Chapter 14. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term

Found on Page


base

center

cone

cubic units

cylinder [SIH-luhn-duhr]

edge

face


vii


Vocabulary Builder

Vocabulary Builder

NAME ________________________________________ DATE ______________ PERIOD _____


Found on Page


height

lateral face

prism [PRIH-zum]

pyramid [PEER-ah-MIHD]

sphere [Sfeer]

surface area

three-dimensional figure

vertex (vertices) [VUHR-tuc-SEEZ]

volume [VAHL-yoom]


viii


NAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian: of the things that we do. We use mathematical skills in many w students how the One of the goals of this class is to sho classroom is relevant to the information they are learning in the g area and volume is real world. For example, understandin phy, navigation, sports, and useful in such diverse fields as geogra architecture. ng Area and Volume, your uri eas M y: etr om Ge 14, er apt Ch In of parallelograms, triangles, child will learn how to find the areas e three-dimensional figures and circles. Your child will also explor a of rectangular prisms. In and find the volume and surface are will complete a variety of the study of this chapter, your child ivities and possibly produce daily classroom assignments and act a chapter project . it with your child, you agree By signing this letter and returning olved. Enclosed is an to encourage your child by getting inv ld that also relates the activity that you can do with your chi 14 to the real world. You math we will be learning in Chapter e Study Tools for selfmay also wish to log on to the Onlin dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any other study help at www.msmath1.n tact me at school. questions or comments, feel free to con Sincerely,

Signature of Parent or Guardian ____________________ ____________________ DATE ______


ix


Family Letter

Family Letter

NAME ________________________________________ DATE ______________ PERIOD _____

Family Activity Finding Areas of Triangles Work with a family member. Find three triangles in your home. For example, you might find triangles on a food container, in a tile pattern, in a wallpaper pattern, or even in a painting. You can also create triangles by drawing the diagonal of a rectangular object. You will need a ruler or tape measure to complete this activity. 1. Describe the first triangle you found. Use a ruler to measure the height and the base of the triangle. Record the measurements. Height:

Base:

2. The area of a triangle is }1} its base times its height. What is the area of 2 the first triangle?

3. Describe the second triangle you found. Use a ruler to measure the height and the base of the triangle. Record the measurements in the space below. Height:

Base:

4. What is the area of the second triangle?

5. Describe the third triangle you found. Use a ruler to measure the height and the base of the triangle. Record the measurements in the space below. Height:

Base:

6. What is the area of the third triangle?


x


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Area of Parallelograms The area A of a parallelogram is the product of any base b and its height h. Symbols A 5 bh

Model height (h ) base (b )

Find the area of each parallelogram. a 2.2 in.

The base is 4 units, and the height is 7 units.

A 5 bh

A 5 bh

A5437

A 5 4.5 3 2.2

A 5 28

A 5 9.9

The area is 28 square units or 28 units2.

The area is 9.9 square inches or 9.9 in2.

Find the area of each parallelogram. Round to the nearest tenth if necessary. 1.

2.

3.

4.

5.

6. 4.2 yd

10.2 m

3.5 cm

5.4 yd

8.7 m

1.8 cm


699


Lesson 14–1

4.5 in.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Area of Parallelograms Find the area of each parallelogram. Round to the nearest tenth if necessary. 1.

2.

3. 3 ft

7 ft

4.

5.

6. 2.5 cm

7 yd

9 yd

5 cm

10 yd 9 yd

7.

8.

9. 10 in.

14 m

16 in. 15 1 in. 2

6m 9 in.

10.

11.

12.

5 cm

5.2 m

9.1 km

12.3 cm

7.3 m

11 km

13.

14. 15 1 ft 4

15.

3 1 yd 2

18 1 yd

12.6 cm

4

20 ft

16. What is the measure of the area of a parallelogram with

4.1 cm

a base of 6}2} inches and a height of 1}1} inches? 3

2

17. Find the area of a parallelogram with base 7}1} yards and 5

height 1}1} yards. 9


700


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Area of Parallelograms 1. SUNFLOWERS Norman is a sunflower farmer. His farm is in the shape of a parallelogram with a height measuring 3 kilometers and a base measuring 4.2 kilometers. To the nearest tenth of an acre, what is the total land area Norman uses?

2. VOLLEYBALL Ella and Veronica are in charge of making a banner for the volleyball game this Saturday. How much poster paper will they need for a parallelogram-shaped banner with height 3}1} feet and base 6 feet? Explain 2

how you found your answer. 21 ft2;

height, 3}1}, to find the area. 2

4. FLAGS Use the flag from Exercise 3. How many square inches will Joseph cover with black paint?

Lesson 14–1

3. FLAGS Joseph is painting the flag of Brunei (a country in Southeast Asia) for a geography project at school. How many square inches will he cover with white paint? White Black

1

8 2 in. 1

7 2 in.

Yellow 72 in.

5. QUILTING The pattern shows the dimensions of a quilting square that Sydney will use to make a quilt. How much blue fabric will she need? Explain how you found your answer.

6. QUILTING Use the quilting pattern from Exercise 5. How much pink fabric will Sydney need?

6 in. red

red pink 3 in.

blue 8 in.

green 12 in.


701


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Area of Parallelograms Pre-Activity Complete the Mini Lab at the top of page 546 in your textbook. Write your answers below. 1. How does a parallelogram relate to a rectangle?

2. What part of the parallelogram corresponds to the length of the rectangle?

3. What part corresponds to the rectangle’s width?

4. Write a formula for the area of a parallelogram.

Reading the Lesson 5. Look back at Lesson 1-8, Geometry: Area of Rectangles. Write the definition for the area of a figure.

6. Look at the models in the Mini Lab at the top of page 546 in your textbook. How can you tell from the models that the areas of the rectangle and the parallelogram are the same?

7. Look at Examples 2 and 3 on page 547. Explain what the dotted lines in the figures represent.

Helping You Remember 8. Work with a partner. Using models, demonstrate that the area of a parallelogram equals the product of any base of the parallelogram and its height.


702


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment You Can Count On It! How many triangles are there in the figure at the right? How many parallelograms? When counting shapes in a figure like this, you usually have to think of different sizes.

There are four small triangles.

There is one large triangle.

There are five triangles in all.

There are three parallelograms in all.

1. Now it’s your turn. How many triangles are in the figure below? How many parallelograms? Use the space at the right to organize your counting.

2. A trapezoid is a quadrilateral with only one pair of sides parallel, as shown at the right. How many trapezoids are in the figure in Exercise 1?

3. CHALLENGE How many triangles, parallelograms, and trapezoids are in the figure at the right?


703


Lesson 14–1

You also have to think of different positions.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Area of Triangles The area A of a triangle is one half the product of any base b and its height h. Symbols A 5 }1}bh

Model

2

height (h ) base (b )

Find the area of each triangle. a

b 6m 14.4 m height

The measure of the base is 5 units, and the height is 8 units.

base

A 5 }1}bh

2 A 5 }1}(5)(8) 2 A 5 }1}(40) 2

A 5 }1}bh

Area of a triangle

2 1 A 5 }}(14.4)(6) 2

Replace b with 5 and h with 8. Multiply. 5 3 8 5 40

Replace b with 14.4 and h with 6.

0.5 3 14.4 3 6

ENTER

43.2

A 5 20 The area of the triangle is 20 square units.

The area of the triangle is 43.2 square meters.

Find the area of each triangle. Round to the nearest tenth if necessary. 1.

2.

3. 5 ft

2 ft

4.

5.

6.

2.3 cm

3.2 cm 6 cm 30 yd

4.5 cm

10 yd © Glencoe/McGraw-Hill

704


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Area of Triangles Find the area of each triangle. Round to the nearest tenth if necessary. 1.

2.

3.

4.

5.

6.

15 in.

4 ft

5 in.

25 yd

12 ft 10 yd

8.

9. 2.2 cm

6 km

9 cm

12 cm

3.1 cm

6 km

10.

11.

10.2 km

12. 8 1 ft

3.1 km

4

12.5 m

24 1 ft 2

15 m

13. base: 4 in. height: 11 in.


14. base: 4}3} yd 4

height: 1}1} yd 3

705

15. base: 5}1} ft 4

height: 2}2} ft 3


Lesson 14–2

7.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Area of Triangles For Exercises 1–6, round to the nearest tenth if necessary. 1. CARPETING Courtney wants to carpet part of her bedroom that is shaped like a right triangle with base 4 meters and height 5.2 meters. How much carpet will she need?

2. LAWN Mrs. Giuntini’s lawn is triangleshaped with a base of 25 feet and a height of 10 feet. What is the area of Mrs. Giuntini’s lawn? Explain how you found your answer.

area of a triangle is }1}bh. So, 1 }} 3 25 3 10 5 125. 2

3. BUILDING Norma has an A-frame cabin. The back is shown below. How many square feet of paint will she need to cover the back of the cabin?

15 ft

2

4. SNACKS The dough that will be used to make a pig in a blanket is shown below. Before it is rolled around a sausage, it is brushed with vegetable oil. What is the area that needs to be covered with oil? Explain how you found your answer.

25 ft

6 cm 14 cm

42 cm2; Sample answer: The

1 }} 3 6 3 14 or 42. 2 5. SAILING Daniel just bought a used sailboat with two sails that need replacing. How much sail fabric will Daniel need if he replaces sail A?

6. SAILING Use the picture from Exercise 5. How much sail fabric will Daniel need if he replaces sail B?

112}1} ft2 2

A 3

9 4 ft


B

18 ft 1

12 2 ft

706


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Area of Triangles Pre-Activity Read the introduction at the top of page 551 in your textbook. Write your answers below. 1. Compare the two triangles.

2. What figure is formed by the two triangles?

3. Make a conjecture about the relationship that exists between the area of one triangle and the area of the entire figure.

Reading the Lesson 4. Look at the figure at the right. Explain how the height can be a, b, or d. a

b

5. Using models, demonstrate that congruent triangles have the same area.

6. Look at the illustrations of h on page 551. What is the symbol found where h and b meet? How does that affect the length of h?

Helping You Remember 7. Work with a partner. Using models, demonstrate that the area of a triangle is one-half the product of the base b and the height h of the triangle.


707


Lesson 14–2

c d

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Area of Composite Figures A composite figure is made up, or composed, of other figures. For example, the L-shaped figure at the right is composed of two rectangles. To find the area of the L-shape, find the area of each rectangle, then add. Area of A

Area of B

A5,3w

A5,3w

A 5 10 3 6

A 5 20 3 8

A 5 60

A 5 160

10 ft 6 ft

8 ft 20 ft

10 ft

So the area of the L-shaped figure is 60 ft2 1 160 ft2, or 220 ft2.

6 ft

8 ft

B 20 ft

Find the area of each composite figure. 1.

A

2.

24 in.

38 cm

32 cm

33 in.

17 cm 24 in. 50 cm 15 in.

3.

4.

5 yd

5m

6 yd 3m

7 yd

8m

5. CHALLENGE Find the area of the shaded region in the figure at the right.

21 in. 35 in.


708


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Area of Circles The area A of a circle is the product of p and the square of the radius r. Symbols A 5 pr 2

Model radius (r )

Find the area of the circle to the nearest tenth.

6 yd

The diameter is 6 yards. So, the radius is 6 4 2 or 3 yards.

A 5 pr2

Area of a circle

A < 3.14 3 32

Replace p with 3.14 and r with 3.

A < 3.14 3 9

Evaluate 3 2.

A < 28.26

Use a calculator.

The area of the circle is about 28.3 square yards.

Find the area of each circle to the nearest tenth. Use 3.14 for p. 1.

2. 2 ft

3.

2m

Lesson 14–3

8 in.

4.

5.

6. 1.2 km

9 cm

5 yd


709


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Area of Circles Find the area of each circle to the nearest tenth. Use 3.14 for p. 1.

2.

3.

1 ft

12 m

4 cm

4.

5.

6.

3 cm 10 km

2 1 in. 2

7.

8.

9. 4.1 yd

4 1 yd 2

16 ft

10.

11.

18 mm

13. What is the area of a circle whose radius is 4.2 yards?


12. 9 in.

3.8 yd

14. Find the area of a circle with a diameter of 13 meters.

710

15. What is the area of a circle whose radius is 6.6 inches?


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Area of Circles For Exercises 1–4, find each area to the nearest tenth. Use 3.14 for p. 1. SWIMMING POOLS Jensen’s parents put him in charge of ordering a cover for their new swimming pool. The pool is in the shape of a circle and has a radius of 14 feet. What will the area of the cover need to be?

2. BASKETBALL Thompson School will paint the center circle of the basketball court with yellow paint, one of the school colors. The circle has a radius of 2 feet. What is the area that will be painted yellow?

3. BASEBALL The pitcher’s mound on a regulation baseball field has a diameter of 18 feet. What is the area of a pitcher’s mound?

4. CAMPING A group of campers needs to clear away twigs and bark on the ground to make a fire circle for people to safely sit around the campfire. What is the area that they need to clear?

8 ft

201.0 ft2 For Exercises 5 and 6, find each area to the nearest tenth. Use 3.14 for p. Use the following information.

first measurement

SCIENCE Hal and Frank are conducting a science experiment. They drop a pebble into a pond and measure the radius of the circles of waves.

2.5 m second measurement

5. What was the area covered by waves the first time it was measured?


6. What was the area covered by waves the second time it was measured? Explain how you found your answer.

711


Lesson 14–3

1.25 m

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Area of Circles Pre-Activity Complete the Mini Lab at the top of page 556 in your textbook. Write your answers below. 1. What shape does the figure look like?

2. What part of the circle represents the figure’s height?

3. Relate the circle’s circumference to the base of the figure.

4. How would you find the area of the figure?

Reading the Lesson 5. The second sentence below the Mini Lab says, ‘‘The parts can then be arranged to form a figure that resembles a parallelogram.’’ How is the parallelogram-like figure in the Mini Lab different from a parallelogram?

6. Draw a circle. Label the circumference, radius, and diameter.

Helping You Remember 7. To help yourself practice computing the area of a circle, find a few circular objects such as plates, cups, and tops of cans. Measure each radius or diameter with a ruler and then find the area of the circle.


712


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Area of Sectors In the circle at the right, the vertex of /AOB is the center of the circle. So, /AOB is called a central angle of the circle, and the shaded region is a sector of the circle. When you know the radius of the circle and the measure of the central angle, it’s easy to find the area of the sector. First find the area of the circle.

Then find what fractional part of the circle is in the sector.

A 5 pr2 A < 3.14 ? (3)2 A < 3.14 ? 9 A < 28.26

degree measure of central angle degree measure of circle

A

120˚

O 3 ft

B

120 1 = 360 3

→ →

So, the area of the sector is about }1} of 28.26 ft2, or about 9.42 ft2. 3

Find the area of each shaded sector. Use 3.14 for p. 2. 135˚

cm 12 60˚

12 cm 12 cm

90˚

72˚

6. cm

5.

20

4.

3.

6 in.

45˚

5 ft 150˚

7. CHALLENGE In the circle at the right, the shaded region is called a segment of the circle. Find the area of the segment.

90˚ 8 in.


713


Lesson 14–3

1.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Three-Dimensional Figures Three-dimensional figures are shapes with length, width, and depth (or height). Some terms associated with three-dimensional figures are face, edge, vertex, and lateral face. The polygons that form three-dimensional figures are called faces.

Prisms have two parallel bases and at least three lateral faces that are rectangles.

The faces intersect to form edges.

The sides are called lateral faces.

The edges intersect to form vertices.

rectangular prism

Pyramids are named by their bases and have at least three lateral faces that are triangles.

triangular pyramid

triangular prism

square prism or cube

Some three-dimensional figures have curved surfaces and no edges.

square pyramid

cylinder

cone

sphere

Identify each figure. 1.

2.

3.

4.

5.

6.


714


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Three-Dimensional Figures Identify each figure. 2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Lesson 14–4

1.


715


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Three-Dimensional Figures 1. TENNIS As professional tennis players, Venus and Serena Williams strike tennis balls with rackets. Draw the figure that represents a tennis ball. What type of figure is this?

2. BACKPACKING Below are pictures of some of the objects Kelly takes with her for backpacking trips. Identify the figure each picture represents.

Tent

triangular prism

Sleeping Bag

cylinder 3. MECHANICS A mechanic uses a funnel when he or she puts fluids into cars. What type of figure does a funnel represent? Draw the figure.

4. DESIGN Rachael Johnson is a toy designer. She uses square blocks of wood to make alphabet blocks. Draw and name the figure that an alphabet block represents.

5. FIGURES Alice and Julie were arguing over the name of this figure. What is the name of the figure? How do you know?

6. CANDLES Kevin arranged several scented candles on his kitchen table before his birthday party started. Use the picture of Kevin’s arrangement to name the type of figure each candle represents.

a. square c a

b


716


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Three-Dimensional Figures Pre-Activity Read the introduction at the top of page 564 in your textbook. Write your answers below. 1. What shape does the delta kite resemble?

2. Name the shape that each side of the box kite resembles.

3. Describe how the shape of the box kite differs from the shape of the delta kite.

Reading the Lesson For Exercises 4–11, tell whether each phrase describes a prism, pyramid, cone, cylinder, or sphere. 4. no faces

5. curved surface

6. no bases

7. lateral faces that are rectangles

8. one base

9. lateral faces that are triangles

10. two bases

11. one vertex

12. What determines the name of a prism or pyramid? 13. Compare a triangular pyramid and a square pyramid. How are they similar? How are they different?

14. Draw an example of each figure. prism


pyramid

cone

717

cylinder

sphere


Lesson 14–4


NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Point of View At the right is a square pyramid as seen from a point of view that is slightly above and to the right. Here is the same pyramid when you look at it from three different points of view. front view

side view

top view

Notice that these views appear two-dimensional. Architects, engineers, and designers often use views like these to provide a detailed description of a three-dimensional object. Identify the figure that each set of views represents. 1. front view

side view

top view

2. front view

side view

top view

front view

side view

top view

front view

side view

top view

3.

4.

5. This figure is called a truncated cone. In the space at the right, sketch front, side, and top views of the figure.

6. CHALLENGE At the right, you see three different views of the same cube. What symbol is on the face opposite the plus sign? © Glencoe/McGraw-Hill

* 1

718

c

c

2

2 $

1

%


NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Lesson 14–5

Volume of Rectangular Prisms The amount of space inside a three-dimensional figure is the volume of the figure. Volume is measured in cubic units. This tells you the number of cubes of a given size it will take to fill the prism.

cubic unit

The volume V of a rectangular prism is the product of its length ,, width w, and height h. Symbols V 5 ,wh

You can also multiply the area of the base B by the height h to find the volume V. Symbols V 5 Bh

Model

Model

B

h

h

w

,

Find the volume of the rectangular prism. Method 1 Use V 5 ,wh. V 5 ,wh V 5 10 3 5 3 2 V 5 100 The volume is 100 ft3.

Method 2 Use V 5 Bh. V 5 Bh B, the area of the base, V 5 50 3 2 is 10 3 5 or 50. V 5 100 The volume is 100 ft3.

5 ft 2 ft 10 ft

Find the volume of each figure. Round to the nearest tenth if necessary. 1.

2.

2 ft

4 in.

3 ft 4 in. 4 ft 4 in.

3. 20 yd

4.

1.5 cm 3 cm 5 cm

5 yd 5 yd © Glencoe/McGraw-Hill

719


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Volume of Rectangular Prisms Find the volume of each rectangular prism. Round to the nearest tenth if necessary. 1.

2.

2 in. 4 in.

1 in.

3. 7m

9 ft

2m 4m 6 ft 5 ft

4.

1.4 mm

5.

6.

4 mm 1.2 yd 1.5 yd

10 mm

10 in.

1 yd

3 in. 2.5 in.

7.

8. 20 ft

2 in.

4.8 in.

2 ft 5 ft

9. 7 mm

3 in.

6 mm 10 mm

10.

11.

2.2 ft

12.

3.1 ft 8.3 m

6.9 ft 6.7 yd 9.2 yd

1.2 m

4.2 m

3.3 yd

13. Find the volume of a rectangular prism with length 9 meters, width 4 meters, and height 5 meters. 14. What is the volume, to the nearest tenth, of a rectangular prism with length 6.2 yards, width 2.6 yards, and a height of 1.5 yards? © Glencoe/McGraw-Hill

720


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Find the volume to the nearest tenth if necessary. 1. OLYMPICS Olympic gold medal winner Ian Thorp competes in a pool with required dimensions 25 meters by 50 meters by 2 meters. What is the volume of the Olympic-sized pool? Explain how you found your answer.

2. DUMP TRUCKS Raphael drives a standard-sized dump truck. The dimensions of the bed of the truck are length 15 feet, width 8 feet, and height 6 feet. What is the volume of the bed of the dump truck?

3. GIFTS William has some antique bottles. He is going to fill the bottles with bath soap and give them away as gifts. Use the figure to find the volume up to the fill line of a bottle.

4. JEWELRY Janine keeps her jewelry in a jewelry box like the figure below. Find the volume of Janine’s jewelry box.

3 in. Fill Line

4.5 in. 9 in.

6 in.

4 in.

121.5 in3

3 in.

5. RECYCLING The town of Riverview provides a rectangular recycling bin for newspapers to each household. What is the greatest volume of newspapers the recycling bin can hold?

6. CANDLE MAKING Kyle will fill the candle mold with liquid candle wax. Find the amount of liquid wax that will be contained in the mold. Explain how you found your answer.

132.9 in3; To find the

NEW SPA PER

11.5 in. 16 in.

20.5 in. 12 in.


3.4 in.

721

3.4 in.


Lesson 14–5

Volume of Rectangular Prisms

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Volume of Rectangular Prisms Pre-Activity Complete the Mini Lab at the top of page 570 in your textbook. Write your answers below. 1. What are the dimensions of the prism?

2. Estimate how many of each group of cubes it will take to fill the prism. Assume that a group of cubes can be taken apart to fill the prism.

3. Use grid paper and tape to construct the prism. Then use centimeter cubes to find out how many of each group of cubes it will take to fill the prism. Compare the results to your estimates.

4. Describe the relationship between the number of centimeter cubes that it takes to fill the prism and the product of the dimensions of the prism.

Reading the Lesson Explain what each of the following formulas means. 5. V 5 ,wh 6. V 5 Bh Write the unit of measure for volume for each of the following. 7. inch

8. foot

9. centimeter

10. meter

11. Tell how a cubic meter is different from a cubic centimeter.

12. Look at the formula and explanation at the top of page 571. Explain what the phrase rows of cubes means.

Helping You Remember 13. Take the measurements of a box and calculate its volume. Explain your answer.


722


NAME ________________________________________ DATE ______________ PERIOD _____

Volume and Liquid Capacity The volume of a three-dimensional figure is the amount of space it contains. Volume is measured in cubic units—cubic meters, cubic inches, and so on. The liquid capacity of a container is the amount of liquid it can hold. Liquid capacity generally is measured in units like liters, milliliters, cups, pints, quarts, and gallons.

Volume and Liquid Capacity Metric 1 cm3 5 1 mL 1 m3 5 1,000 L Customary 1 in3 ≈ 0.544 fl oz 1 ft3 ≈ 7.481 gal

The chart at the right shows the relationship between volume and liquid capacity. If a container were shaped like the rectangular prism below the chart, this is how you would find its liquid capacity. Volume

Liquid Capacity

V 5 ,wh V573534 V 5 140

1 in3 < 0.544 fl oz 140 in3 < (140 3 0.544) fl oz 140 in3 < 76.16 fl oz

4 in.

7 in. 5 in.

So the liquid capacity of the container is about 76 fluid ounces.

For Exercises 1–4, find the liquid capacity of a container shaped like a rectangular prism with the given dimensions. If necessary, round to the nearest whole number. 1. length, 8 cm width, 4 cm height, 6 cm

2. length, 7 ft width, 2 ft height, 3 ft

3. length, 3.5 m width, 1.5 m height, 5 m

4. length, 5 in. width, 1}1} in.

2 height, 3}1} in. 2

5. An aquarium is 36 inches long, 18 inches wide, and 18 inches tall. It is filled with water to a height of 12 inches. How many gallons of water are in the aquarium? (Round to the nearest gallon.)

6. CHALLENGE How many cubic inches of space are occupied by one quart of water? Round to the nearest whole number. © Glencoe/McGraw-Hill

723


Lesson 14–5

Enrichment

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention Surface Area of Rectangular Prisms The surface area S of a rectangular prism with length ,, width w, and height h is the sum of the areas of the faces. Symbols S 5 2,w 1 2,h 1 2wh Model h

w

,

Find the surface area of the rectangular prism. Find the area of each face. top and bottom 2(,w) 5 2(8 3 5) 5 80

3m

5m

front and back 2(,h) 5 2(8 3 3) 5 48

8m

two sides 2(wh) 5 2(5 3 3) 5 30 Add to find the surface area. The surface area is 80 1 48 1 30 or 158 square meters.

Find the surface area of each rectangular prism. Round to the nearest tenth if necessary. 1.

2.

2 in.

3.

5 cm

10 ft

2 cm

5 ft

2 in. 1 cm

2 ft 2 in.

4.

5.

6.

2.3 yd

6 in. 5 yd

6m

1.2 m 3m

10 in.

5 yd

5.2 in.


724


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Skills Surface Area of Rectangular Prisms Find the surface area of each rectangular prism. Round to the nearest tenth if necessary. 1.

2.

3. 4 in. 7 in.

5 cm

8 ft

9 in.

Lesson 14–6

1 cm 2 cm

3 ft 4 ft

4.

5.

6.

2 ft 4 ft

2 yd

8.6 ft

7.2 ft

2 yd 3.5 yd 3 ft 5 ft

7.

8.

9. 3 in. 3.2 mm

9m

7.2 in. 3.2 mm

6.3 in. 3.2 mm 4.4 m 2.1 m

10. Find the surface area of a rectangular prism that is 3}1} feet by 4}1} feet 2 4 by 6 feet.

11. What is the surface area of a rectangular prism that measures 2}1} meters 3

by 2}1} meters by 4 meters? 2 © Glencoe/McGraw-Hill

725


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems Surface Area of Rectangular Prisms For Exercises 1–6, round each surface area to the nearest tenth if necessary. 1. GIFTS Fatima is wrapping a gift box for her nephew’s birthday. The box’s dimensions are 16 inches long by 10 inches wide by 5 inches high. What is the surface area of the box?

2. FOOD Antoine is wrapping a block of cheese that is 22 centimeters long by 6.5 centimeters high by 10 centimeters wide with plastic wrap. What is the surface area of the cheese block?

856 cm2

3. PAINTING Kyle is painting the front door of his house. The dimensions of the door are 80 inches by 30 inches by 2 inches. If he paints all of the surfaces, how much area will he paint? Explain.

4. CARPENTRY Bryan is sanding a set of speaker boxes that he built for his room. What is the surface area of each box?

13 ft2 2 ft

1.5 ft 1 ft

5. CARPENTRY Cindy is putting oak veneer (thin wood covering) on the entire surface of her hope chest. How much veneer will she need?

6. TOY MAKING Trey is covering blocks of wood with wallpaper to make building blocks for his baby sister. If he covers all the surfaces, how much wallpaper will he need? Think of a short way to solve this problem and explain.

3.5 ft 3 in.

5 ft

3 in.

2.5 ft

3 in.

54


726

in2;

Sample answer: Since a


NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn Mathematics Surface Area of Rectangular Prisms Pre-Activity Complete the Mini Lab at the top of page 575 in your textbook. Write your answers below. 1. Find the area of each face of the prism.

3. What do you notice about the area of opposite sides of the prism? How could this simplify finding the sum of the areas?

Reading the Lesson 4. Describe in words each step shown for finding the surface area of a rectangular prism. S 5 2,w 1 2,h 1 2wh S 5 2(17 3 5) 1 2(17 3 6) 1 2(5 3 6) S 5 2(85) 1 2(102) 1 2(30) S 5 170 1 204 1 60 S 5 434 5. What is the unit of measure for surface area?

6. What is the difference between a rectangular prism and a net of the prism?

7. What is the difference between the surface area of a rectangular prism and the volume of the prism?

Helping You Remember 8. Using a net, demonstrate that the surface area of a rectangular prism is equal to 2,w 1 2,h 1 2wh.


727


Lesson 14–6

2. What is the sum of the areas of the faces of the prism?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment Nets A net is a two-dimensional pattern that can be folded to form a threedimensional figure. For example, the figure at the right is a net for a rectangular prism. Identify the figure that would be formed by folding each net. 1.

2.

3.

4.

A cube is a rectangular prism in which all the edges have the same length. A net for a cube is made up of six squares. However, not every pattern of six squares is a net for a cube. For example, it would be impossible to fold the pattern at the right to form a cube. Tell whether each of these patterns is a net for a cube. 5.

8.

6.

7.

9.

10.

11. CHALLENGE In all, there are eleven different patterns of six squares that form a net for a cube. Sketch the eleven patterns in the space below.


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6th Grade Math Workbook

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