Lisa McNulty

Direct Proportion

• Percentages

• Fractions

• Ratios

• Similar Shapes

• Conversions

• Pie Charts

Lisa McNulty

6

3

20

12

7

4

20

15

10

5

8

5

Which fraction is the same as

this one?

Lisa McNulty

6

3

20

12

7

4

20

15

4

3

8

5

Which fraction is the same as

this one?

Lisa McNulty

6

3

20

12

7

4

20

15

40

25

8

5

Which fraction is the same as

this one?

Lisa McNulty

6

3

20

12

7

4

20

15

5

3

8

5

Which fraction is the same as

this one?

Lisa McNulty

40 0

1 2 3 4 5 6 7 8 9

4 8 12 16 20 24 28 32

36

0 10

If 1 book costs £4 and 2 books cost £8 etc…

We can represent this by using a number line like the one below

Number of books

Cost (£)

Lisa McNulty

0 40

1 2 3 4 5 6 7 8 9

4 8 12 16 20 24 28 32 36

0 10

If we write the pairs of numbers as fractions we get the following:

4

1

8

2

12

3

16

4

20

5

24

6

28

7

32

8

36

9

40

10== == == == =

1

4

2

8

3

12

4

16

5

20

6

24

7

28

8

32

9

36

10

40== == == == =

Lisa McNulty

0 50

1 2 3 4 5 6 7 8 9

5 10 15

20 25 30 35 40

45

0 10

If 1 CD costs £5 and 2 CD’s cost £10 etc…

We can represent this by using a number line like the one below

Number of books

Cost (£)

Lisa McNulty

1 2 3 4 5 6 7 8 9

5 10 15 20 25 30 35 40 45 0 50

0 10

If we write the pairs of numbers as fractions we get the following:

5

1

10

2

15

3

20

4

25

5

30

6

35

7

40

8

45

9

50

10== == == == =

1

5

2

10

3

15

4

20

5

25

6

30

7

35

8

40

9

45

10

50== == == == =

Lisa McNulty

If 6 apples cost £1.50 then what is the cost of

10 apples?

Lisa McNulty

6 Apples cost £1.50, what would be the

cost of 10 Apples?

Extract Information:

Apples 6 10

Cost £1.50 ?

Question:

Calculation: Answer in Context:

10

?

6

50.1

?106

50.1x

50.2? The cost of 10

Apples would be £2.50

Laying out the solution

Lisa McNulty

If an ipod costing £94 is reduced by 16% in a sale, then what is the

sale price?

Lisa McNulty

An ipod cost £94, what is the

cost if it is reduced by 16%

Extract Information:

Cost ? 94

% 84 100

Question:

Calculation: Answer in Context:

84

?

100

94

?84100

94x

96.78? The cost of the ipod

would be £78.96

Laying out the solution

Lisa McNulty

If Jimmy scores 32 out of 46 in a test what percentage is this?

Lisa McNulty

Jimmy scores 32 out of 46 in a

test. What % is this?

Extract Information:

Score 32 ?

Out of 46 100

Question:

Calculation: Answer in Context:

100

?

46

32

?10046

32x

6.69? Jimmy got 69.6% in

the test.

Laying out the solution

Lisa McNulty

80 students were asked about their favourite type of music. 27 said they preferred Rock music, how large would the angle be in a Pie

Chart?

Lisa McNulty

27 out of 80 people like Rock

music – what angle is this in a

Pie Chart?

Extract Information:

Votes 27 ?

Sections 80 360

Question:

Calculation: Answer in Context:

360

?

80

27

?36080

27x

5.121? The angle for Rock

music would be 121.50

Laying out the solution

Lisa McNulty

Misia has her wages increased by 6%. If her new wages are £8.45 per hour, what was she

earning before?

Lisa McNulty

If I earn £8.45 after a 6%

increase – what was I earning

before?

Extract Information:

Wage ? 8.45

% 100 106

Question:

Calculation: Answer in Context:

100

?

106

45.8

?100106

45.8x

97.7? Misia used to earn £7.97 before the wage increase.

Laying out the solution

Lisa McNulty

Billy is mixing some paint and is told to used 5 litres of red paint for every

4 litres of white. He has to use 42 litres of red paint – how much white

paint will he need?

Lisa McNulty

If 5 litres of red needs 4 litres of white – then 42

litres of red needs ? white

Extract Information:

Red 5 42

White 4 ?

Question:

Calculation: Answer in Context:

42

?

5

4

?425

4x

6.33? You would need 33.6 litres of white paint to go with the 42 litres of

red

Laying out the solution

Lisa McNulty

Jane gives a gift of £900 to her two friends Celia and Ray in the ratio 3:5.

How much money does Celia receive?

Lisa McNulty

£900 is to be split in the ratio 3:5.

How much was the smaller amount?

Extract Information:

Question:

Calculation: Answer in Context:

8

900

3

?

?38

900x

5.337? Celia received

£337.50 from her friend

Laying out the solution

Money ? 900

Share 3 5 8

Lisa McNulty

I bought some shares for £2400 and sold them recently for £3150 – what

percentage increase is this?

Lisa McNulty

Shares costing £2400 were sold for £3150 What % increase is

this?

Extract Information:

Question:

Calculation: Answer in Context:

3150

?

2400

100

?31502400

100x

25.131? My shares have

increased in value by 31.25%

Laying out the solution

Value 2400 3150

% 100 ?

Lisa McNulty

If two shapes below are similar, then what is the missing length?

23cm

36cm

8cm

? cm

Lisa McNulty

If 23 scales down to 8 then what does 36 scale

down to?

Extract Information:

Question:

Calculation: Answer in Context:

36

?

23

8

?3623

8x

52.12? The missing length is

12.52 cm

Laying out the solution

Large 23 36

Small 8 ?

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5 miles = 8 km approximately.

The distance between Southampton and Birmingham is 133 miles. What

is the distance in km?

Lisa McNulty

If 5miles = 8km

How far is 132 miles in km?

Extract Information:

Miles 5 132

Km 8 ?

Question:

Calculation: Answer in Context:

132

?

5

8

?1325

8x

2.211? 132 miles is

approximately 211km

Laying out the solution

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