1. Fractions, decimals and percentages
Equivalence
Fractions, decimals and percentages

2. 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
Individual whiteboards
Revision of multiplying and dividing by powers of 10
Pick pupil, number, operation, and power of 10 × ÷ 10
100
1000

3. Some of these mean the same
1/2
3/4
2/4
50%
75%
1/25
1/4
0.75
This could be done using the interactive whiteboard so the pairs can be physically moved together
Match pairs. Spot odd one out and equivalent fractions
25%
0.25
0.5

4. How can we convert decimals to percentages and fractions?
To convert decimals to percentages we multiply by 100.
So, 0.6 =
60%
Have example percentage to decimal conversion on whiteboard to emphasise connection and inverse operation.
Remember, when we multiply by 100 we move the decimal point 2 places to the right.

5. 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:
Percent means ‘out of 100’
1/4

6. Decimals to percentages and fractions
10/100 =
1/10
0.1 =
10% =
1/5
0.2 =
20% =
20/100 =
30% =
0.3 =
30/100 =
3/10
Pupils do question 1 of exercise 4D page 46: decimals to percentages and fractions
45% =
0.45 =
45/100 =
9/20

7. How can we convert a percentage to a decimal?
Divide by 100
25/100 = 0.25
So, 25% is the same as
Divide by 100
REMEMBER: WHEN WE DIVIDE BY 100 WE MOVE THE DECIMAL POINT 2 PLACES TO THE LEFT

8. Percentages to decimals
10/100 =
10% =
0.1
25% =
25/100 =
0.25
38% =
38/100 =
0.38
Pupils do question 2 of exercise 4D page 46: converting percentages to decimals and fractions
92% =
92/100 =
0.92

9. 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%

10. Fractions to decimals and percentages
1/10 =
10/100 =
0.1 =
10%
1/5 =
20/100 =
0.2 =
20%
3/10 =
30/100 =
0.3 =
30%
Use calculator
Pupils do question 3 of exercise 4D page 46: converting fractions to percentages and decimals
Already covered decimals to fractions in lesson 4.2.
Pupils can hold up answers on individual whiteboards
9/20 =
45/100 =
0.45 =
45%

11. 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

12. 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% = = 93
Pupils do question 5 of exercise 4D page 46: calculating percentages in multiples of 5 and 10
What would 20% of 620 be?
124
And 35% of 620?
217

13. 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
3/10
30%
3/5
0.6 8%
0.08
0.18
9/50
24/25
96%
50%
0.5
1/25
0.04
75%
0.75

14. Quick conversions FRACTION DECIMAL PERCENTAGE Extension work
Pupils copy diagram and complete with steps

15. 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

16. Then work out the answer.
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) 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