Welcome!
This is the third in a series of teaching aids designed by teachers for teachers at level 6.
The worksheets are designed to support the delivery of the National Curriculum in a variety of
teaching and learning styles. They are not designed to take the pedagogy away from the teacher.
The worksheets are centred around the shown level, but spiral from the level below to the level
above. Consult the National Numeracy Strategy for definitive National Curriculum levels.
They can be used by parents with the support of the on-line help facility at www.10ticks.co.uk.
Contents and Teacher Notes.
Pages 3/4.
Pages 5/6.
Pages 7/8.
Pages 9/10.
Pages 11/12.
Pages 13/14.
Page 15.
Page 16.
Page 17.
Page 18.
Pages 19/20.
Level 6 Pack 3. Page 1.
Percentages 1.
There is a huge amount of percentage work to be covered at level 6. This first
sheet covers finding percentages of quantities and percentage increases and
decreases of quantities. It ends by putting these questions into context with
worded questions.
Percentages 2.
Finding the original quantity in a question, again putting it into context with
worded questions.
Percentages 3.
Finding a percentage.
Percentages 4.
Percentage increase and decrease.
Percentages 5.
Percentage profit and loss. Simple and Compound interest.
Vulgar Fractions, Decimal Fractions and Percentages.
Interchanging between these three number systems. The use of the dot above a
number is used to indicate recurring numbers. Using trial and improvement
to find fractions that are equivalent to recurring decimals is a very difficult
skill. Use these sections only with the more able pupils.
Fraction Hexagon Puzzle Grid.
The master grid needed for the hexagon puzzle cards.
Percentage, Decimal, Fraction Equivalent Hexagon Puzzle Cards.
Place the correct hexagon on the correct spot on the master board.
Rotate the hexagons until the adjoining hexagon has the equivalent
fraction/decimal/percentage next to it. How many hexagons can you get in
place that are fully equivalent?
The Decimal Number Line.
A series of questions that lead to deeper understanding of the decimal system.
This is a precursor to trial and improvement and the decimal skills needed to
attempt this type of question.
Investigations with Decimals, Fractions and Percentages.
Some investigations surround the number systems. Some are quite difficult and
go beyond level 6, but more able pupils should cope.
Rounding Off.
Rounding off to decimal places and significant figures. Page 20 shows numbers
that have already have been rounded off and looks at the upper and lower limits
that the values could possibly take.
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Pages 21/22. Fractions 1.
Revision of improper fractions, cancelling and common denominators.
Pages 23/24. Fractions 2.
Addition and subtraction of fractions. Starting with the same denominators and
moving quickly to addition/subtraction by finding common denominators.
Pages 25/26. Fraction Pyramid.
This style of worksheet should be familiar to pupils by now and should need
little explanation. To get the fraction above add the two fractions below. As the
questions progress subtraction is needed.
Pages 27/28. Magic Squares (Fractions).
Lots of addition and subtraction involved in the magic squares. This sheet is
particularly useful for the more able. Question 16 could be used in isolation
as a board exercise, with pupils choosing fractions and the class making the
magic square.
Pages 29/30. Hit 12/Hit 15.
Shove penny game adapted to fractions. Hit 12 is centred on the fractions 1/2,
1/3, 1/4 and by necessity 1/12. Similarly Hit 15 is centred on the fractions 1/3,
1/6, 1/9 and by necessity 1/18.
Pages 31/32. Addition/Subtraction of Fractions (Worded Questions).
These pages put all the fraction skills learnt to date into context.
Pages 33/34. Multiplication and Division of Fractions 1.
Multiplying fractions by whole numbers. Answers start as whole numbers
but graduate to mixed numbers.
Pages 35/36. Multiplication and Division of Fractions 2.
Multiplying fractions by fractions. This leads to cancelling down before
multiplying out and multiplying mixed numbers together. Diagrams are used to
show the multiplication, this is more clearly demonstrated by repeating the
diagrams when folding a sheet of paper. The “overlap” is the answer.
Pages 37/38. Multiplication and Division of Fractions 3.
Division of fractions. Introduction of inverse. Dividing a whole number by a
fraction and looking for rules to help with division.
Pages 39/40. Fraction Multiplication Grids.
Again, this style of worksheet should be familiar to pupils by now and should
need little explanation. Multiplication and division skills are necessary.
Questions 23 and 24 are very difficult and you may want to prompt the class by
giving them 1 of the surrounding fractions.
Pages 41/42. Multiplication/Division of Fractions (Worded Questions).
Putting all the multiplication and division skills into context.
Copyright in Worksheets. ©Fisher Educational Ltd. 2000.
Copyright in the worksheets belongs to Fisher Educational Ltd. Each purchase of the worksheets represents a
licence to use and reproduce the worksheets as set out in the Terms and conditions shown on the 10ticks website.
'10TICKS', and '10TICKS.co.uk' and/or other 10TICKS services referenced on this web site or on the Worksheets
are trademarks of Fisher Educational Ltd in the UK and/or other countries.
Details of copyright ownership in the clip art used in these worksheets:
Copyright in the clip art used entirely in this pack is owned by Nova Development Corporation, California, USA.
Level 6 Pack 3. Page 2.
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Percentages.
A). Finding a Percentage of a Quantity.
Find
1).
5).
9).
13).
17).
21).
25).
29).
33).
37).
41).
45).
49).
53).
57).
28% of 50
16% of 250
15% of 300
7% of 400
31% of 720
16% of £240
24% of £89
52% of £63
29% of 56 Kg
37% of 7 Kg
69% of 2 m
12% of 170 cm
33% of 9 m
72% of £130
44% of 78 m
2).
6).
10).
14).
18).
22).
26).
30).
34).
38).
42).
46).
50).
54).
58).
20% of 400
4% of 150
35% of 200
96% of 900
34% 0f 340
92% of £18
19% of £72
88% of £140
53% of 500 Kg
8% of 3 Kg
27% of 37 m
58% of 1800 m
13% of £72
74% of 20 cm
32% of 230 cm
3).
7).
11).
15).
19).
23).
27).
31).
35).
39).
43).
47).
51).
55).
59).
15% of 240
40% of 600
45% of 720
21% of 720
39% of 960
23% of £26
41% of £84
63% of £12
43% of 400 Kg
83% of 9 Kg
14% of 4 m
34% of 16 m
45% of 38 Kg
59% of £96
72% of £13
4).
8).
12).
16).
20).
24).
28).
32).
36).
40).
44).
48).
52).
56).
60).
36% of 125
75% of 440
2% of 500
54% of 400
17% of 730
66% of £42
5% of £63
28% of £8
35% of 6 Kg
94% of 7 Kg
46% of 210 m
62% of 4 m
79% of 94 m
91% of 104 Kg
4% of 63 Kg.
B). Percentage Increase and Decrease of a Quantity.
Increase
1). 30 by 20%
5). 300 by 48%
9). 170 by 34%
13). 440 by 68%
17). 320 by 74%
21). £260 by 15%
25). £89 by 17%
29). £63 by 99%
33). 58 Kg by 24%
37). 7 Kg by 92%
41). 2 m by 35%
45). 170 cm by 6%
2).
6).
10).
14).
18).
22).
26).
30).
34).
38).
42).
46).
70 by 40%
200 by 4%
215 by 46%
960 by 12%
340 by 47%
£16 by 30%
£72 by 39%
£146 by 9%
580 Kg by 6%
8 Kg by 23%
57 m by 74%
1800 m by 1%
3).
7).
11).
15).
19).
23).
27).
31).
35).
39).
43).
47).
60 by 15%
120 by 35%
720 by 4%
740 by 8%
960 by 33%
£28 by 90%
£84 by 11%
£12 by 18%
400 Kg by 17%
14 Kg by 78%
14 m by 82%
16 m by 34%
4).
8).
12).
16).
20).
24).
28).
32).
36).
40).
44).
48).
120 by 5%
440 by 85%
90 by 17%
490 by 24%
30 by 19%
£44 by 12%
£63 by 57%
£8 by 44%
6 Kg by 36%
27 Kg by 19%
210 m by 63%
4 m by 84%
Decrease
1). 60 by 20%
5). 500 by 48%
9). 370 by 34%
13). 940 by 68%
17). 120 by 72%
21). £290 by 45%
25). £29 by 17%
29). £83 by 39%
33). 54 Kg by 24%
37). 9 Kg by 92%
41). 1 m by 35%
45). 190 cm by 8%
2).
6).
10).
14).
18).
22).
26).
30).
34).
38).
42).
46).
90 by 20%
800 by 4%
115 by 46%
760 by 12%
640 by 27%
£18 by 30%
£42 by 39%
£196 by 9%
380 Kg by 6%
3 Kg by 53%
97 m by 94%
1300 m by 1%
3).
7).
11).
15).
19).
23).
27).
31).
35).
39).
43).
47).
80 by 15%
120 by 35%
320 by 4%
780 by 8%
260 by 73%
£48 by 70%
£54 by 11%
£22 by 68%
800 Kg by 27%
34 Kg by 68%
64 m by 12%
19 m by 4%
4).
8).
12).
16).
20).
24).
28).
32).
36).
40).
44).
48).
220 by 5%
440 by 85%
80 by 17%
590 by 34%
60 by 9%
£54 by 22%
£83 by 5%
£7 by 44%
5 Kg by 36%
97 Kg by 19%
610 m by 53%
2 m by 74%
Level 6 Pack 3. Page 3.
Licensed to Dr Challoner's Grammar School
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Worded Questions.
1).
A stereo costs £320. In a sale it is reduced by 25%. What is the sale price ?
2).
An antique clock cost £540. It's price is increased by 18% in a year. What is it now worth ?
3).
£600 is put in a bank. After a year the money has increased by 8%.
How much is now in the bank ?
4).
A second-hand car costs £2400. The price falls by 45% when it is
sold again. How much is it sold for ?
5).
A season ticket for Bolton F.C. this season costs £410. It is to go up by 34% next season.
How much will a season ticket cost next season ?
6).
A shirt is slightly shop soiled so it is reduced by 30%. It was £40.50, how much is it to be
sold for ?
7).
The bill for a meal came to £65.40 plus 15% service charge. What was the total bill ?
8).
In Durry's winter sale the following items were offered at 35% reductions.
Find the sale price.
a). Stereo £340
b). Television £620
c). Video recorder £180
d). Walkman £18 e). Camcorder £1200
f). Blender £6.
9).
A salesperson earns £16000 a year. She is offered a rise of 22%. How much will she now
receive ?
10). A rotund gentleman weighs 92 Kg. After two months at weight watchers
he loses 20% of his weight. How heavy is he now ?
11). The number of pupils in a school rises by 8%. There used to be 850
pupils, how many are there now ?
12). The Spice Girls latest single sells 40% fewer singles this week than last
week. Last week it sold 120 000 singles. How many did it sell this week ?
13). A town had a population of 26 200. The total fell by 8%. What is the new population ?
14). A woman buys a house for £62 000. Ten years later she sells it for a 30% profit. How much
does she sell the house for ?
15). In a terrible storm 45% of the trees in a forest are felled. If the forest originally had 9 200
trees, how many are left standing ?
16). Billy has all 32 of his teeth. After a chance encounter with a bulldozer
he loses 75% of his teeth. How many has he left ?
17). After Christmas Bob's weight has increased by 32%. He was 60 Kg,
what is his current weight ?
18). John throws the javelin 52 metres. His next throw is 12% better.
How far has he thrown the javelin this time ?
Level 6 Pack 3. Page 4.
Licensed to Dr Challoner's Grammar School
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C. Finding the original quantity.
Fill in the table, finding the original prices for these percentage increases.
Original
Price, £
1).
3).
5).
7).
9).
11).
13).
15).
17).
19).
21).
23).
25).
27).
29).
Percentage
Increase, %
12
25
8
32
18
32
63
8
9
31
47
41
16
45
30
New
Price, £
22.40
58.75
61.56
125.40
299.72
42.24
244.50
853.20
52.32
93.01
1764
109.98
14.79
14.79
34.45
Original
Price, £
2).
4).
6).
8).
10).
12).
14).
16).
18).
20).
22).
24).
26).
28).
30).
Percentage
Increase, %
15
16
12
45
26
41
19
3
12
23
72
20
32
5
75
New
Price, £
41.40
106.72
156.80
188.50
122.22
100.11
285.60
638.60
103.04
1168.50
5848
5.40
159.06
10.08
98
Fill in the table, finding the original prices for these percentage decreases.
Original
Price, £
1).
3).
5).
7).
9).
11).
13).
15).
17).
19).
21).
23).
25).
27).
29).
Level 6 Pack 3. Page 5.
Percentage
Decrease, %
20
30
20
10
35
35
24
18
62
71
3
78
55
30
75
New
Price, £
80
56
9.60
30.60
143
29.25
13.68
4.92
30.40
13.92
3.88
18.59
5.94
8.89
3.08
Original
Price, £
2).
4).
6).
8).
10).
12).
14).
16).
18).
20).
22).
24).
26).
28).
30).
Licensed to Dr Challoner's Grammar School
Percentage
Decrease, %
10
15
25
40
60
32
16
34
48
63
28
67
16
25
80
New
Price, £
216
102
52.50
39
6
40.80
117.60
415.80
78
170.20
56.16
462
78.96
105.36
3.94
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Worded Questions.
1).
A camera is reduced by 5% in a sale. The sale price is £15.20. What was the original price?
2).
An antique clock's price increases by 40% in a year. It now costs £112. What was it worth ?
3).
Jean puts some money into shares. After a year the share price has increased by 16%. It is
now worth £139.20. How much was originally spent on shares ?
4).
Ian buys a second-hand car. The price falls by 24%. He sells it for £2356.
How much did he pay for it ?
5).
A season ticket for Bolton F.C. this season is to go up by 20%.
It will cost £288. How much was a season ticket last season ?
6).
A shirt is slightly shop soiled so it is reduced by 25%. It is now £12, how much was it to be
sold for ?
7).
The bill for a meal came to the cost of the meal plus 15% service charge.
The total cost was £80.50. What was just the cost of the meal ?
8).
In Durry's winter sale the following items where offered at 35% reductions.
Here is the sale price, find the original price.
a). Stereo £130
b). Television £351
c). Video recorder £97.50
d). Walkman £9.10 e). Camcorder £520
f). Blender £5.85.
9).
A salesperson is offered a rise of 12%. She will now earn £268.80 weekly.
How much did she get before her rise ?
10). A slim gentleman, after two months at weight watchers, loses 35% of his weight. He is
weighed at 41.6 Kg. How heavy was he before he joined weight watchers ?
11). The number of pupils in a school rises by 15%. There are now 805 pupils, how many did
there used to be ?
12). The Herb Boys latest single sells 65% fewer singles this week than last week. It sold
29 750 singles this week. How many did it sell last week ?
13). A village has a population of 2058 after falling by 2%. What was the earlier population ?
14). A woman sells a house for £104 000. She makes 30% profit. How much did she buy the
house for originally ?
15). In a terrible storm 45% of the trees in a forest are felled. If the forest has 12 100 trees left
standing, how many trees were originally standing in the forest ?
16). Billy, after a chance encounter with a bulldozer, loses 25% of his teeth.
He has 24 left. How many did he start with ?
17). Since Christmas Bob's weight has increased by 18%. He weighs 73.16 Kg,
what was his weight before Christmas ?
18). Jenny throws the javelin 52.08 metres. This is 24% better than her last throw.
How far was her last throw with the javelin ?
Level 6 Pack 3. Page 6.
Licensed to Dr Challoner's Grammar School
[email protected]
D. Finding a Percentage.
Where necessary leave the answers to 1 decimal place. Find
1).
3).
5).
7).
9).
11).
13).
15).
17).
19).
21).
23).
25).
27).
29).
31).
33).
35).
37).
39).
41).
43).
45).
47).
49).
51).
53).
55).
57).
59).
15 as a percentage of 60
200 as a percentage of 2000
80 as a percentage of 200
74 as a percentage of 200
112 as a percentage of 160
36 as a percentage of 50
216 as a percentage of 360
189 as a percentage of 420
6 as a percentage of 150
45 as a percentage of 60
598 as a percentage of 920
80 as a percentage of 320
48 as a percentage of 192
183 as a percentage of 600
170 as a percentage of 400
21 as a percentage of 40
65 as a percentage of 200
48 as a percentage of 128
80 as a percentage of 150
48 as a percentage of 350
56 as a percentage of 90
140 as a percentage of 360
46 as a percentage of 73
30cm as a percentage of 2m
12mins as a percentage of 2 hrs
15mm as a percentage of 6cm
450m as a percentage of 2Km
320ml as a percentage of 4 litres
2 ft as a percentage of 4yds
90ml as a percentage of 5 litres
2).
4).
6).
8).
10).
12).
14).
16).
18).
20).
22).
24).
26).
28).
30).
32).
34).
36).
38).
40).
42).
44).
46).
48).
50).
52).
54).
56).
58).
60).
120 as a percentage of 600
30 as a percentage of 60
60 as a percentage of 300
42 as a percentage of 168
42 as a percentage of 56
132 as a percentage of 150
45 as a percentage of 225
222 as a percentage of 370
324 as a percentage of 360
153 as a percentage of 180
342 as a percentage of 380
224 as a percentage of 400
36 as a percentage of 288
54 as a percentage of 144
33 as a percentage of 264
27 as a percentage of 250
25 as a percentage of 40
220 as a percentage of 480
5 as a percentage of 80
50 as a percentage of 225
72 as a percentage of 92
472 as a percentage of 500
600g as a percentage of 1Kg
450mm as a percentage of 1.5m
3p as a percentage of £1.50
340mm as a percentage of 85cm
12cm as a percentage of 2m
10 hrs as a percentage of 2 days
480m as a percentage of 1.4Km
80mg as a percentage of 6g .
Worded Questions.
1).
In a school of 400 pupils, 250 are girls. What percentage are girls ?
2).
In a crate of apples 33 are bad. The crate holds 264 apples. What percentage are bad ?
3).
A boy gets 29 marks out of 50 in his maths exam. What percentage did he score ?
4).
A farmer has 350 birds, of which 140 are ducks. What percentage of ducks does he have ?
5).
In a class of 40 children 24 are girls. What percentage are girls ?
6).
In September it rained for 15 days. What percentage of days did it rain for ?
7).
The captain of a football team scored 17 out of the 85 goals they scored
that season. What percentage of the goals did he score ?
Level 6 Pack 3. Page 7.
Licensed to Dr Challoner's Grammar School
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8).
In the last maths test 18 out of 54 pupils failed. What percentage of pupils failed ?
9).
In a general election in Numberland where 6400 people live. 2560 voted labour, 1600 voted
Conservative, 1920 voted Liberal and 320 did not vote. Find what percentage of people
voted for each party.
10). In a box of 500 eggs 32 were broken. What percentage of eggs were broken ?
11). On a Friday night 18 pupils were in detention from a school of 800 pupils.
What percentage of the school were in detention that Friday night ?
12). 360 buses run from a depot, but 72 are being repaired.
What percentage of the total are in service ?
13). One day 132 trains arrive at a railway station and 99 are on time. What percentage of them
are late ?
14). In an exam a pupil gets 54 out of 72 marks. What percentage of the exam does he get wrong ?
15). A dentist looks at Jean's 32 teeth, 12 of them have fillings.
What percentage don't have fillings ?
16). Billy has 250 school meals in a year. He has chips for 195 meals.
What percentage of school meals does Billy not have chips ?
17). In a classroom there are 18 girls and 14 boys. What percentage in the classroom are girls ?
18). A farmer has 120 sheep and 180 cows. What percentage of these animals are cows ?
19). For her birthday Beth gets 6 presents wrapped in red paper and 14 presents wrapped in
blue paper. What percentage of her presents are wrapped in red paper ?
20). Alex has 3 dolls, 12 teddy bears and 5 cuddly toys. What percentage of these are
a). teddy bears,
b). dolls,
c). cuddly toys ?
21). In a popularity vote, Hazel gets 65 votes, Nigel 40 votes, Billy 90 votes and Lynne 105
votes. Find what percentage of the vote each person received.
22). Only three people in the hockey team scored last season. Hayley scored 9, Sam scored 15
and Hazel scored 1 goal. What percentage of the goals did each score ?
23). Bertie collects leaves. He has 2000 in total. He has 700 green leaves,
500 red leaves and 800 mouldy leaves.
a). What percentage are red leaves ?
b). What percentage are not mouldy leaves ?
c). What percentage are not green leaves ?
24). At the zoo there are 5 ice-cream kiosks. The first sold 900 ice-creams, the second 350
ice-creams, the third 450 ice-creams, the fourth 1050 ice-creams and the fifth 700
ice-creams. Find the percentage of ice-creams sold at each kiosk.
Level 6 Pack 3. Page 8.
Licensed to Dr Challoner's Grammar School
[email protected]
E. Percentage Increase and Decrease.
A.
Find the percentage increase for the following questions.
Leave answers, where appropriate, to 1 decimal place.
1).
3).
5).
7).
9).
11).
13).
15).
17).
19).
21).
23).
25).
27).
29).
B.
400 is increased to 600
125 is increased to 170
80 is increased to 96
340 is increased to 357
530 is increased to 901
90m is increased to 108m
£64 is increased to £86.40
72m is increased to 88.2m
$96 is increased to $127.20
40g is increased to 45g
24m is increased to 25.32m
17g is increased to 33.66g
125Kg is increased to 248.125Kg
6Km is increased to 10.47Km
£2 is increased to £2.45
2).
4).
6).
8).
10).
12).
14).
16).
18).
20).
22).
24).
26).
28).
30).
40 is increased to 50
50 is increased to 55
25 is increased to 35
140 is increased to 182
2.4 is increased to 3.6
£150 is increased to £187.50
420cm is increased to 472.5cm
80Km is increased to 90Km
630Kg is increased to 973.35Kg
12 litres is increased to 19.86 litres
35ft is increased to 40ft
£84 is increased to £84.84
92ml is increased to 131.1ml
18p is increased to 25p
16mg is increased to 19mg.
Find the percentage decrease for the following questions. Leave answers, where
appropriate, to 1 decimal place.
1).
3).
5).
7).
9).
11).
13).
15).
17).
19).
21).
23).
25).
27).
29).
500 is decreased to 200
20 is decreased to 16
240 is decreased to 72
25 is decreased to 15
48 is decreased to 36
32p is decreased to 20p
84Kg is decreased to 75.6Kg
40mg is decreased to 25mg
342Kg is decreased to 282.15Kg
£196 is decreased to £113.68
18cm is decreased to 0.27cm
7 litres is decreased to 3.598 litres
1.5m is decreased to 0.51m
$36 is decreased to $35.64
62p is decreased to 43p
2).
4).
6).
8).
10).
12).
14).
16).
18).
20).
22).
24).
26).
28).
30).
150 is decreased to 120
40 is decreased to 32
60 is decreased to 42
92 is decreased to 23
420 is decreased to 302.4
140cm is decreased to 45.5cm
8Km is decreased to 1.776Km
12ml is decreased to 9ml
64m is decreased to 37.2m
24m is decreased to 22.68m
2.4Km is decreased to 2.352Km
£3.60 is decreased to £2
25g is decreased to 3.5g
84cm is decreased to 81.9cm
£1.72 is decreased to 98p.
Worded Questions.
1).
In a storm 144 fruit trees were left standing out of 180 fruit trees
in an orchard. What is the percentage decrease in the number of trees ?
2).
A javelin thrower has best throw of 60m. In the next competition he throws 72m.
What is the percentage increase of his personal best ?
3).
A wine manufacturer puts down 250 bottles for 3 years. After 3 years only 220 bottles
are in tact. What is the percentage decrease in the number of bottles ?
4).
A man weighs 65Kg. After two weeks on a diet he weighs 58Kg. What is his percentage
decrease in weight ?
Level 6 Pack 3. Page 9.
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5).
A board 130 cm long is trimmed to 104 cm. What percentage has been removed ?
6).
A piece of elastic 48 cm long is stretched to 60 cm. What percentage of the
original length is the increase ?
7).
There are now 29 girls in a class that originally had 25 girls in it.
What is the percentage increase in the number of girls in the class ?
8).
After an accident, there are 222 litres of water left in a tank which originally held 240
litres. What is the percentage loss of water ?
9).
Last year there were 500 children in a school. This year there are 565. What is the
percentage increase in the number of pupils ?
10). A man's weekly wage was £336, but now he earns £420. What is the percentage increase in
the man's wage ?
11). An article which used to cost £2.40 now only costs £1.60. What is the percentage
decrease in the cost of this article ?
12). The average number of school dinners taken by children fell from 180 to 165. What is the
percentage decrease in the number taking school dinners ?
13). A woman collects pairs of shoes. At the start of the year she has 150 pairs, by the end of
the year she has 175 pairs. What is the percentage increase in the number of pairs of shoes
she has ?
14). A small child weighs herself at the start of year 5. She weighs 25 Kg, at the end of year 5
she weighs 26 kg. Find the percentage increase in her weight.
15). A gardener measures the height of his sunflower. In the morning it is 400 cm tall and in the
evening it is 440 cm tall. By what percentage has the sunflower increased during the day ?
16). A child aged 6 is weighed at 15 Kg, by the time the child is 13 he
weighs 40 kg. What is his percentage increase in weight ?
17). At weight watchers a man is weighed at 95 Kg before his diet
and 76 Kg after his diet. What is his percentage decrease in weight ?
18). A piece of wood 810 mm long is reduced to 729 mm long. What is the
percentage decrease in its length ?
19). A flask of water is heated from 20˚C to 26˚C, find the percentage increase in the
temperature of the water ?
20). A box of matches originally holds 84 matches, when counted only 63 were
left. What percentage of matches had been used ?
21). The time required to make an article was reduced from 8h 20 mins
to 7 h 45 mins. What was the percentage saving in time ?
Level 6 Pack 3. Page 10.
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Percentage Profit and Loss.
For the following table find the percentage profit or loss.
Where necessary round to 1 decimal place.
1).
3).
5).
7).
9).
11).
13).
15).
17).
19).
21).
23).
25).
27).
29).
Cost Price, £.
4.00
3.20
0.80
6.50
1.24
12.00
34.60
62.00
13.40
34.00
15.50
65.00
18.08
0.08
9.90
Selling Price, £.
6.00
3.84
1.32
5.85
0.93
13.44
19.03
63.24
18.09
26.86
18.70
74.90
15.80
0.15
15.99
2).
4).
6).
8).
10).
12).
14).
16).
18).
20).
22).
24).
26).
28).
30).
Cost Price, £.
2.50
4.10
9.00
3.20
0.70
24.00
18.50
0.90
12.00
16.00
24.90
5.06
32.00
54.05
1200
Selling Price, £.
3.00
5.74
7.20
2.08
0.21
18.96
31.45
0.72
9.12
17.92
20.50
8.72
28.00
60.90
1800
Worded Questions.
31). A sheep is bought for £40 and sold for £33. What is the percentage loss ?
32). A man bought a vase for £9 and sold it for £30. What was his percentage profit ?
33). A woman buys a car for £8500 and sells it a year later for £5100, what is her percentage
loss ?
34). A man buys a house for £55 000 and sells it ten years later for £72 600.
What is his percentage profit ?
35). A retailer buys bars of chocolate for 18p and sells them for 24p.
What is his percentage profit ?
36). Asways sells bread as a loss leader. It costs them 45p to make a loaf but
they charge the public only 32p a loaf. What is the percentage loss ?
37). Durrys get televisions for £260 and sell them at £272.50. What is the percentage profit they
make on each television ?
38). A shop buys a shirt for £15, but as it is stained, sells it for £14.50. What is the percentage
loss they make on the shirt ?
39). A man buys the Dandy in 1970 for 45p. He sells it today for £1.10.
What is his percentage profit on the comic ?
40). A man buys a brand new car for £18000. As soon as he drive it off
the garage it is second hand and only worth £15500. What is his
percentage loss for that short drive ?
Level 6 Pack 3. Page 11.
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F. Simple and Compound Interest.
A).
1).
3).
5).
7).
9).
11).
13).
15).
17).
19).
B).
For the table below, find the amount of simple interest earned and
the total amount of money the person would have at the end of the time period.
Amount
£'s
100
80
350
700
250
140
92
382
846
16
Interest
%
5
9
9
13
2
3
5
14
4
17
Time
Years
2
5
4
3
8
3
3
2
9
4
2).
4).
6).
8).
10).
12).
14).
16).
18).
20).
Amount
£'s
150
200
450
600
50
230
142
34
45
118
Interest
%
8
12
14
23
6
7
11
19
15
27
Time
Years
3
4
3
4
5
2
4
6
7
9
For the table below, use compound interest to find the total amount of money the person
would have at the end of the time period. After each year round the total to the nearest
penny and use this figure in your next calculation.
Amount
£'s
100
80
140
650
700
290
95
382
946
86
Interest
%
4
7
5
9
12
2
4
16
8
13
Time
Years
2
3
3
4
3
5
3
6
5
4
Amount
£'s
150
260
230
440
600
50
342
134
75
418
Interest
%
3
9
7
19
23
5
11
14
15
25
Time
Years
3
4
2
3
4
5
4
6
7
8
1).
2).
3).
4).
5).
6).
7).
8).
9).
10).
11).
12).
13).
14).
15).
16).
17).
18).
19).
20).
C).
1). A man borrows £2000 from a bank. The bank will charge him 13% interest every year. He
needs the money for 6 years. The bank don't tell him if they will charge simple interest or
compound interest.
a). Work out, using simple interest, how much he will owe the bank at the end of the
time period.
b). Work out, using compound interest, how much he will owe the bank at the end of the
time period.
c). On a graph plot time on the x-axis and amount of money owing on the y-axis. The
y-axis can start at £2000 and go up to £4200.
i).
Plot a line to represent simple interest.
ii). Plot a line to represent compound interest.
d). Write down any differences you notice between the two lines ?
2).
Another man borrows £4000 from a bank. The bank will charge him 24%
interest every year. He needs the money for 8 years. Repeat a). to d). for
the question above, changing the axes on the graph as appropriate.
Level 6 Pack 3. Page 12.
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Vulgar Fractions, Decimal Fractions and Percentages.
A).
Change each vulgar fraction into a decimal fraction and a percentage.
1).
1
2
2).
1
4
3).
1
8
4).
3
4
5).
3
8
6).
7
8
7).
1
5
8).
5
8
9).
3
5
10).
3
10
11).
1
20
12).
1
10
13). 2
5
14).
7
10
15).
3
20
16).
9
20
17). 4
5
18).
7
20
19). 11
16
20).
3
32
21). 19
20
22).
1
32
23).
9
16
24).
4
25
25). 17
32
26). 17
50
27).
3
16
28). 27
32
29).
9
10
30).
4
100
31). 227
500
32).
497
1000
33).
57
200
34). 167
250
35).
47
100
36). 2 3
4
37). 5 4
5
38). 2 5
8
39). 1 11
20
40). 3 23
50
42).
43).
44).
45).
41).
5 11
25
2 7
40
1 5
16
3 9
12
5 3
8
Change these fractions to decimals. Give the answer to 3 decimal places.
B).
46). 2
7
47). 11
14
48).
9
14
49). 1
3
50). 1
9
51). 1
6
52). 11
21
53). 10
11
54). 2
3
55). 14
15
56). 4
9
57).
58).
59).
60).
7
9
5).
10).
15).
20).
25).
30).
80 %
75 %
4%
2%
37 %
19 %
9
13
3
14
3
11
Change each percentage into a decimal fraction and a vulgar fraction.
1).
6).
11).
16).
21).
26).
Level 6 Pack 3. Page 13.
40 %
25 %
48 %
74 %
13 %
20 %
2).
7).
12).
17).
22).
27).
90 %
5%
92 %
6%
87%
45 %
3).
8).
13).
18).
23).
28).
50 %
95 %
12 %
26 %
91 %
88 %
4).
9).
14).
19).
24).
29).
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70 %
35 %
52 %
82 %
1%
58 %
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31).
36).
41).
46).
12.5 %
92.5 %
37.25 %
181.5 %
32).
37).
42).
47).
87.5 %
62.5 %
75.25 %
316.5 %
33).
38).
43).
48).
37.5 %
57.5 %
45.65 %
231.25 %
34).
39).
44).
49).
72.5 %
82.5 %
78.25 %
121.25 %
35).
40).
45).
50).
42.5 %
73.5 %
19.5 %
241.25 %
You may need to use trial and improvement to solve these.
51). 66.6 %
56). 91.6 %
61). 61.1 %
C).
52). 22.2 %
57). 41.7 %
62). 86.36 %
53). 77.7 %
54). 18.18 %
58). 46.6 %
59). 93.93 %
63). 14.8148 % 64). 17.17 %
55). 72.72 %
60). 77.27 %
65). 21.5215 %
Change each decimal fraction into a vulgar fraction and a percentage.
1).
6).
11).
16).
21).
26).
31).
36).
0.1
0.95
0.955
0.125
0.88
0.735
0.185
1.4125
2).
7).
12).
17).
22).
27).
32).
37).
0.3
0.85
0.28
0.725
0.925
0.875
0.165
2.9125
3).
8).
13).
18).
23).
28).
33).
38).
0.75
0.9
0.09
0.425
0.1275
0.855
0.3125
4.7625
4).
9).
14).
19).
24).
29).
34).
39).
0.65
0.37
0.44
0.375
0.4565
0.935
0.2125
3.8435
5).
10).
15).
20).
25).
30).
35).
40).
0.35
0.05
0.64
0.675
0.3725
0.325
0.6125
5.0145
Change these recurring decimals to fractions. (You may want to use trial and improvement).
41). 0.1
46). 0.16
51). 0.48
D).
42). 0.4
.
47). 0.17
52). 0.472
43). 0.63
48). 0.25
53). 0.318
44). 0.90
49). 0.21
54). 0.73
45). 0.81
50). 0.36
55). 0.84
Put the following into ascending (smallest to biggest) order.
1).
0.6
72%
4
7
2).
1 18% 0.19 25% 3 0.17 3
5
8
20
3).
87% 9 69% 0.7 0.58 9 60%
13
16
4).
0.4 35% 33% 3 0.38 3 0.3
10
8
5).
0.06 1 8% 15% 0.1 1 2
11
9 17
6).
0.9
7).
56% 5 0.5 58% 7 0.53 3
11
13
5
8).
0.7 77% 13 0.68 66% 7 14
20
9 19
9).
4 0.4 38% 0.39 5 0.45 42%
9
13
10). 0.6 55% 6 0.71 62% 4 0.59
11
7
3 68% 4
4
5
0.54
11). 0.2 2 0.2 19% 1 23% 16%
11
6
12).
13). 0.86 81% 0.8 7 78% 9 0.8
8
11
14). 52%
Level 6 Pack 3. Page 14.
93% 20 0.89 85% 15 0.8
21
16
1 7% 0.1 12% 0.08 1 0.05
13
8
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.
0.6 8 0.59 60% 9 13
15
17 22
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Level 6 Pack 3. Page 15.
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Card 2.
Card 1.
Card 3.
Card 8.
Card 7.
Card 10.
Card 9.
Number of hexagons correctly placed against each other :
1
A plant can do this
7
Now that's good
2
A very clever plant
8
Very Clever
3
Well it's a start !
9
Wonderful
4
Getting there
10 Albert Einstein
5
Pretty good
11 Superb
6
Cool
12 Brain the size of Mars
See how well you scored.
Card 5.
Card 4.
Card 6.
Card 11.
Place your hexagon cards onto the grid where shown. Now rotate the hexagons to match up
the equivalent fractions. See how many you can get to fit correctly.
Fraction Hexagon Puzzle Grid.
Card 13.
Card 12.
5
0.6
7
12
7
10
0
.5%
12
%
70
1
20
.4%
44
2
3
77
5
12
83
.
0.7
.
Card 7
4
%, Dec,
Frac. 4
9
9
.6%
7
9
7
.3%
.
0.5
83
.7%
%
.4
44
.3%
58
.3%
83
6
1
.75
%
70
0.8
.5%
62
5
2
0.1
3
4
3
11
5
6
9
7
0.1
%
6.6
7
27.27%
58.3%
0.5
5
0.0
%
70
%
80
5
0.6
5%
4
5
7
10
3
8
0.6
9
4
0.416
9
.
1
0.4
.
6
.3%
Card 11
0.4
16
25
0.1
0.3
75
%
.5
37
5
0.7
0.16
0.7
83.3%
83
0.7
.
41.6%
5%
8
66.6%
3
11
.
%, Dec,
Frac. 4
.6%
Licensed to Dr Challoner's Grammar School
66
0.4
4
9
7
12
6
.
Card 8
0.1
.
.
%, Dec,
Frac. 4
Card 6
1
6
80%
75%
7
12
.
3
.
.
%, Dec,
Frac. 4
0.8
.
.7%
16
62.5%
0.4
Card 3
Card 8
3
11
7
10
5
7
10
1
8
13
20
77
.
16
.6%
Card 4
3
.
..
%, Dec,
Frac. 4
0.8
..
4
5
6
58
0.05
37.5%
4
4
5
0.7
5
0.6
5
12
5
Card 2
.
.
%, Dec,
Frac. 4
3
8
5
8
0.85
4
5
1
5
6
%, Dec,
Frac. 4
27.27%
3
11
Level 6 Pack 3. Page 16.
%, Dec,
Frac. 4
.
9
1
6
.
3
3
.
..
6
2
0.8
Card 5
7
.6%
83
0.5
%, Dec,
Frac. 4
.
0.2
.6%
.
.
Card 13
.
.
.
Card 10
44.4%
.
Card 9
%, Dec,
Frac. 3
.
41.6
.
66
41
4
9
%, Dec,
Frac. 4
6
1
%, Dec,
Frac. 4
%, Dec,
Frac. 4
%
16
6
.
7
12
.
.
0.4
0.6
.7%
.
%
25
2
77
5
12
65
0.1
3
.
7
10
Card 11
0.125
Percentage,
Decimal, Fraction
Equivalents 3/4.
80%
.
%, Dec,
Frac. 4
Card 1
%
5
0.0
Hexagon Puzzle
Cards.
.
Card 12
70
0.7
5
0.7
Card 10
Card 3
%, Dec,
Frac. 3
1
20
%
%
Card 6
%, Dec,
Frac. 3
1
8
65
0.625
%, Dec,
Frac. 3
0.8
.5%
%
Card 5
Card 13
62
75
65
65
25
0.6
%, Dec,
Frac. 3
0.7
0.8
1
20
5
0.3
7
Card 12
0.05
.
.
5
1
0.6
2
13
20
Card 4
%, Dec,
Frac. 3
%, Dec,
Frac. 3
%, Dec,
Frac. 3
13
20
.
3
4
12.5%
Card 7
.
Card 9
%, Dec,
Frac. 3
12.5%
%, Dec,
Frac. 3
.
%, Dec,
Frac. 3
0.8
.5%
8
%, Dec,
Frac. 3
Card 2
62
8
3
8
%
1
Card 1
75
0.7
5
%, Dec,
Frac. 3
..
0.27
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The Decimal Number Line.
You may find the rulers drawn helpful.
1).
How many 1 digit decimals are there between
a).
d).
g).
j).
m).
p).
2).
b).
e).
h).
k).
n).
q).
2.3 and 2.9
3.4 and 3.9
3.5 and 4.4
0.5 and 2.1
5.0 and 6.0
2 and 5
How many 2 digit decimals are there between
a).
d).
g).
j).
m).
p).
s).
v).
3).
1.4 and 1.7
7.1 and 7.9
1.6 and 2.1
6.4 and 7.9
1.0 and 2.0
7 and 9
1.61 and 1.68
8.51 and 8.59
1.67 and 1.75
7.98 and 8.05
1.60 and 1.70
7.3 and 7.5
3 and 4
0 and 3
b).
e).
h).
k).
n).
q).
t).
w).
1.0
2.0
c).
f).
i).
l).
o).
r).
0.4 and 0.8
5.3 and 5.8
8.5 and 9.8
7.5 and 9.9
3 and 4
1 and 6
?
1.60
3.42 and 3.49
5.93 and 5.98
3.58 and 3.66
0.45 and 0.64
4.50 and 4.60
3.2 and 3.5
8 and 9
6 and 10
1.70
c).
f).
i).
l).
o).
r).
u).
x).
1.03 and 1.08
5.37 and 5.39
8.02 and 8.17
3.96 and 4.14
3.9 and 4.0
0.9 and 1.3
2 and 4
12 and 17 ?
c).
f).
i).
l).
o).
r).
u).
x).
1.741 and 1.747
2.511 and 2.519
4.371 and 4.382
4.395 and 4.416
8.45 and 8.47
8.49 and 8.52
2.6 and 2.8
3.7 and 4.3 ?
How many 3 digit decimals are there between
a).
d).
g).
j).
m).
p).
s).
v).
0.752 and 0.759
2.372 and 2.375
8.518 and 8.526
0.058 and 0.073
2.340 and 2.350
2.65 and 2.69
3.5 and 3.6
0.8 and 1.1
b).
e).
h).
k).
n).
q).
t).
w).
2.045 and 2.049
1.903 and 1.909
0.046 and 0.059
8.936 and 8.962
6.720 and 6.740
0.09 and 0.12
1.2 and 1.3
6.3 and 6.8
Investigation.
1).
a).
b).
c).
d).
e).
How many 2 digit decimals lie between 2.4 and 2.5 ?
How many 3 digit decimals lie between 2.4 and 2.5 ?
How many 4 digit decimals lie between 2.4 and 2.5 ?
How many 5 digit decimals lie between 2.4 and 2.5 ?
How many n digit decimals lie between 2.4 and 2.5 ?
2).
a).
b).
c).
d).
e).
How many 2 digit decimals lie between 0.37 and 0.89 ?
How many 3 digit decimals lie between 0.37 and 0.89 ?
How many 4 digit decimals lie between 0.37 and 0.89 ?
How many 5 digit decimals lie between 0.37 and 0.89 ?
How many n digit decimals lie between 0.37 and 0.89 ?
3).
How many n digit decimals lie between 0.479 and 0.734 ?
4).
Find a general rule to decide how many n digit decimals lie between two starting
numbers.
Level 6 Pack 3. Page 17.
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Investigations with Decimals, Fractions and Percentages.
1).
Investigate the fraction 1 when you turn it into a decimal.
x
a). Start by trying out various numbers for x.
x = 1,
2).
1 = 1.0
1
x = 2,
1 = 0.5
2
x = 3,
1 = 0.33333...
3
b).
c).
Continue this list for numbers up to 20.
Which of these give recurring decimals ?
What is the next number after x = 20 that definitely gives an exact decimal ?
a).
Change to decimals the sequences :-
i).
1 , 1 , 1
1.1 1.11 1.111
ii).
1 , 1 , 1
2.2
2.22 2.222
iii).
1 , 1 , 1
3.3 3.33 3.333
iv). What do all the sequences have in them ?
b). Write down, without the use of a calulator, the next two numbers for each
of the above sequences.
c). Create sequences similar to the ones above, using these starting points.
Write down the first 5 terms for each sequence.
i).
1
ii).
1
iii).
1
4.4
5.5
6.6
3).
Using the numbers 1 - 9 inclusive find as many ways of making the whole numbers 2 - 9.
You may only use the digits once e.g.
75249 = 9
8361
If you want help look below:
2 = ***58
672*
3 = 1***9
5**3
6 = 1***8
2**3
4).
4 =
7 = **7**
*394
***68
39**
5 = **4** or **845 or 148** or **645
2697
***9
***3
3***
8 = 25496
****
9 = *5249 or ***** or ***29
836*
6471
63**
.
To convert 0.7 into a fraction:
let x = 0.77777777777777777777777777777777777777......
10x = 7.777777777777777777777777777777777777......
x = 0.777777777777777777777777777777777777......
9x = 7
so
x= 7
9
Show these recurring decimals in fraction form
a). 0.44444....
b). 0.666666....
c).
e). 0.611111111... f). 0.8333333....
g).
i). 0.09090909...
j). 0.11111...
k).
m). 0.148148....
n). 0.13333...
o).
Level 6 Pack 3. Page 18.
__
0.88888....
0.4166666...
0.636363....
0.327327327...
Licensed to Dr Challoner's Grammar School
by subtraction
d).
h).
l).
p).
0.454545.....
0.266666...
0.46666...
0.191919...
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Rounding Off.
Decimal Places.
A).
Round the following to one decimal place.
1).
6).
11).
16).
21).
B).
2).
7).
12).
17).
22).
6.32
3.41
16.47
13.642
24.738
3).
8).
13).
18).
23).
7.43
0.96
13.24
12.261
40.851
4).
9).
14).
19).
24).
5.14
12.42
19.99
23.493
26.872
5).
10).
15).
20).
25).
9.25
18.79
13.64
27.246
29.962
4).
9).
14).
19).
24).
0.486
3.721
9.996
0.9147
0.4719
5).
10).
15).
20).
25).
0.372
4.799
8.648
8.5961
0.7852
4).
9).
14).
19).
24).
0.0172
7.2953
2.0907
0.03276
9.392451
5).
10).
15).
20).
25).
3.4961
0.5729
3.0902
3.47962
6.200732
4).
9).
14).
19).
24).
29).
0.000352
0.0000131
0.97243
72600
990000
6479217
5).
10).
15).
20).
25).
30).
0.0000161
0.000952
0.000000724
9476200
652000
783567328
4).
9).
14).
19).
24).
29).
0.000359
0.0000106
0.906712
78600
995100
6446767
5).
10).
15).
20).
25).
30).
0.00008276
0.00079511
0.000000812
9976200
605200
783567328
4).
9).
14).
19).
24).
29).
0.0003527
0.0008131
0.97243
7006720
899500
6479217
5).
10).
15).
20).
25).
30).
0.000069952
0.0009573
0.0000007207
9496200
652430
780567328
Round the following to two decimal places.
1).
6).
11).
16).
21).
C).
4.79
2.58
17.55
12.739
18.893
0.473
0.595
6.473
0.5721
8.9954
2).
7).
12).
17).
22).
0.725
0.723
7.157
0.6294
3.1352
3).
8).
13).
18).
23).
0.391
0.994
4.132
0.5322
1.9949
Round the following to three decimal places.
1).
6).
11).
16).
21).
0.0246
0.0395
3.7996
0.04763
7.039521
2).
7).
12).
17).
22).
0.0049
0.0257
4.0264
0.003279
6.203486
3).
8).
13).
18).
23).
2.1375
1.4739
5.9949
0.00729
5.279316
Significant Figures.
A).
Round the following to one significant figure.
1).
6).
11).
16).
21).
26).
B).
2).
7).
12).
17).
22).
27).
0.0037
0.000892
0.00138
2661
719992
1823564
3).
8).
13).
18).
23).
28).
0.00042
0.3691
0.09378
594000
423500
84066382
Round the following to two significant figures.
1).
6).
11).
16).
21).
26).
C).
0.0056
0.0427
0.000784
1420
67200
950210
0.00482
0.04821
0.000703
1430
60500
950910
2).
7).
12).
17).
22).
27).
0.003387
0.0008901
0.00193
2911
719992
1624564
3).
8).
13).
18).
23).
28).
0.000194
0.32697
0.09952
503500
423500
89036382
Round the following to three significant figures.
1).
6).
11).
16).
21).
26).
Level 6 Pack 3. Page 19.
0.004371
0.042648
0.0007849
1428
696400
999510
2).
7).
12).
17).
22).
27).
0.0036391
0.0008925
0.0013961
3761
719994
1823564
3).
8).
13).
18).
23).
28).
0.0004205
0.36052
0.09378
596700
423500
84066382
Licensed to Dr Challoner's Grammar School
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Rounding Off (Upper and Lower Limits).
Decimal Places.
A).
The following numbers have already been rounded off to one decimal place.
Use inequalities to describe the lower and upper limits of each number.
1). 4.7
6). 2.9
11). 17.0 m
B).
4). 5.5
5). 9.8
9). 12.0
10). 18.6
14). 19.9 mm 15). 13.0 Kg
The following numbers have already been rounded off to two decimal places.
Use inequalities to describe the lower and upper limits of each number.
1). 0.43
6). 0.59
11). 6.41 Kg
C).
2). 6.3
3). 7.4
7). 3.1
8). 0.9
12). 16.1 mm 13). 13.7 m
2). 0.25
7). 0.28
12). 7.10 m
3). 0.94
8). 0.99
13). 4.12 l
4). 0.46
5). 0.72
9). 3.71
10). 4.70
14). 9.96 Km 15). 8.40 m
The following numbers have already been rounded off to three decimal places.
Use inequalities to describe the lower and upper limits of each number.
1). 0.046
2). 0.049
3). 2.375
6). 0.395
7). 0.257
8). 1.439
11). 3.790 Kg 12). 4.021 Km 13). 5.049 l
4). 0.172
5). 3.961
9). 7.290
10). 0.523
14). 2.907 Kg 15). 3.090 l
Significant Figures.
A).
The following numbers have already been rounded off to one significant figure.
Use inequalities to describe the lower and upper limits of each number.
1).
6).
11).
16).
B).
2).
7).
12).
17).
0.007
0.0009
6000
700000
3).
8).
13).
18).
0.0002
0.1
10000
400000
4).
9).
14).
19).
0.0005
0.00001
70000
900000
5).
10).
15).
20).
0.01
0.003
100000
6000000
The following numbers have already been rounded off to two significant figures.
Use inequalities to describe the lower and upper limits of each number.
1).
6).
11).
16).
C).
0.006
0.04
400
60000
0.0082
0.021
1400
610000
2).
7).
12).
17).
0.0087
0.00080
2900
780000
3).
8).
13).
18).
0.00094
0.000097
59000
40000
4).
9).
14).
19).
0.00059
0.000081
7500
9100000
5).
10).
15).
20).
0.000076
0.000070
9100
6000000
The following numbers have already been rounded off to three significant figures.
Use inequalities to describe the lower and upper limits of each number.
1).
6).
11).
16).
Level 6 Pack 3. Page 20.
0.00437
0.0421
1420
69100
2).
7).
12).
17).
0.00363
0.000890
3710
713000
3).
8).
13).
18).
0.000425
0.360
56700
4100
4).
9).
14).
19).
Licensed to Dr Challoner's Grammar School
0.000351
0.000811
7900
89100
5).
10).
15).
20).
0.0000699
0.000953
949000
6000000
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Fractions 1.
Revision.
A).
Change the following mixed numbers to improper (top heavy) fractions.
1).
6).
11).
16).
21).
B).
11
/3
/6
86
/9
127
/6
150
/13
2).
7).
12).
17).
22).
53
4 1/2
5 4/5
7 1/8
9 6/7
19 1/2
3).
8).
13).
18).
23).
2 2/3
3 3/4
10 6/11
12 5/6
15 5/6
4).
9).
14).
19).
24).
6 3/4
5 1/2
9 5/8
6 7/9
8 3/14
5).
10).
15).
20).
25).
3 1/6
6 3/5
12 3/4
11 5/6
14 7/12
19
/5
/9
67
/6
137
/11
309
/10
38
3).
8).
13).
18).
23).
23
/4
/4
73
/5
213
/10
293
/12
57
4).
9).
14).
19).
24).
38
/3
/6
137
/9
164
/9
335
/11
35
5).
10).
15).
20).
25).
37
/2
/7
77
/8
165
/7
335
/12
43
Copy the two fractions. Write between them correct symbol < , > or =.
1). 2 1/4
5). 27/5
9). 9 7/8
13). 70/7
17). 127/9
D).
2).
7).
12).
17).
22).
Change the following improper fractions to mixed numbers.
1).
6).
11).
16).
21).
C).
3 1/3
2 2/7
4 1/10
10 2/7
13 3/8
11
/4
3
5 /5
79
/8
9 5 /7
13 8/9
2). 9/2
4 1 /2
6). 29/3
9 1/3
40
10). 12 2/3
/3
14). 101/8
12 3/8
18). 12 11/12 157/12
3). 33/6
7). 8 2/7
11). 9 5/9
15). 103/12
19). 148/13
5 1/6
58
86
/7
/9
8 11/12
11 5/13
25
4). 6 3/4
/4
43
8).
/6
7 5/6
12). 83/12
7 1/12
16). 10 5/11 113/11
20). 218/15 14 11/15
Cancel down these fractions and leave them in their lowest terms.
1).
6).
11).
16).
21).
26).
31).
36).
41).
Level 6 Pack 3. Page 21.
45
50
28
56
36
84
20
85
42
81
60
96
56
72
126
196
192
285
2).
7).
12).
17).
22).
27).
32).
37).
42).
18
21
24
56
45
72
13
52
45
60
32
80
64
80
84
126
77
132
3).
8).
13).
18).
23).
28).
33).
38).
43).
18
24
30
54
24
64
42
75
24
108
34
51
72
99
112
128
52
195
4).
9).
14).
19).
24).
29).
34).
39).
44).
Licensed to Dr Challoner's Grammar School
36
48
12
52
21
45
68
80
100
125
78
104
77
143
126
147
123
328
5).
10).
15).
20).
25).
30).
35).
40).
45).
35
40
18
81
28
70
12
90
96
100
54
66
63
84
104
130
225
405
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E).
Copy the question, then fill in the missing number for these equivalent fractions.
1).
6).
11).
16).
21).
26).
31).
32).
33).
34).
F).
More
Please!
= _
32
= _
42
= _
66
= 44
2).
17).
= 98
22).
7).
12).
= 136 27).
Change 2/3 to
Change 4/5 to
Change 3/8 to
Change 7/9 to
1 = _
2 34
3 = _
4
48
3 = _
8
96
2 = 38
5
2 = 52
3
5 = 140
7
a).
a).
a).
a).
1
/12’s
1
/15’s
1
/32’s
1
/36’s
3).
8).
13).
18).
23).
28).
b).
b).
b).
b).
2 = _
3
39
5 = _
6
54
4 = __
9
126
5 = 40
6
4 = 92
5
8 = 128
11
1
/24’s
1
/30’s
1
/48’s
1
/63’s
c).
c).
c).
c).
4).
9).
14).
19).
24).
29).
1 = _
3
57
3 = _
4
60
4 = __
15 105
3 = 27
4
2 = 42
7
5 = 115
13
1
/30’s
1
/45’s
1
/64’s
1
/99’s
d).
d).
d).
d).
5).
10).
15).
20).
25).
30).
1
/57’s e).
1
/60’s e).
1
/96’s e).
1
/117’s e).
4 = _
7
63
9 = _
10
70
12 = _
13
78
4 = 52
7
3 = 75
5
7 = 266
9
1
/72’s
/85’s
1
/112’s
1
/135’s.
1
Copy the two fractions. Use equivalent fractions to change them so they have the same
common denominator. Write between them the correct symbol < or > .
1).
5).
9).
13).
17).
21).
25).
29).
33).
37).
G).
1
4
2
3
5
6
2
3
7
8
4
9
1
1
2
4
/4
/3
7
/10
7
/9
7
/12
2). 1/2
6). 3/4
10). 1/3
14). 3/5
18). 5/11
22). 3 2/5
26). 2 2/5
30). 5/3
34). 4 4/5
38). 83/11
/3
/5
5
/8
5
/8
3
/5
1 5/6
4 1/3
2 7/11
311/12
1 3/4
4 3/7
11
/4
31
/8
5 7/12
39
/7
1
/3
/5
2
/5
5
/9
3
/10
3 3/8
2 1/3
1 7/10
43
/9
7
7 /10
3
3).
7).
11).
15).
19).
23).
27).
31).
35).
39).
2
3
4
5
/3
/5
3
/4
3
/4
5
/12
2 5/8
1 7/8
5 3/8
42
/11
6 3/10
/4
/6
7
/9
5
/6
4
/11
2 2/3
1 9/10
49
/9
3
3 /4
77
/12
4).
8).
12).
16).
20).
24).
28).
32).
36).
40).
3
1
1
2
/5
/4
2
/3
7
/9
7
/8
1 3/4
3 1/6
2 5/12
17
/9
8 7/12
/2
/7
5
/7
4
/5
9
/11
1 4/5
3 2/7
17
/
7
10
11
1 /
94
/11
Copy the fractions. By changing them so they have the same common denominator, or
otherwise, put them in ascending order (smallest to biggest).
1).
4).
7).
1
/4
5
/6
3
/4
10).
12).
14).
16). 1 1/4
19). 5/2
22). 3 3/4
25).
27).
29).
Level 6 Pack 3. Page 22.
2
/3
3
/4
2
/5
3
/4
3
/4
7
/9
7
/4
2 4 /5
19
/6
11
5 /12
2 4/5
6 11/16
1
/2
7
/12
7
/10
1
/6
5
/6
5
/6
3
2).
5).
8).
1
/2
7
/12
3
/4
2
/4
5
/8
11
/12
/3
/8
17
/18
1
1 /2
17). 3 2/5
2 3/4
20). 4 3/4
3 1/2
23). 2 1/2
5 3/8 5 5/6 23/4
13
/6 2 7/10 8/3
41
/6 6 17/24 6 7/12
5
5
/6
2
/3
7
/8
1
/2
5
/12
5
/6
11). 5/6
13). 3/5
15). 8/15
3 2/3 19/6
9
/2 4 5/7
31
/14 2 4/7
26). 3 5/9
28). 4 5/6
30). 7 5/8
Licensed to Dr Challoner's Grammar School
3
1
3). 1/2
/8
/4
7
2
5
6).
/9
/3
/6
3
5
2
9).
/5
/6
/3
2
13
5
/3
/18
/9
13
5
2
/15
/6
/3
5
4
3
/6
/5
/4
11
4
18). /6 1 /9
1 2/3
21). 2 5/6 2 3/8 9/4
3
24). 7/4
/2
1 5/7
11
/3 3 1/2 3 5/6
4 7/9 19/4 4 7/12
52
/7 7 13/28 7 9/14
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Fractions 2.
Addition and Subtraction of Fractions.
A.
If the fractions have the same denominator then we add/subtract the numerators.
E.g.
3
10
+
9
10
=
3+9
10
=
12
10
=
6
5
1 1
=
5
Copy and complete these questions, cancel down where appropriate.
1).
2
7
+
3
7
=
__
2).
4
9
+
3
9
=
__
3).
5
6
+
5
6
=
__
4).
5
8
+
7
8
=
__
5).
8
9
+
5
9
=
__
6).
4
5
+
2
5
=
__
7).
__ + 7
12
=
11
12
8).
2
7
+
_
=
6
7
9).
4 + _
13
=
12
13
5
9
=
__
11). 5
8
+
__
=
13
12). __ +
9 = 13
14
14
2
7
=
__
14). 7
9
-
4
9
=
__
15).
9
10
-
7 =
10
__
- 5
12
=
__
17). 8
9
- __
=
2
9
18). 13
15
-
3 =
15
__
3
13
=
8
13
20).
-
=
3
10
21). 11 12
22). __ + 3
5
=
1 1
23). 1 4
7
-
6 =
7
__
24). 1 3 - 9
10
10
25). __ + 7
8
=
26). 1 1
6
-
10). 7
9
+
13). 5
7
-
16). 11
12
19). __ -
28). 13
15
B.
+
5
13
8
7 =
15
__
8
7
10
29). 7
8
+
_
13
=
=
30). __
-
4
9
14
7
12
= __
27). 2 2 - 1 3 =
5
5
5 = __
6
__
_
__
= 1
2
If the fractions have different denominators then we must find a common denominator
before we add/subtract.
E.g. 3 4
2 The common denominator
3
is 12
3 = 9
4 12
2 = 8
3 12
so
3 - 2 = 9 - 8 = 1
4
3
12 12 12
Leave answers as mixed numbers if appropriate, cancel down where possible.
1).
3
4
+
Level 6 Pack 3. Page 23.
1
8
2).
2
3
+
1
6
3).
3
4
-
5
8
Licensed to Dr Challoner's Grammar School
4).
4
9
+
1
3
[email protected]
5).
3
4
-
1
2
6).
1
4
+
5
12
7).
8
9
-
2
3
8).
7
8
-
1
2
9).
3
4
-
2
3
10). 2
5
+
1
3
11). 4
5
-
1
2
12). 1
5
+
2
3
13). 3
4
+
1
6
14). 1
4
+
3
5
15). 5
7
-
2
3
16). 3
8
+
1
6
17). 7
9
-
1
2
18). 5
6
-
3
5
19). 4
5
+
3
4
20). 7
8
-
2
3
- 3
4
22). 5
6
+
3
5
23). 1 2
5
-
2
3
24). 4
7
+
2
3
+ 13
5
26). 6
7
+
2
5
27). 1 3
4
-
4
5
28). 5
8
+
5
6
- 4
7
31). 11
15
+
5
6
32). 1 1 10
2
3
21). 1 1
3
25). 1
4
29). 2 1
3
30). 1 1
2
- 1
2
C.
Copy and complete these questions.
1).
3
4
+
2
5
=
__
2).
2
3
+
3
7
=
__
3).
3 +
10
2
3
=
__
4).
5
6
+
3
4
=
__
5).
1
4
+
__
=
7
12
6).
3
5
1
2
=
__
7).
__ + 1
3
=
5
6
8).
1
5
+
_
=
8
15
9).
3 + _
4
=
19
20
2
7
=
__
11). 3
4
+
__
=
11
12). __ +
1
6
= 17
30
+
10). 5
6
+
13). 4
5
-
1
6
=
__
14). 6
7
-
2
3
=
__
15).
5
6
-
3
4
=
__
16).
-
2
3
=
__
17). 3
4
- __
=
1
4
18).
5
8
-
1
3
=
__
19). __ - 1
8
=
5
24
20). 3
5
-
=
13
30
21). 3
4
=
9
20
22). __ + 2
3
=
1 11
23). 1 2
5
3 =
4
__
24). 1 4
7
25). __ + 5
8
=
7
10
28). 11
12
Level 6 Pack 3. Page 24.
30
+ 7 =
10
1 7
24
__
4
_
-
-
_
- 2 = __
3
26). 7
8
-
3
10
=
__
27). 1 1 12
29). 3
8
+
__
=
1 11
30). __ +
72
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3
5
= __
7 = 1 11
12
24
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Fractions Pyramids.
To find the next fraction, add the two bricks below it.
Copy each pyramid and fill in the missing fractions.
Leave answers as mixed numbers if appropriate, cancel down where possible.
1).
2).
4
5
2
5
3
5
3).
2
3
2
3
5).
6).
2
1
3
4).
7).
3
4
9).
10).
3
4
4
7
16).
5
8
2
5
5
12
15).
1
8
3
8
17).
4
2
5
9
2
9
Level 6 Pack 3. Page 25.
8
9
3
8
5
6
5
6
1
4
9
9
10
1
15
14).
5
7
12).
2
3
7
12
5
6
2
7
18
3
8
1
1
3
8
3
7
1
7
8
11).
12
7
8
8).
2
9
5
26
1
2
13).
5
8
1
8
7
9
3
4
5
6
1
6
3
4
4
19
1 14
5
6
3
4
1
4
11
12
18).
5
12
5
12
1
12
1
3 12
7
1 12
1
6
5
6
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11
12
5
12
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19).
20).
1
4
2
3
1
3
21).
7
10
3
5
23).
1
2
1
5
27).
3
10
5
6
1
3
5
6
1
17
18
1
15
2
3
5
6
34).
3
4
1
4
1
4
5
6
9
2 20
3
110
1
6
2
5
33).
1
6
2
3
1
2
35).
1
2
3
7
9
3
5
1
2
1
2
7
8
30).
32).
4
9
1
2
29).
1 12
31).
5
6
26).
3
8
28).
3
4
1
4
25).
4
9
2
5
12
2
3
24).
3
4
22).
5
8
2
3
36).
11
12
5
6
5
48
17
11
2 4 2 12
2 24
2
13
20
1
13
3
5
1
2
7
1 12
15
1
2
5
6
Difficult.
37).
38).
2 16
39).
2
15
1
3
Level 6 Pack 3. Page 26.
7
1 20
5
6
2
3
2
5
2 19
24
5
8
3
4
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Magic Squares (Fractions).
In a Magic Square the rows, columns and diagonals all add up
to the same number. This is the Magic Number.
Complete the following Magic Squares and find their Magic Numbers.
1).
2).
3
4
11
12
11
12
4
5
7
12
5
6
Magic Number =______
Magic Number =______
7
12
5
12
Magic Number =______
4).
1
2
3
4
2
3
7
12
3).
5).
11
24
3
4
1
1
10
6).
7
8
1
7
10
1
6
9
10
1
4
1
30
1
2
7
1
22
Magic Number =______
7).
Magic Number =______
8).
2 10
Magic Number =______
9).
1
9
2 10
1
5
6
3
4
23
30
7
230
Magic Number =______
10).
11
12
2
1
2
1
4
1
5
Magic Number =______
11).
1
1
6
25
5
58
Magic Number =______
1
12
5 12
220
1
8
12).
1
19
1 10
1
4
1
3 18
13
18
1
12
3
3 10
1
Magic Number =______
Level 6 Pack 3. Page 27.
11 4
Magic Number =______
8
Magic Number =______
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13).
14).
15).
19
29
724
8 40
11
1
512
4
920 4 5
11
11
20
3
524
19
610
3
4
17 4
Magic Number =______
19 5
Magic Number =______
Magic Number =______
The template shown here was used to make the
the magic fraction squares in questions 1 - 15.
Pick any three fractions a, b and c and substitute
them into the formulae to make a magic square.
16). Use the template shown and draw the magic squares when
a).
a=5 ,b=1 ,c=1.
6
5
3
a=7 ,b=3 ,c=1.
8
16
6
a=13 ,b=5 ,c=2.
4
8
3
a=32 ,b=3 ,c=19.
5
4
10
c).
e).
g).
1
4 40 5 40
b).
d).
f).
h).
a-c
a-b+c
a+b
a+b+c
a
a-b-c
a-b
a+b-c
a+c
a=9 ,b=2 ,c=1.
10
5
4
a = 11 , b = 3 , c = 1 .
12
4
8
a = 2 1 , b = 7 , c = 13 .
6
9
18
a=51 ,b=13 ,c=22.
6
4
3
17). For each of the magic squares in questions 1 - 15, find the values of a, b and c.
...and finally....
18).
19).
2
5
1
10
18
9
10
15
11
3
3
5
3
10
15
7
10
1
5
19
30
11
5
1 19
30
6
20).
4
5
9
10
10
21
5
1 9
11
10
1 3
5
13
14 1 1
2
21
Magic Number =______
21
10
12
7
10
4
5
1
10
5
5
10
12
15
1 14
15
1 7
30
58
15
Magic Number =______
5
2
5
1 7
10
Magic Number =______
Level 6 Pack 3. Page 28.
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Hit 12
12.
Put a penny where shown.
Flick it forward with your nail.
The number it lands on is how many points you get.
If it touches any line you get 1/12 of a point only. Take it in turns.
Keep a running total of your score.
The first to get 12 points or over wins
wins.
11
3
1
4
11
2
3
4
2
3
7
12
13
4
5
12
3
4
2
3
1
2
1
3
1
4
1
12
Level 6 Pack 3. Page 29.
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Hit 15
15.
Put a penny where shown.
Flick it forward with your nail.
The number it lands on is how many points you get.
If it touches any lines you get 1/18 of a point only. Take it in turns.
Keep a running total of your score.
The first to get 15 points or over wins
wins.
12
3
1
6
17
9
5
9
5
6
1
3
21
9
8
9
5
9
5
6
2
9
1
6
1
3
1
18
Level 6 Pack 3. Page 30.
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Addition/Subtraction of Fractions. (Worded Questions).
1).
John and Claire each bake a cake. John eats 5/8 of his cake and Claire eats 7/10 of her cake.
Who has eaten more (you must show working out) ?
2).
In the marathon Edward, James and Charles all give up during the race.
Edward completes 3/4 of the race, James 7/12 of the race and Charles 2/3 of the race.
In the race who completed a). the most,
b). the least ?
3).
To place an advert in a magazine it charges £10 for each 1/8 of a page used. How much
would an advert cost in this magazine if the advert is 3/4 of a page.
4).
Javid gets sponsored for a swim. He works out he is paid £5 for each 1/20 of the distance to
be covered. He only completes 3/5 of the distance. How much should Javid be paid ?
5).
Jenny and Billy each has a bag of marbles. In Jenny’s bag 15 out of 20 are blue.
In Billy’s bag 8 out of 12 are blue.
a). What fraction of the marbles is blue in each bag ?
b). Who has the bigger proportion of marbles that are blue ?
6).
In Mrs. Morris’s class there are18 girls out of 30 pupils. In Mrs. Payne’s there are 12 girls
in the class of 20.
a). What fraction of girls are there in each class ?
b). Who has the bigger proportion of girls ?
7).
There are 23/4 litres of milk in a bowl. 7/8 of a litre of milk is added to the bowl.
How much milk is now in the bowl ?
8).
Henry walks 33/4 miles towards Paul’s house. The actual distance is 51/4 miles.
How far does he have to walk to finish the journey to Paul’s house ?
9).
Two parcels weigh 23/5 Kg and 49/10 Kg. What is their combined weight ?
10). A full bottle of lemonade holds 21/2 litres. Lynne fills a glass to the top with lemonade from
the full bottle. The glass holds 1/3 litre. How much lemonade is left in the bottle ?
11). An urn contains 81/4 litres of tea before the drinks break. After the drinks break it
contains 53/8 litres of tea. How much tea has been used from the urn ?
12). A plank of wood is 61/3 m long. 25/8 m is sawn off. What length of the plank is left ?
13). Three pieces of wood are joined together end to end. They are 41/3 m, 21/4 m and 51/6 m
long. What is the length of the new piece of wood ?
14). In the elections 1/5 of the people voted for Mr. Preston, 5/8 voted for Mrs. Douglas.
Everyone else voted for Mr. Fisher. What fraction voted for Mr. Fisher ?
15). Beth got her pocket money yesterday. She spent 3/4 of it straight way. She spent 1/5 of it
today. What fraction has she
a). spent,
b). got left ?
Level 6 Pack 3. Page 31.
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16). Pocket money is shared out between the 3 children. Abigail receives 3/5 of the money,
Bobby receives 1/8 of the money and Colin the rest. What fraction does Colin receive ?
17). A group of friends travel to London. 2/5 go by bus, 1/3 by train and the rest by car.
What fraction travel by car ?
18). In the school netball team Hazel scored half the goals in a match. Sam scored 1/12 of the
goals.
a). What fraction of the goals did the rest of the team score ?
b). If the team scored 36 goals, how many goals did the rest of the team score ?
19). Dad bakes a chocolate cake. He eats 1/3 of it straight away. Mum then eats 1/4 of it when she
sees it. The children get the rest.
a). What fraction do the children get ?
b). There are 2 children and the cake is shared equally. What fraction do they each get ?
20). On one page of a magazine there are 3 adverts. One is 1/4 of the page, another 1/8 of a page
and the last 3/16 of a page.
What fraction of the page is a). covered by adverts,
b). not covered by adverts ?
21).
1
/4 of my salary is spent on food, 1/5 is spent on the mortgage.
What fraction of my salary is left for other things ?
22). Farmer Bill plants corn on 3/8 of his land, trees on 1/5 of his land and grazes cows
on the rest. What fraction of the land does he graze cows on ?
23). Find the perimeter for each of the following rectangles:
a).
b).
c).
31/5 m
21/3 m
1
1 /4 m
22/3 m
21/5 m
d).
47/10 m
45/8 m
52/3 m
24). In a new relay race the 4 runners can pass the baton at any time in the race. Sally completes
1
/3 of the race before handing over to Jill. Jill completes 1/4 of the race and hands over to
Jean. Jean completes 1/8 of the race. Shabina is last competitor, what fraction of the race
must she run to complete the race ?
25). Jane has a stick 10 m long. She cuts off 21/3 m for Tom, 3 1/4 m off for Amy and 1 5/6 m off
for Rosie. What length of stick does Jane have left ?
Difficult.
26). For each of the following rectangles the size of one side and the perimeter are given.
Find the size of the missing side.
31/8 m
a).
b).
c).
d).
3
2 /4 m
14/5 m Perimeter
21/4 m Perimeter
Perimeter
Perimeter
9
= 102/45 m
= 12 /10 m
= 177/12 m
= 81/6 m
Level 6 Pack 3. Page 32.
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Multiplications and Division of Fractions 1.
A).
Find
1). 1 of 65
5
2).
1 of 60
12
3).
1 of 99
11
4).
1 of 108 5).
9
6).
7).
1 of 117 8).
9
1 of 98
7
9).
1 x 144
9
1 x 132
12
11). 1 x 148
4
12). 1 x 370
5
13). 1 of 366 14). 1 x 783
6
9
1 of 64
8
10). 1 x 159
3
15). 1 x 1276
4
16). 1 x 1074 17). 1 x 1065 18). 1 x 3504 19). 1 x 2156 20). 1 x 3496
3
5
4
7
8
B).
Find
1). 2 of 39
3
6).
4 x 105
5
2).
2 of 45
5
3).
3 of 60
4
4).
2 x 56
7
5).
3 x 80
5
7).
2 x 96
3
8).
3 x 108
4
9).
2 x 132
3
10). 2 x 220
5
11). 3 x 172
4
12). 4 x 285
5
13). 2 x 276
3
14). 3 x 345
5
15). 3 x 364
4
16). 5 x 840
6
17). 3 x 730
5
18). 4 x 147
7
19). 3 x 119
7
20). 4 x 288
9
21). 3 x 200
8
22). 2 x 322
7
23). 3 x 1420 24). 4 x 567
5
7
25). 8 x 756
9
26). 5 x 1016 27). 6 x 2651 28). 7 x 5244 29). 6 x 4326 30). 5 x 8352
8
11
12
7
9
C).
When finding a fraction of some numbers the answer may not be whole.
Here are two methods to deal with these questions:
Method 1.
Method 2.
1
E.g. 1 x 10
/3 x 9 = 3
3 r1
1
1
3
/3 x 1 = /3
3
10
so
1
/3 x 10 = 3 1/3
=
1
E.g. 1 x 37
5
/5 x 35 = 7
/5 x 2 = 2/5
1
so
7 r 2
37
5
1
/5 x 37 = 7 2/5
3 1/3
=
7 2/5
Use any method to find
1).
Level 6 Pack 3. Page 33.
1 x 16
3
2).
1 x 17
5
3).
1 x 23
4
4).
Licensed to Dr Challoner's Grammar School
1 x 29
3
5).
1 x 35
6
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6).
1 x 43
5
11). 1 x 59
6
16).
D).
7).
1 of 80
7
12). 1 x 92
7
1 x 149 17). 1 x 119
12
8
8).
1 of 67
6
9).
13). 1 of 79
9
14). 1 x 99
7
18). 1 x 164
9
19).
Here is another way of attempting multiplications.
3r1
E.g.
1 x 11
=
11 =
4 11
4
4
E.g.
2 x 17
3
=
34
3
1 x 62
3
3
3).
2 of 12
5
15).
1 x 116
11
1 x 159 20). 1 x 235
13
12
=3 1
4
11r1
34
=
10). 1 x 75
8
= 11 1
3
Use this method to find
1).
2 of 8
3
2).
1 of 9
5
4).
2 x 13
3
5).
3 x 15
4
Here is a second way of attempting harder multiplications.
E.g.
Find 1/5 x 19
3 x 19
5
so
3
/5 x 19
= 3 4/5
=
3 r4
=
3 x 3 4/5 = 9 12/5
=
9 + 2 2 /5
= 11 2/5
Use this method to solve
6).
3 x 42
5
7).
1 x 33
4
8).
5 x 17
6
9).
3 x 21
4
10). 3 x 13
8
Use any method to solve
11). 4 x 25
7
12). 5 x 25
8
13). 3 x 19
4
14). 7 x 32
9
15). 3 x 43
8
16). 5 x 53
6
17). 6 x 46
7
18). 7 x 39
8
19). 5 x 62
9
20). 5 x 59
6
21).
4 x 73
11
22).
3 x 87
10
23). 7 x 49
9
24). 5 x 95
8
25).
26).
4 x 67
15
27).
8 x 55
13
28). 11 x 77
12
29).
30). 13 x 88
15
Level 6 Pack 3. Page 34.
Licensed to Dr Challoner's Grammar School
9 x 97
14
7 x 83
12
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Multiplications and Division of Fractions 2.
A).
The diagrams show how to multiply a fraction by another fraction.
1
3
1
2
1 of 1 is shown by the overlap
2
3
=1
6
1 of 4 is shown by the overlap
3
5
=4
15
4
5
1
3
You can do fraction multiplication by folding paper! Try it.
Copy each diagram, and by shading solve the following.
1).
1
2
x
3
4
2).
1
3
x
2
5
3).
1
5
x
2
3
4).
1
4
x
1
3
5).
4
5
x
2
3
6).
1
2
x
5
6
7).
Look at the questions and answers. Write a rule about how to multiply fractions.
Use your rule to answer the following.
8).
1 x 3
2
7
10). 1 x 3
4
5
11). 1 x 5
2
7
12). 1 x 4
3
7
13). 1 x 2
5
9
14). 1 x 5
6
8
15). 1 x 2
7
5
16). 1 x 5
4
6
17). 1 x 4
7
5
18). 1 x 7
4
8
19). 1 x 3
8
4
20). 4 x 2
9
5
21). 1 x 7
10 12
22). 1 x 4
5
7
23). 1 x 5
9
6
24). 1 x 5
8
6
25). 1 x 2
7
3
26). 1 x 7
6 12
27). 1 x 7
11 12
28). 1 x 9
7 10
29). 1 x 11
6
12
30). 1 x 7
4
13
31). 1 x 5
9 12
32). 1 x 9
12 11
Level 6 Pack 3. Page 35.
1 x 2
5
5
9).
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B).
Now answer these using the same rule.
1).
2 x 4
3
5
2).
2 x 2
5
3
3).
4 x 3
7
5
4).
5 x 1
6
4
5).
3 x 5
8
7
6).
3 x 7
4
8
7).
6 x 4
11
7
8).
5 x 2
9
7
9).
7 x 5
12
11
10). 3 x 8
4
15
11). Why is question 10 different from the other questions ?
C).
Some answers cancel down. The easiest way to do this is to cancel before multiplying.
E.g.
E.g.
3 x 63
4
7
2
=
2 x 93 =
3
10
1
3 x 3
2
7
=
1
=
2 x 3
1
105
This is usually done as one calculation
looking like this :
9
14
Sometimes there is more to cancel.
1 x 3
1
5
=
3
5
2 x 93 =
3
105
1
3
5
1
Work out the following, cancel down where appropriate.
1).
2 x 6
3
7
2).
3 x 8
4
11
3).
15 x 4
17
5
4).
7 x 19
10
21
5).
6).
1 x 14
2
15
7).
11 x 3
21
4
8).
2 x 20
5
21
9).
7 x 2
22
3
10). 4 x 23
7
28
11). 15 x 4
28
5
12). 5 x 3
6
5
13). 3 x 16
4
21
14). 20 x 3
33
8
16).
17).
18). 3 x 4
8
15
19).
9 x 5
10
6
3 x 21
7
27
9 x 2
14
3
4 x 15 20). 4 x 15
5
32
5
24
21). 15 x 7
28
10
22). 26 x 10
35
13
23). 15 x 39
26
42
24). 20 x 14
21
35
26). 6 x 14
7
9
27).
28). 2 x 27
3
14
29).
35 x 2
28
5
15).
2 x 15
3
17
25). 16 x 35
21
42
72 x 5 30). 9 x 56
25
8
32
33
These are harder, but see if you can work out how to calculate the answers.
Look at questions 26 to 30 for a clue!
31). 1 1 x 8
4
9
32). 2 x 2 1
3
4
33). 2 2 x 3
9
4
34). 4 x 2 11 35). 3 1 x 3
5
12
21
8
36). 1 1 x 3 1 37). 1 1 x 2 2 38). 1 1 x 3 3 39). 3 2 x 2 5 40). 3 1 x 2 1
5
4
4
3
5
4
7
8
9
7
Level 6 Pack 3. Page 36.
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Multiplications and Division of Fractions 3.
2 means 2 whole ones and can be written as 2.
1
1 and 2 are called the inverse of each other.
2
1
A).
1 1 1
3 3 3
E.g.
2 ÷ 1 can be shown as
3
E.g.
1 ÷ 2 means 1 cut in two.
4
4
1 1 1
3 3 3
.
So 2 ÷ 1 = 6
3
So 1 ÷ 2 = 1
4
8
By drawing out appropriate diagrams, or otherwise, find
1).
3 ÷ 1
4
2).
4 ÷ 1
2
3).
4 ÷ 1
3
4).
2 ÷ 1
5
5).
3 ÷ 1
5
6).
1 ÷ 2
3
7).
1 ÷ 3
4
8).
1 ÷ 2
6
9).
1 ÷ 4
5
10). 1 ÷ 5
3
11). 6 ÷ 1
5
12). 7 ÷ 1
6
13). 10 ÷ 1
4
14). 8 ÷ 1
9
15). 9 ÷ 1
10
16). 1 ÷ 5
7
17). 1 ÷ 7
6
18). 1 ÷ 8
8
19). 1 ÷ 9
11
20). 1 ÷ 12
9
21). Write down a rule how to find the answer without drawing a diagram.
B).
To divide a number by a fraction, multiply the number by the inverse of the fraction.
E.g.
E.g.
5 ÷ 2
3
=
8 ÷ 3
5
=
5 x 3
2
=
8 x 5
3
=
15
2
=
40
3
=
71
2
13 1
3
Find
1).
7 ÷ 2
3
2).
3 ÷ 2
5
3).
7 ÷ 5
6
4).
4 ÷ 3
8
5).
5 ÷ 2
9
6).
8 ÷ 3
4
7).
6 ÷ 5
8
8).
7 ÷ 2
3
9).
5 ÷ 3
10
10). 4 ÷ 7
10
11). 9 ÷ 2
3
12). 5 ÷ 3
4
13). 8 ÷ 5
6
14). 9 ÷ 7
8
15). 10 ÷ 3
4
16). 13 ÷ 2
5
17). 16 ÷ 3
8
18). 14 ÷ 5
6
19). 21 ÷ 2
3
20). 23 ÷ 4
7
Level 6 Pack 3. Page 37.
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C).
To divide a fraction by another fraction, we use the same method.
E.g.
1 ÷ 4
3
5
=
1 x 5
3
4
=
5
12
E.g.
2
3
÷
=
2 x 9
3
4
=
1
4
9
2 x 93
3
42
1
=
3 = 11
2
2
Find
D).
1).
2 ÷ 5
3
7
2).
3 ÷ 2
4
5
3).
4 ÷ 1
5
3
4).
2 ÷ 3
7
8
5).
6).
4 ÷ 3
7
4
7).
5 ÷ 2
6
5
8).
3 ÷ 2
4
9
9).
4 ÷ 5
7
8
10). 2 ÷ 7
9
10
11). 2 ÷ 5
3
9
12). 4 ÷ 8
7 11
16). 6 ÷ 9
7
10
17).
21). 4 ÷ 8
5
15
22). 3 ÷ 9
4
20
26). 35 ÷ 7
48 8
27).
3 ÷ 4
10 25
8 ÷ 12
15 25
13). 3 ÷ 6
4
7
18).
7 ÷ 13
12 20
23). 8 ÷ 2
9
3
14). 5 ÷ 2
9
3
19).
6 ÷ 14
11 15
24). 20 ÷ 5
35 6
5 ÷ 1
6
2
15). 5 ÷ 13
8
16
20).
8 ÷ 11
21
35
25). 3 ÷ 21
4
40
28).
9 ÷ 39
10 40
29).
5 ÷ 55
12
72
30). 28 ÷ 16
77
21
Mixed Revision Questions.
1).
3 x 128 2).
8
95 x 4
5
3).
2 x 16
3
4).
5 ÷ 4
7
5).
6).
7 ÷ 3
4
15 x 5
8
8).
1 ÷ 4
2
9).
7 x 24
10
10). 18 ÷ 5
8
7).
2 ÷ 5
3
11). 2 x 5
3
7
12). 4 ÷ 5
5
8
13). 7 x 4
8
9
14). 5 ÷ 15
9
16
16). 8 ÷ 32
9 63
17).
18). 21 ÷ 28
25 45
19). 27 ÷ 39 20). 42 x 10
44
55
55
21
5 x 21
14 35
15). 4 ÷ 12
7
28
21). 2 x 1 1
3
2
22). 4 1 ÷ 7 1
2
2
23). 2 1 x 1 2
7
5
24). 1 3 ÷ 2 7
5
10
25). 4 4 ÷ 5 1
5
3
26). 10 1 ÷ 2 1
2
4
27). 6 3 x 2 1
10
7
28). 12 1 ÷ 4 3
2
8
29). 9 2 x 1 1
3
29
30). 13 1 ÷ 5 1
2
4
31). 2 2 x 1 5
9
16
32). 3 1 ÷ 1 5
7
21
Level 6 Pack 3. Page 38.
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Fraction Multiplication Grids.
Fill in all the spaces in these fraction multiplication grids.
All the spaces are filled with fractions.
Cancel down where appropriate.
1).
x
2).
1
2
2
5
3
4
1
5
1
3
4
5
1
4
2
3
1
2
1
3
5
6
2
3
1
6
x
x
5
6
1
2
x
1
12
1
4
3
8
2
5
1
6
7
10
5
6
3
4
1
3
1
5
3
4
4
7
2
9
3
8
5
9
2
3
9
10
1
3
27
40
3
10
1
2
5
6
7
8
1
7
3
8
1
10
2
3
3
4
8
15
7
8
4
10
2
9
12).
5
6
3
4
1
2
2
5
x
9
10
12
35
Level 6 Pack 3. Page 39.
x
x
x
11).
1
8
1
2
9).
4
5
10).
2
3
9
10
4
5
2
3
3
4
2
9
3
20
3
5
6).
8).
1
5
5
6
4
5
1
3
1
6
3
4
5
8
2
3
4
5
1
8
7).
x
2
5
5).
1
5
3
4
4
5
3
8
x
1
3
2
3
1
4
3
5
1
2
4).
x
x
3).
3
4
3
4
9
10
9
20
8
15
3
7
15
32
1
2
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5
12
3
7
6
21
3
10
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13).
x
4
5
Again, fill in all the spaces in these fraction multiplication grids.
All the spaces are filled with fractions.
Cancel down where appropriate.
14).
15).
5
7
3
4
4
1
6
9
4
5
7
4
5
1
1
14
2
6
35
2
2
72
3
7
1
3
5
5
8
28 56
8
2
3
3
40
x
8
15
1
6
3
5
16).
17).
4
5
x
5
9
4
7
1
2
x
8
15
7
8
21
32
19).
4
9
1
6
3
5
9
40
3
20
5
12
5
9
8
15
3
10
1
5
21).
x
x
1
18
1
12
1
4
5
18
35
96
8
27
2
7
4
11
23).
24).
x
x
x
35
72
1
4
3
14
11
24
5
6
1
4
Level 6 Pack 3. Page 40.
1
3
3
48
1
12
4
5
8
25
5
12
4
9
2
7
4
45
8
15
22).
6
35
8
27
2
15
10
21
5
8
20).
2
3
1
8
2
3
x
8
63
3
5
x
2
3
5
6
1
3
1
3
18).
7
20
1
2
3
4
x
12
35
3
10
3
8
1
6
5
18
3
70
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2
7
3
14
1
4
5
16
1
12
5
36
3
20
1
8
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Multiplication/Division of Fractions. (Worded Questions).
1).
Andy earns £96.27 a week. After deductions from his wage he takes home 2/3 of the wage.
How much does he take home ?
2).
A beach bucket that holds 2400 ml of water is filled to the top. It has a hole in it, and as it
is carried around the garden it loses 3/5 of the water.
How much water
a). has been lost,
b). is still in the bucket ?
3).
A brand new car cost Sue £12462. After a week she takes it back to the garage and they
tell her it is only worth 5/6 of what she paid for it.
How much
a). is the car now worth, b). has it depreciated in value ?
4).
A table designer makes tables using 3/8 metal and the rest wood. Each table is 72 Kg.
What weight are
a). the metal parts, b). the wooden parts ?
5).
At school 7/10 of the pupils have a snack at break time. There are 780 pupils in the school.
How many don’t have a snack at break time ?
6).
A magazine contains 7/12 articles and the rest are adverts.
If there are 204 pages in the magazine how any pages are adverts ?
7).
Farmer Jill keeps cows, sheep and horses. 1/5 are cows, 2/3 are sheep and the rest are horses.
a). What fraction are horses ?
b). Farmer Jill has 135 animals in total. How many are
i). cows,
ii). sheep,
iii). horses ?
8).
Pupils at a school either arrive by bus, car or on foot. 3/10 walk and 1/3 come by bus.
a). What fraction come by car ?
b). There are 420 pupils at the school. How many arrive
i). on foot,
ii). by bus,
iii). by car ?
9).
In a garden there are grass areas, flower beds and bushes. The grassed area covers 2/3 of the
garden and the flower beds cover 1/5 of the garden.
a). What fraction of the garden is covered by bushes ?
b). If the garden is 195m2, what area is
i). grass,
ii). flower beds,
iii). bushes ?
10). Jenny has 9Kg of flour. She drops 1/4 of it. What weight of flour has she dropped ?
11). Beth has a rope 23 m long. She cuts off 1/5 of it. How long are the two pieces ?
12). Keith buys 16 bars of chocolate and eats 2/3 of them straight away.
How much has he
a). eaten,
b). got left ?
13). At the village fete 23 cakes are sliced ready to eat. At the end of the fete 3/4 of the cake
had been sold. How much had been
a). sold b). left ?
14). In the local 50 page magazine 3/7 of the area of the magaine contained adverts.
What area of the magazine a). contained adverts,
b). didn’t contain adverts ?
Level 6 Pack 3. Page 41.
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15). There are 11/2 litres of lemonade in a bottle. Nancy drinks 1/3 of it.
How much does she drink ?
16). Ron spends 31/2 hours gardening. He spends 3/7 of this time mowing the lawn.
How long does he spend mowing the lawn ?
17). A chef has 31/3 litres of cooking oil. He uses 2/5 of it during an evenings cooking.
How much does he
a). use,
b). have left over ?
18). A small field is 31/2 hectares. Sheep graze on 11/14 of it.
What area do the sheep
a). graze on, b). not graze on ?
19). A garden fence is 121/2 m long though 3/5 is rotten.
What length of fence is
a). rotten,
b).
fine ?
20). A small rectangular room is to be carpeted. The length is 21/2 m and width is 11/5 m.
What area of carpet is needed ?
21). Find the area of these rectangles:
a).
b).
33/5 m
41/5 m
31/3 m
21/2 m
c).
d).
42/7 m
21/10 m
51/4 m
21/7 m
22). 73/5 Kg of coffee is put into 11/3 Kg packets. How many packets will be needed ?
Give your answer as a). a fraction,
b). the number of packets needed.
23). A small barrel of washing up liquid contains 111/2 litres.
This is to be transferred to 3/4 litre containers. How many containers will be needed ?
Give your answer as a). a fraction,
b). the number of containers needed.
24). A field is 17 2/5 hectares. The farmer ploughs 11/5 hectares a day of the field.
How many days will it take him to plough the field ?
Give your answer as a). a fraction,
b). the number of days needed.
25). A metal bar is 141/10 m long. How many 3/4 m strips can be cut from the bar ?
Give your answer as a). a fraction,
b). the number of 3/4 m strips.
26). For each of the following rectangles the size of one side and the area are given.
Find the size of the missing side.
a).
b).
c).
d).
13/4 m
21/3 m
1
1 /2 m
Area
= 11/8 m2
Level 6 Pack 3. Page 42.
Area
= 42/3 m2
Area
= 77/15 m2
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25/6 m
Area
= 132/9 m2
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