MEP Y9 Practice Book A
4 Fractions and Percentages 4.1 Equivalent Fractions Equivalent fractions are revisited in this section.
Example 1 Write down in 2 different ways, the fraction of this large square which been shaded.
Solution 3 9 1 3
, as 3 of the 9 squares squares are shaded. shaded.
, as the shape could have been been drawn like this:
Example 2 Complete each of the following f ollowing expressions: (a)
(c)
3
=
4
5
(b)
12
=
6
(d)
18
2
=
3
15
4
=
12
3
Solution (a)
(c)
3 4
5 6
3 =
=
×
3
4
×
3
5
×
3
6
×3
9 =
=
(b)
12
15
(d)
18
58
2 3
2 =
4 12
×
5
×
5
4
÷
4
12
÷
4
3
=
10 =
15
=
1 3
MEP Y9 Practice Book A
Example 3 Write each of the following fractions in their simplest form: (a)
8
(b)
18
5
(c)
40
12 32
Solution (a)
(b)
(c)
8
=
18
5
32
(dividing top and bottom by 2)
9
=
40
12
4
1
(dividing top and bottom by 5)
8
=
3
(dividing top and bottom by 4)
8
Exercises 1.
2.
Write rite,, in two dif differ ferent ent way wayss the the fract fraction ion of each each sha shape pe whi which ch has bee been n shaded: (a )
(b)
(c )
(d)
Filll in the mis Fil missin sing g numb number er in ea each ch of the fol follow lowing ing sta statem tement ents: s: (a)
(c)
3
=
5
4 7
(b)
20
=
(d)
35
59
3
=
4
5 9
12
= 18
MEP Y9 Practice Book A
4.1 (e)
(g)
(i)
(k)
3.
(c)
(e)
(g)
(i)
7
4
(f)
28
=
5
9
30
=
10
7
(h)
(j)
60
=
11
(l)
66
3
=
8
2
40
=
9
4
36
=
7
5
28
=
8
64
10
=
15
20
3
=
60
30
(d)
3
=
36
4
(b)
(f)
6
=
28
14 100
(h)
7
=
(j)
50
11
=
44
10
4
=
16
10
8
=
50
18
5
=
24
24 56
4
= 7
Writ ritee each each of of the the foll follow owin ing g frac fracti tion onss in its its sim simpl ples estt form form:: (a)
(e)
(i)
5.
=
Fill Fi ll in in the the miss missin ing g numb number erss in th thee follo followi wing ng sta state teme ment nts: s:
(a)
4.
3
4 8 20 100 21 28
(b)
(f)
(j)
6
(c)
9 20
(g)
50 16
(k)
24
20 25 16 40 15 21
(d)
(h)
(l)
3 18 32 40 28 35
Wri rite te ea each ch of th thee fol follo lowi wing ng fr frac acti tion onss in in two different ways: (a)
2 7
(b)
3
(c)
8
60
5 9
MEP Y9 Practice Book A
6.
Is ea each ch of th thee fo foll llow owin ing g st stat atem emen ents ts true or false: (a)
(c)
7.
(a)) (a
4
=
7 4
=
(d)
3
=
8 5
12 32
=
9
25 45
Fill Fi ll in th thee mi miss ssin ing g nu numb mber er in ea each ch of th thee fo foll llow owin ing g st stat atem emen ents ts:: 5
= 40
=
8 4
5
Whic Wh ich h of of the the fr frac acti tio ons
(a)) (a
Fill Fi ll in th thee mi miss ssin ing g nu numb mber er in ea each ch of th thee fo foll llow owin ing g st stat atem emen ents ts::
7
(b)) (b
5
and
40
(b)) (b
5
10.. 10
16 20
5
9.
(b)
21
5
4
8.
16
8
is the larger ?
2
= 21
3
Whic Wh ich h of of the the fr frac acti tio ons
5 7
and
2 3
= 21
is the smaller ?
Whic Wh ich h of of the these se fr frac acti tio ons is th thee largest ? 1
3
4
2
5
7
Write the foll followi owing ng fract fraction ionss in orde orderr of size, size, with the smallest first: first: 1
1
2
1
5
5
4
9
2
9
61
MEP Y9 Practice Book A
4.2 Fractions of of Qu Quantities In this section we review how to find fractions of quantities; for example,
Example 1 Calculate: (a)
1 3
of of £60,
(b)
1 5
of £40.
Solution (a)
60
÷3= 1
So
(b)
40
3
÷
5
of £60 = £20 .
=8
1
So
20
5
of £40 = £8 .
Example 2 Calculate: (a)
3 4
of of 700,
(b)
5 7
of 21.
Solution (a)
700
÷
175
× 3 = 525
So
(b)
3 4
×3
So
5 7
= 175
of 700 = 525.
21 ÷ 7 5
4
= 3 = 15
of 21 = 15.
62
3 4
of 60.
MEP Y9 Practice Book A
Exercises 1.
Calculate: (a)
(d)
(g)
2.
5 1 7 1 9
of of 10
(b)
of of 28
(e)
of of 18
(h)
1 3 1 6 1 3
of of 12
(c)
of of 24
(f)
of of 24
(i)
of of 15
(c)
of of 28
(f)
of of 30
(i)
1 4 1 5 1 8
of 20
of 30
of 32
Calculate: (a)
(d)
(g)
3.
1
3 4 2 3 5 8
of of 20
(b)
of of 24
(e)
of of 32
(h)
In a cl claass th theere ar aree 28 pup upil ilss;
2 5 3 7 4 5
1 2
3 8 3 5 5 9
of 24
of 40
of 36
of these pupils are girls.
How many girls are in the class?
4.
5.
6.
A ca can n ho hold ldss 33 330 0 ml of dr drin ink. k. Ja Javi vind ndaa dr drin inks ks (a)) (a
How Ho w muc much h has has Ja Javi vind ndaa dru drunk nk??
(b)) (b
How Ho w muc much h drin drink k is is lef leftt in in the the ca can? n?
1 3
Ther Th eree ar aree 32 320 0 sw swee eets ts in a la larg rgee ti tin. n. La Laur uraa ea eats ts (a)) (a
How Ho w man many y swe sweet etss doe doess she she ea eat? t?
(b)) (b
How Ho w ma many ny sw swee eets ts ar aree le left ft??
A ca carr jo jour urne ney y is 12 120 0 mi mile les. s. Ri Rich char ard d ha hass dr driv iven en
of the contents of the can.
3 8
of the sweets.
3 5
of this distance.
(a)) (a
How Ho w far far ha hass Ric Richa hard rd dr driv iven en??
(b)
How much much furt further her does does he have have to drive drive to compl complete ete the the journ journey? ey?
63
MEP Y9 Practice Book A
4.2 7.
8.
9.
Ther Th eree ar aree 30 300 0 pa pass ssen enge gers rs on a tra train in.. At a st stat atio ion, n, (a)) (a
How Ho w ma many ny pe peop ople le ge gett off off th thee tra train in??
(b)) (b
How Ho w many many pas passe seng nger erss are are left left on on the the trai train? n?
Alis Al ison on ha hass £3 £30. 0. Sh Shee de deci cide dess to sa save ve
2 5
3 5
of the passengers get off.
of this and to spend
(a)) (a
How Ho w muc much h mon money ey do does es sh shee sav save? e?
(b)) (b
How Ho w muc much h doe doess she she sp spen end d on on boo books ks??
(c)) (c
How Ho w muc much h doe doess she she ha have ve le left ft??
A far farme merr own ownss 360 360 he hect ctar ares es of la land nd.. He pl plan ants ts po pota tato toes es on
1 6
on books.
3 10
of his land.
How many hectares are planted with potatoes? 10.. 10
An engi enginee neerr tests tests a box box of of 120 120 flopp floppy y disks disks.. He find findss that that
1 20
of the disks are
damaged. How many of the disks disks are damaged? damaged? 11.
Suee and Su and Be Ben n eac each h hav havee 12 12 bis biscu cuits its.. (a)
Sue ea eats ts a qua quarte rterr of her bis biscui cuits. ts. How man many y biscu biscuits its doe doess Sue Sue eat? eat?
(b)
Ben eat eatss 6 of of his bis biscui cuits. ts. Wha Whatt fracti fraction on of of his bis biscui cuits ts does does Ben ea eat? t?
(c)) (c
How Ho w man many y bis biscu cuit itss are are le left ft al alto toge geth ther er?? (KS3/97/Ma/Tier 3-5/P1)
4.3 Operations wi witth Fra ract ctiions Here we review how to add, subtract, multiply and divide fractions.
Example 1 Calculate: (a)
3
+
5
1
(b)
4
5
−
7
2 3
Solution Before fractions can be added or subtracted, they must each have the same denominator (known as a common denominator). (a)
3 5
+
1
=
4
12 20
=
+
5 20
17 20
64
MEP Y9 Practice Book A
(b)
5
−
7
2
=
3
15
−
21
=
14 21
1 21
Example 2 Calculate: (a)
4
×
5
3
(b)
7
5
×
8
2 7
Solution (a)
4
×
5
3
=
7
=
4
×
3
5
×
7
12 35 1
(b)
5
×
8
2
=
7
=
5
×
2
8
×
7
4
10
5
Example 3 Calculate: 3
÷
5
2
(b)
3
5
÷
7
3
÷
5
2
=
3
3
×
5
=
3 2
9 10
(b)
5 7
÷
3
=
4
5
×
7
=
3 4
Solution (a)
2
=
7
5
×
1
4
×
7
5 28
28
(a)
8
×
=
56
=
5
OR
4 3
20 21
65
MEP Y9 Practice Book A
4.3 Example 4 Calculate: (a)
1
1
×1
2
1
(b)
4
1
1
÷
5
1 2 4
Solution (a)
1
1
×1
2
1
=
4
3
×
2
=
5 4
15 8
=
1
7 8
(b)
1
1 5
÷
2
1
=
4
6
÷
5
=
6
4
×
5
=
9
4
(You could cancel at this stage to give
9
2
24
5
×
4 3
, etc.)
45
=
8 15
Exercises 1.
Calculate: (a)
(d)
2.
1
+
7 1
4 7
+
5
3 5
(b)
(e)
3
+
8 4
5 8
+
9
2 9
(c)
(f)
3 10 1
1
+
+
6
10 5 6
Calculate: (a)
(d)
1
+
2 2 5
1 3
+
3 4
(b)
(e)
1
+
5 1
1 4
+
7
3 8
66
(c)
(f)
1
+
7 1 6
1 3
+
2 3
MEP Y9 Practice Book A
(g)
(j)
3.
(d)
(g)
(j)
(d)
(g)
(j)
6.
4
(h)
3
5
2
+
6
(k)
3
3
+
5 1
2 3
+
8
4
(i)
2
7 4
(l)
3
+
2 5
+
5
5 6
1
1
×
2
(b)
3
5
3
×
6
(e)
4
4
1
×
5
(h)
2
3
2
×
7
(k)
3
4
×
5 4
×
3 4
5
3
×
8
3
3
5
1
×
4 2
×
8 7
(l)
4
3
8
(i)
4
2
×
8
(f)
7
×
1
(c)
3
5 2
2
3 2
×
8
3
Calculate: (a)
5.
2
+
Calculate: (a)
4.
3
1
1
÷
2
3
2
2
÷
3
(e)
5
4
2
÷
15 4
(b)
(h)
3
÷
9
2
(k)
3
3
÷
4 3
÷
3 3
3
5
÷
8
5
3
6 7
÷
7
3 4
÷
7
(l)
2 3
8
(i)
7
÷
5
(f)
4
÷
4
(c)
3
7 2
2
3 5
÷
9
2 3
Calculate: (a)
1
(d)
3
1
×
2
1
2 1 4
4
×1
1 3
(b)
2
(e)
2
1
×1
2 1
1 3
×1
2
1 2
(c)
2
(f)
1
1
×1
3 1 5
Calcul Calc ulat atee the the ar area ea an and d per perim imet eter er of th thee rectangle shown:
3 4
×1
1 2
2 5
3 4
67
m
m
MEP Y9 Practice Book A
4.3 7.
2
Julie Ju lie ha hass a ve vege geta tabl blee plo plott tha thatt has has an ar area ea of She plants potatoes on
1 4
3
of an acre.
of the plot.
What fraction of an acre does she plant with potatoes?
8.
Which is the larger 3 4
9.
1
or
2
3
÷
4
1 2
?
Solve th these eq equations: 2
(a)
10.. 10
×
x
=
3
4
3
(b)
9
x
5
=
9 4
If the the ar area ea of th thee rec recta tang ngle le sh show own n is
1
1 2
m
2
2
, what is the length of the
3
m
rectangle?
11.
(a)) (a
In a mag magaz azin inee the there re ar aree thr three ee ad adve vert rtss on on the the sa same me pa page ge.. Advert 1 uses
Advert 2 uses
Advert 3 uses
1 4 1 8 1 16
of the page
of the page
of the page
In total, what fraction of the page do the three adverts use? Show your working.
(b)) (b
Thee cos Th costt of of an an adv adver ertt is £1 £10 0 for for ea each ch An advert uses
3 16
1 32
of a page.
of a page. How much much does the advert advert cost? (KS3/99/Ma/Tier 4-6/P1)
68
MEP Y9 Practice Book A
12.
(a)
Ala lan n had th thiis specia iall rectangle. He cut off
1 3
of the rectangle. ↓
subtract
1 3
He had this square left.
↓
add on ?
↓
subtract
Alan put back the piece he had cut off. He said: " I've added on
1 3
of the square."
He was wrong. Explain why. why. What fraction of the square did he add on? (b)
Look at shape 1 and shape 2.
shape 1 1 4
of shape 1 shape 2 What fraction of shape 2 is added on to get back to shape 1? ↓
add on . . . .
of shape 2 shape 1
(c)
Look Loo k at the the number numberss on the the botto bottom m of the the fracti fractions ons in (a) (a) and (b) (b).. Suppose you subtract
1 8
of a shape.
You want to get back to the shape you started with. What fraction of the new shape would you add on? (d)) (d
Supp Su ppos osee yo you su subt btra racct
1
of a shape.
n
You want to get back to the shape you started with. What fraction of the new shape would you add on? (KS3/94/Ma/5-7/P1) 69
MEP Y9 Practice Book A
4.4 4. 4 Frac Fracti tion on,, Dec Decim imal al an and d Pe Perc rcen enta tage ge Equivalents In this section we revisit the equivalence of fractions, fr actions, decimals and percentages; for example, we could write
1 2
as 0.5 or as 50%.
Example 1 Write each of the following percentages as decimals and f ractions in their simplest form: (a )
75%
(b)
3 2% 32
Solution (a )
75% =
75 100
= 0.7 .75 5 as a dec ecim imaal 75% = =
75 100 3 4
(b)
32% =
as a fraction in its simplest form
32 100
= 0.3 .32 2 as a dec ecim imaal 32% = =
32 100 8 25
as a fraction in its simplest form
Example 2 Write each of the following decimals as a percentage and as a fraction in its simplest form: (a )
0.72
(b)
0.08
70
MEP Y9 Practice Book A
Solution (a )
=
0.72
72 100
= 72 72% % as a pe perc rcen enta tage ge =
0.72
72 100
=
18 25
(b)
8
=
0.08
as a fraction in its simplest form
100
= 8% 8
=
0.08
as a percentage
100
=
2 25
as a fraction in its simplest form
Example 3 Write each of the following fractions as a decimal and as a percentage: (a)
3
(b)
10
4
(c)
25
Solution (a)
3
=
10
30 100
= 0.3
(multiply top and bottom by 10)
as a decimal
= 30 30% % as a pe perc rcen enta tage ge 4
=
25
16 100
(multiply top and bottom by 4)
= 0. 0.1 16 as a de deccim imal al = 16 16% % as a pe perc rcen enta tage ge
(b)
3 8
=
37.5 100
(multiply top and bottom by 12.5)
= 0.3 0.375 75 as a de decim cimal al = 37.5% as a percentage percentage
71
3 8
MEP Y9 Practice Book A
4.4
Exercises 1.
2.
3.
4.
5.
Writ ritee each each of of the the follo followi wing ng per perce cent ntag ages es as as a dec decim imal al:: (a )
60%
(b)
70%
(c)
20%
(d)
45%
(e)
31%
(f )
82%
(g)
14%
(h)
4%
(i)
63%
(j )
2%
(k)
1% 1%
(l)
19%
Write eac each h of the fol follow lowing ing per percen centag tages es as as a fract fraction ion in its its simpl simplest est for form: m: (a )
80%
(b)
25%
(c)
40%
(d)
35%
(e)
65%
(f )
4%
(g)
64%
(h)
82%
(i)
28%
(j )
6%
(k)
7% 7%
(l)
92%
Writ ritee each each of of the the follo followi wing ng dec decim imal alss as as a per perce cent ntag age: e: (a )
0.74
(b)
0.99
(c)
0.5
(d)
0.06
(e )
0.26
(f )
0.02
(g)
0.3
(h)
0.002
(i)
0.042
Write eac each h of of the the follo followin wing g deci decimal malss as as a fra fracti ction on in in its its simpl simplest est for form: m: (a )
0.5
(b)
0.25
(c )
0.4
(d)
0.7
(e )
0.62
(f )
0.44
(g)
0.37
(h)
0.04
(i)
0.05
(j )
0.24
(k)
0.1
(l)
0.74
Writ ritee eac each h of of the the follo followi wing ng fr frac actio tions ns as a dec decim imal al:: (a) (d) (g) (j)
1 2 9 20 19 100 8 25
(b) (e) (h) (k)
3
(c)
4 7 10 23 50 1
(f) (i) (l)
8
72
4 5 3 100 7 25 5 8
MEP Y9 Practice Book A
6.
Writ ritee each each of of the the follo followi wing ng fra fract ctio ions ns as as a per perce cent ntag age: e: (a) (d) (g) (j)
7.
9
(b)
10 3
(e)
20 9
(h)
20 3
(k)
50
17
(c)
100 2
(f)
5 9
(i)
100 7
(l)
8
Copy and complete this table of equivalent fractions, decimals and percentages:
Fraction
14 25 3 5 1 100 7 200
Decimal
Percentage
4 5
0.68 85% 0.76 8 25
3% 0.005
8.
In a sur survey vey,, 400 400 peopl peoplee were were aske asked d how how they they wou would ld vote vote at the the nex nextt election. The results are listed below: Labour
220
Conservative
160 20
Other
Express these results as percentages. 9.
In a sch school ool the there re are are 50 50 Manch Manches ester ter Cit City y suppo supporte rters rs out out of of a tota totall of 200 2000 0 pupils. (a)
Whatt perce Wha percenta ntage ge of of the the pupil pupilss suppo support rt Manc Manches hester ter Cit City? y?
(b)) (b
What Wh at pe perc rcen enta tage ge of th thee pu pupi pils ls do not support Manchester City?
73
MEP Y9 Practice Book A
4.4 10.. 10
In a grou group p of 40 pupi pupils ls ther theree are are 7 who who cann cannot ot swim swim.. What percentage of the pupils can swim?
11.
Simon Sim on is grow growing ing vege vegetab tables les in in three three veget vegetab able le patch patches. es. (a)) (a
Abou Ab outt 50% 50% of of this this veg veget etab able le pa patc tch h is fo forr carrots.
Cabbages Carrots Lettuces
percentages entages: Write down the missing perc
(b)
(i)) (i
about . . . % of th thee patch is fo forr cabbages,
(ii) (i i)
abo bout ut . . . % of th thee pa patc tch h is fo forr lettuces.
About
1 8
of this vegetable patch is for beetroot . Beetroot Broad Beans Beans
Peas
Write down the missing fractions:
(c )
(i)) (i
about . . . of the patch is for broad beans.
(ii) (i i)
abo bout ut . . . of th thee pat atcch is fo forr peas.
About
4 5
of this vegetable patch is for potatoes.
Copy the diagram below and draw a straight line to show how much of the patch is for potatoes. Shade in the area for potatoes.
The rest of the patch is for turnips. About what fraction of the patch is for turnips ? (KS3/96/Ma/Tier 4-6/P1)
74
MEP Y9 Practice Book A
12.
1 2
of the diagram below is shaded.
(a)) (a
Loo ook k at th this is di diag agra ram m:
What fraction is shaded? What perce percentage ntage is shaded? (b)) (b
Copy Co py th thee dia diagr gram am be belo low w and and sh shad adee
2 5
of it.
What percentage of the diagram have you shaded? (KS3/97/Ma/Tier 3-5/P1)
4.5 4. 5 Pe Perc rce ent ntag age e Incr Increa ease ses s and and Decr Decre eas ase es Often prices are increased or decreased decreased by a percentage. percentage. In this section we consider how to increase or decrease quantities by using percentages.
Example 1 Katie earns £40 per week for her part-time job. She is to be given a 5% pay rise. How much will she earn per week after the pay rise?
75
MEP Y9 Practice Book A
4.5 Solution 5% of £40 =
5
× £40
100
OR
= £2 =
New pay
100%
+
5%
= 105%
which is 1.05 as a decimal
£40
+
£2
=
New pay
= £42
£40
× 1.05
= £42
Example 2 The prices of all the televisions in a shop are to be increased increased by 8%. Calculate the new price of a television that originally cost £150.
Solution 8% of £150 =
8
× £150
100
OR
= £12 New price =
£150
+
100%
+
8%
= 108%
which is 1.08 as a decimal New price =
£12
= £162
£150
× 1.08
= £162
Example 3 In a sale the cost of a computer is reduced by 30%. 30%. The normal price of the computer was £900. Calculate the sale price of the computer. computer.
Solution 30% of £900 =
30
× £ 900
100
OR
= £270 Sale price =
£900
−
100%
− 30 30% = 70%
which is 0.7 as a decimal New price =
£270
= £630
£900
= £630
76
×
0.7
MEP Y9 Practice Book A
Exercises 1.
2.
3.
(a)
Increase £100 by 20%.
(b)
Increase £400 by 30%.
(c )
Increase £80 by 25%.
(d)
Increase £50 by 6%.
(e )
Increase 40 kg by 3%.
( f)
Increase 250 m by 7%.
(a)
Decrease £60 by 30%.
(b)
Decrease 8 m by 5%.
(c )
Decrease 80 kg by 10%.
(d)
Decrease £44 by 20%.
(e )
Decrease 90 m by 2%.
(f )
Decrease 420 kg by 25%.
A comp company any inc increa reases ses the cos costt of all its pro produc ducts ts by 5%. Cal Calcul culate ate the new price of each of the items listed below: (a)) (a
a te tent nt th that at pr prev evio ious usly ly co cost st £6 £60. 0.
(b)) (b
a ru ruck cksa sack ck th that at pr prev evio ious usly ly co cost st £1 £15, 5,
(c)) (c
a sle sleep epin ing g ba bag g th that at pr prev evio ious usly ly co cost st £2 £24. 4.
4.
Joe was pai paid d £30 £30 per wee week k for for del delive iverin ring g pape papers. rs. He was giv given en a 3% 3% pay pay rise. How much will he now earn each week?
5.
A sma small ll firm emp employ loyss 4 sta staff. ff. The They y are all giv given en a 4% pay ris rise. e. The original salaries are as follows: John Smith
£24 000
Alice Holland
£22 500
Graham Hall
£14 000
Emma Graham
£8500
Calculate the new salary for each member of staff.
6.
Rachell puts Rache puts £50 £50 int into o a ban bank k acco account unt.. Aft After er one yea yearr 5% 5% inter interest est is adde added d to her money. How much does she have then?
7.
Add (a )
8.
17
1 2
% VAT to each of the following prices:
£200
(b)
£70
(c )
£42
A rop ropee is is 8 m long long but it shrin shrinks ks whe when n it get getss wet. wet. Wha Whatt would would be the new length of the rope if its i ts length is reduced by: (a )
2%
(b)
7%
77
(c )
12% ?
MEP Y9 Practice Book A
4.5 9.
In a sal salee the the pric prices es of of each each of of the the items items lis listed ted bel below ow is is to be red reduc uced ed by by 35%. £28 £42 Coat Jeans £36
Trainers
Shirt
£14
Calculate the sale price of each item. 10.
A moun mountain tain bike was price priced d at £180 £180.. Its price was incre increased ased by 8%. Later Later,, this increased price was reduced by 20% in a sale. Calculate the sale price of the bike.
11.
Thiss is how Car Thi Caryl yl work workss out out 15% 15% of 120 in her her head head.. 10% of 120 is 12, 5% of 120 is 6, so
15% of of 120 is is 18.
(a)
Copy Cop y and comp complet letee the follo followin wing g calcul calculati ations ons to to show show how Cary Caryll can work out
1
17 2
% of 240 in her head.
.... .. .... .... % of 24 240 0 is is .. .... .... .... .... .... .. .... .... % of 24 240 0 is is .. .... .... .... .... .... .. .... .... % of 24 240 0 is is .. .... .... .... .... so (b)) (b
17 12
% of 24 240 0 is .. .... .... .... ....
Wor ork k out out 35 35% % of of 250 250.. Sh Show ow yo your ur wo work rkin ing. g. (KS3/98/Ma/Tier 3-5/P1)
12.
Look Lo ok at th this ta tabl ble: e: Birth rate per 1000 population population
1961
(a)
England
17.6
Wales
17.0
1994
12.2
In Engl England and,, from from 1961 1961 to to 1994, 1994, the bir birth th rate rate fel felll by 26.1 26.1% % What was the birth rate in England in 1994 ? Show your working.
(b)) (b
In Wal ales es,, the the bi birt rth h rat ratee als also o fel fell. l. Calculate the percentage percentage fall from 1961 to 1994. 1994. Show your working. (KS3/98/Ma/Tier 5-7/P2)
78
MEP Y9 Practice Book A
13.
The table show showss the land area of each each of of the World's conti continents nents.. Continent
Land Area (in 1000
Affrica A
30 264
Antarctica
13 209
Asia
44 250
Europe
km
2
)
9 907
North America
24 398
Oceania
8 534
South America
17 793 148 355
World
(a)
Which Whi ch contin continent ent is is approx approxima imatel tely y 12% of of the Worl World's d's land land area area??
(b)
What perc percentag entagee of the World's land area is Antar Antarctica ctica?? Show your working.
(c)
Aboutt 30% Abou 30% of the World's area is land land.. The rest is water water.. The amou amount nt of land in the World World is about 150 million
km
2
.
Work out the approximate total area (land and water) of the World. Show your working. (KS3/98/Ma/Tier 6-8/P2)
14.
In 1995, 1995, the Alpha Comp Company any employ employed ed 4000 4000 people. people. For each each of of the next 2 years, the number of people employed increased by 10%.
(a )
1995
employed 4000 people
1996
employed 10% more people
199 19 97
empl em ploy oyed ed 10 10% % mo more re pe peo opl plee
Tony said: year, the Alpha Alpha Company employed employed another another 400 people. people. " " Each year, Tony was wrong. Explain why.
(b)
Which of the Which the calcu calculat lation ionss below below shows shows how how many many peopl peoplee worked worked for for the company in 1997: (i) (iv)
4000 × 0.1 × 2
(ii)
× 1.1 × 2
(v)
4000
4000 × 0.1
79
4000
2
× 1.1 2
(iii)
(4000 × 0.1)
2
(vi)
(4000 × 1.1)
2
MEP Y9 Practice Book A
4.5 (c)) (c
Look Lo ok at at thes thesee figu figure ress for for the the Beta Beta Com Compa pany ny:: 1995
employed n people
1996 19 96
empl em plo oye yed d 20% fe few wer pe peo opl plee
1997 19 97
empl em plo oye yed d 10% mo more re peo eopl plee
Write an expression using n to show how many people the company employed in 1997. 1997. Show your working and and write your expression expression as simply as possible. (KS3/99/Ma/Tier 6-8/P1)
15.
A cloth clothes es shop shop had a closing closing down sale. The sale starte started d on Tu Tuesda esday y and and finished on Saturday. Saturday. For each day of the sale, prices were were reduced by 15% of the prices on the day before. (a)
A shi shirt rt had had a pric pricee of of £19.9 £19.95 5 on on Monda Monday y. Kev Kevin in boug bought ht it it on Wednesday. How much did he pay? Show your working.
(b)
Ghita bou Ghita bought ght a dress dress on Tues uesday day for £41. £41.48. 48. Wha Whatt was was its pri price ce on on Monday? Show your working. working.
(c)
A jac jacket ket had a price price of £49. £49.95 95 on on Monda Monday y. Wha Whatt was was its its price price on Friday? Show your working.
(d)
Anotherr shop Anothe shop is reduci reducing ng its pric prices es each each day day by 12% 12% of the pric prices es on the day before. How many days would it take for its original prices prices to be reduced by more than 50%? Show your working. working. (KS3/96/Ma/Tier 6-8/P2)
80
