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Equivalence

- Fractions, decimals and percentages

Mental starter

15 75 23 156 0.7 2.5

52 9 6 50 25 80

10 63 4 0.2 0.03 0.5

0.4 1 3.5 6.25 7.2 0.9

10

100

1000

Some of these mean the same

1/2

3/4

2/4

50

75

1/25

1/4

0.75

25

0.25

0.5

How can we convert decimals to percentages and

fractions?

To convert decimals to percentages we multiply

by 100.

So, 0.6

60

Remember, when we multiply by 100 we move the

decimal point 2 places to the right.

How can we convert a percentage to a fraction?

- Per cent means out of 100
- 25 25 out of 100 25/100
- We can then cancel this fraction down, so,

dividing the numerator and denominator by 25

gives us

1/4

Decimals to percentages and fractions

1/10

10/100

10

0.1

1/5

20/100

20

0.2

30

3/10

30/100

0.3

45

9/20

45/100

0.45

How can we convert a percentage to a decimal?

- Divide by 100

25/100 0.25

So, 25 is the same as

REMEMBER WHEN WE DIVIDE BY 100 WE MOVE THE

DECIMAL POINT 2 PLACES TO THE LEFT

Percentages to decimals

10/100

10

0.1

25

25/100

0.25

38

38/100

0.38

92

92/100

0.92

How can we convert fractions to decimals and

percentages?

- If we divide the numerator by the denominator we

get a decimal

So, ¼ 1 divided by 4

0.25

As a percentage, ¼ 0.25 25

Fractions to decimals and percentages

1/10

10/100

10

0.1

1/5

20/100

20

0.2

3/10

30/100

30

0.3

9/20

45/100

45

0.45

How can we find percentages?

10 of 100

100 /10

10

5 of 100

Half of 10 of 100

5

10 of 260

26

260/10

5 of 260

Half of 10 of 260

13

Harder percentages

We can use our answers for 10 and 5 of any

number to find further percentages

So, if 10 of 620

62

And 5 of 620

31

Then 15 will equal 10 5

62 31

93

What would 20 of 620 be?

124

And 35 of 620?

217

Equivalent Fractions, Decimals, and Percentages

- Copy and complete the following equivalence table

FRACTION PERCENTAGE DECIMAL

0.3

60

2/25

18

0.96

1/2

4

3/4

30

3/10

3/5

0.6

8

0.08

0.18

9/50

96

24/25

50

0.5

1/25

0.04

0.75

75

Quick conversions

- FRACTION

PERCENTAGE

DECIMAL

Extension

As a decimal, a fraction, and a percentage are

all different ways of writing the same thing, we

can sometimes make a calculation easier by using

an equivalent form instead of the decimal,

fraction or percentage given.

Example 1.

20 of 35. As 20 is 1/5, this is the same as 1/5

x 35 1/7

Example 2.

0.3 x 340. As 0.3 is 30, this is the same as 30

of 340. 10 of 340 is 34. So, 30 of 340 3 x 34

102

Example 3.

3/25 of 40. As 3/25 is 0.12, this is the same as

0.12 x 40 4.8

Rewrite the following using an alternative to the

percentage, decimal or fraction given. Then work

out the answer.

a) 20 of 75 b) 2/25 of 60 c) 25 of 19 d)60 of 550

e) 3/20 of 90 f) 0.5 x 64 g) 3/5 of 7 h) 0.4 x 270

i) 75 of 44 j) 0.333 x 180

1/5 x 75 15

0.08 x 60 4.8

¼ x 19 4 ¾

0.6 x 550 330

0.15 x 90 13.5

½ x 64 32

0.6 x 7 4.2

4/10 x 270 108

¾ x 44 33

1/3 x 180 60