Disclaimer No part of this publication may be duplicated, reproduced or translated in any form or by any means, electronic, mechanical, photocopying, recording or by any information storage and retrieval system, without prior permission from the author/publisher. The author, publisher and distributor of this product disclaim any responsibility for the use or misuse of this product, or for any errors, omissions, injury, damage and/or financial loss sustained to persons or property as a result of using this book. In no event shall the author or publisher be held liable for any loss, risk, damage, user or misuse of any of the information either directly or indirectly presented herein. While every effort has been made to ensure reliability of the information within, the liability, negligence or otherwise, or from any use, misuse or abuse of the operation of any methods, strategies, instructions or ideas contained in the material herein is the sole responsibility of the reader.
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D ear R ead er… … I would like firstly to thank you for your investment in th is eb ook, “M en tal A rith m etic Th rou gh A bacu s”. I am confident that you will find the information in this ebook useful for your mental arithmetic calculation. In writing this book I have assumed that you, the reader, have a some basic knowledge of abacus. This is a fairly simple book to understand, as I have tried to keep this book concise and very focused on the objective of monitoring mental arithmetic. In this book you will find hands-on exercises to many of the problems faced by users to calculate the numbers in mind – using easy and legitimate techniques that have worked for me and many others. Through the pages of this book, I will teach you the exact same techniques that I used to figuring out the numbers. Techniques that you can apply yourself and see the real results. I g u aran tee you w ill fin d in sigh ts h ere th at you w ou ldn ‟t fin d an yw h ere else. “M en tal A rith m etic T h rou g h A b acu s” allow you to initiate and accelerate your mental counting sequence – away from difficult summarize traditional methods! I sincerely hope that you will greatly benefit from reading th is b ook. M y w ish is th at you ‟ll reach a h igh er level of achievement. Your success is a representation of our success. We hope that your success will be an inspiration to others.
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Should you have any feedback or comments please feel free to contact me at
[email protected] We would like to hear from you and of your success. If you feel that this ebook has benefited you, we welcome your testimonial.
God Bless
Charles O www.KidsMathBlog.com
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About The Author Charles O Charles O is w id ely con sid ered on e of th e w eb ‟s leading math consultants. He has been teaching math since 1996 and is the owner of Super Math Company, serving dozens of students in its network. H e‟ h as b een on e of th e featu red sp eakers in M alaysia mental math seminars and recognized as mental counting, power math teacher. Charles O has helped many his students to gain the confidence and establish strong fundamental of math since 1996. W h en h e‟s n ot w orkin g, C h arles is spen din g tim e w ith h is family (lovely wife Elizabeth and two daughters Jacinta and Emily). Some of his ebooks are as below: Success in Math Mental Arithmetic Through Abacus Advance Mental Arithmetic Through Abacus
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Preface An abacus also called a counting frame, is a calculating tool for performing arithmetic processes. Nowadays, abacus are often constructed as a wooden frame with beads sliding on wires, but originally they were beads or stones moved in grooves in sand or on tablets of wood, stone, or metal. The abacus was in use centuries before the adoption of the written modern numeral system and is still widely used by merchants and clerks in China, Japan, Africa, India and elsewhere. However, mental arithmetic is the practice of doing mathematical calculations using only the human brain, with no help from any computing devices. Mental calculations are not only helpful when computing tools are not available, but they also can be helpful in situations where it is beneficial to calculate with speed. This abacus system of mental calculation is a system where users mentally visualize an abacus to do calculations. No physical abacus is used; only the answers are written down. This system is being propagated in China, Singapore, South Korea, Thailand, Malaysia, and Japan. Mental calculation is said to improve mental capability, increases speed of response, memory power, and concentration power. Many veteran and prolific abacus users in China, Japan, South Korea, and others who use the abacus daily, naturally tend to not use the abacus anymore but perform calculations by visualizing the abacus. This was verified when the right brain measured heightened EEG activity when calculating and compared with non-veterans who were using the abacus to perform calculations.
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Y o u ’ll learn : The quick and easy way of abacus learning formula. Illustrated explanation of calculating using the abacus. Visualizing operations and results. Step by step abacus practices. Provide the best visual model for arithmetic operations. Perform MENTAL arithmetic computations using abacus. Develop computational competency. Provide a tool to understand the concept of addition and subtraction. Able to develop basic mental calculation abilities. Sharpen observation towards the figures. A quick and easy technique for using right brain to produce speed counting results.
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Table of Contents Chapter 1 Introduction ......................................... 8 1.1 Sitting posture and holding the abacus. ............... 8 1.2 The function of right hand ................................10 1.3 Parts of abacus ...............................................12 1.4 Place Value of Upper & Lower Beads ..................13 1.5 Moving the Beads ...........................................18 1.6 Representation of numbers...............................20 Chapter 2 Addition...............................................23 2.1 Direct Addition ...............................................23 2.2 Pool Five Method or Little Friend Theory .............30 2.3 Addition with Carrying of Numbers ....................39 2.4 Integration of addition with pool five and carrying numbers method. .................................................56 Chapter 3 Subtraction ..........................................66 3.1 Direct Subtraction ...........................................66 3.2 Break 5 Method ..............................................72 3.3 Subtraction with removing of numbers ...............80 3.4 Integration of subtraction with break five and removing of numbers method. ...............................97 ANSWERS .......................................................... 107
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Chapter 1
Introduction
1.1 Sitting posture and holding the abacus. (i) Sitting Posture Sit upright, relax both shoulders, slightly lean forward, both feet placed naturally opened with toes pointing outward. Keep your feet at a distance of about 10 cm apart and inclined at about 15 degrees between them. Keep your chest at a fixed distance from the edge of the table and do not let the body lean against the chair. The picture below shows the side view of the proper sitting posture.
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(ii) Placing & Holding of Abacus The abacus may be placed at 8 – 10 cm away from the edge of the desk and parallel to it as well as directly in front of your body. Remember to place the middle finger of your left hand on the clearing device. Improper placing of abacus will affect the prompt and accuracy of calculation. The picture below shows the proper sitting posture while holding abacus.
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1.2 The function of right hand (i) Holding of Abacus Hold on to the left side of the abacus with your left hand when you are performing the calculation operation.
(ii) Holding of Pen/Pencil The ability to move the beads and hold the pen/pencil correctly will influence the prompt calculation operation. Therefore, it is crucial to master the proper pen/pencil holding method. Since there are several ways of holding the pen/pencil, a better way is the whole holding method. The length of the pen/pencil is suggested to be 14 – 18 cm and medium in size. One end of the pen/pencil should be facing the right direction while the other end is to be held between the thumb and forefinger. Slightly curve the ring finger and the little finger to the palm and gently hold the pen/pencil, so that the beads can be moved easily.
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(iii) Fingering
Middle finger
Forefinger
Thumb
Thumb : Move lower beads towards the beam. Forefinger: Move lower beads away the beam. Middle finger: Move upper bead toward & away the beam. 11
1.3 Parts of abacus (i)
Frame
(ii) Beam
The little rectangular wood surrounding the abacus is called the frame : The little wood that divides the abacus into two parts is called the beam
(iii) Rod
: The little rod piercing through the beads is called the rod
(iv) Upper Bead
: The bead pierced by the rod above the beam is called upper bead
(v) Lower Bead
: The bead pierced by the rod below the beam is called lower bead
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1.4 Place Value of Upper & Lower Beads
Starting point to place value can be started at any possible rod such as the second rod from the right side of abacus or others.
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The pictures below show the value of lower beads.
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The pictures below show the value of upper bead at abacus.
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1.5 Moving the Beads
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1.6 Representation of numbers
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Chapter 2 Addition 2.1 Direct Addition Direct addition is used to calculate the lower beads or upper beads without carrying numbers.
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Exercises Try the exercises below.
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2.2 Pool Five Method or Little Friend Theory Pool five or Little Friend Theory is used to calculate when the lower beads are not enough for addition.
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You can see how theory of little friend been applied at the following examples to calculate when the lower beads are not enough for addition.
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2.3 Addition with Carrying of Numbers Addition with carrying of numbers is used to calculate when there are not enough beads for addition for the amounts more than 9. For example 13, 16, 27, 54 and etc. In abacus, we use concept of supplement to solve these problems.
Concept of Supplement or Big Friend Theory means that if the sum of two numbers is 10, then these two numbers are the supplement for each other.
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Do the exercises below.
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2.4 Integration of addition with pool five and carrying numbers method. There is some addition where there is not enough beads for calculation, we have to use combination of addition with pool five method and carrying numbers method to solve the problems.
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Do the exercises below.
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Chapter 3 Subtraction 3.1 Direct Subtraction Direct subtraction is used to calculate the lower beads or upper beads without carrying numbers.
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3.2 Break 5 Method Break 5 method is applying the same little friend theory from pool 5 method. It used to calculate when the lower beads are not enough for subtraction, by moving the upper beads together with lower beads to solve the problems. As we know from pool 5, little friend of 2 is 3 and little friend of 1 is 4, break 5 method is using exact the same little friend theory in calculating pool 5 method.
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Try the following exercises.
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3.3 Subtraction with removing of numbers. Subtraction with removing of numbers is used to calculate when there are not enough beads for subtraction. It also uses big friend method to solve the problems. Just like big friend for addition, big friend for subtraction also use the concept of supplement where if the sum of two numbers is ten, then these two numbers are supplement with each other. This has been shown in the picture below.
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Try the exercises below.
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3.4 Integration of subtraction with break five and removing of numbers method. Some subtraction cannot be solved by using direct subtraction, break five or removing of numbers method along. So we have to use the combination of these together in order to find the answer. The following show the step necessary to carry out the calculation and summary of the whole subtraction.
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Try the exercises below.
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ANSWERS
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C o n clu sion … The tactics and strategies outlined in this ebook are just the beginning. By combining these techniques and testin g you r ow n , you ‟ll fin d all sorts of th in g s to tweak and test on mental math calculation. And your math result will undoubtedly improve as a result, sometimes by a lot. B u t for all th e tech n iq u es an d strategies in th e w orld, it‟s only by taking action following the system that works th at you ‟ll see resu lts. A n d I sin cerely h ope you will. I can ‟t h elp you w ith th e „takin g action ‟ p art becau se you ‟re th e p erson deciding that. But I can definitely help you with the right system to increase your mental math with my mental arithmetic through abacus. A Few Last Words It's been my pleasure to be able to show you how easy it really is to perform powerful mental arithmetic through abacus that gets the results you're really after. I hope this course has inspired you to get started right away.
Best Wish Charles O
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