1. Percentages
Prior knowledge:
Understand :
How to find a fraction of a quantity – by cancelling factors
That multiplication is commutable, i.e. 2 × 3 = 6
and 3 × 2 = 6

2. Finding a fraction of a quantity
Percentages
Finding a fraction of a quantity
Method 1 (non-calculator)
Find of 20 5
or × 20 5
Find of 20 5
20 ÷ 5 = 4 4
So: of is 5 4 ×
= 16
To do this in one step we can look at the question
Divide by 5 and show it by crossing out the 5 on the bottom
and cross out the 20 and replace with 4 (the answer to 20 ÷ 5) 4
4 × 20 5
= 16

3. Using this method to find percentages of a quantity
Example 1: 2
Find 12% of 200
12 × 200
100
= 24
cancel common factors
Example 2: 4 10 ≡
Find 40% of 270
× 270
100
= 108
cancel common factors
Example 3:
0.7
Find 35% of 14 7 20 ≡
× 14
100
= 4.9
cancel common factors

4. Percentages Now do these: 1. Find 10% of 250 1 10 × 250 = 25≡
× 250
100
= 25
6 × 500
100
= 30 6 1 4 ≡
× 24
100
= 6 3 10 ≡
× 80
100
= 24 21 3 20 ≡
× 420
100
= 63p
Convert £ to pence

5. Percentages
Now do these:
1. Find 10% of 25
2. Find 5% of 700
3. Find 30% of 50
4. Find 15% of 70
5. Find 75% of 9.6
2.5 35 15
11.5
7.2

6. Percentages
Using a calculator we use the same method
Example 1:
means divide
Find 6.4% of 15.95
6.4 ×
100 =
Press the buttons on your calculator as follows:
6.4 ÷
100 ×
15.95 =
Example 2:
Find 8.6% of £25.84
= £2.22
6.4 ×
100
Press the buttons on your calculator as follows:
8.6 ÷
100 ×
25.84 =
Notice how the answer is rounded to 2 d.p. because the question
is about money

7. Percentages
Now do these:
1. Find 11.2% of
2. Find 83% of 34
3. Find 26% of 62
4. Find 36.5% of £170
5. Find 16% of 120cm
6. Find 95% of 240g
7. Find 22% of £423
8. Find 12% of £19.6
21.58
28.22
16.12
£63.05
19.2cm
228
£93.06
£2.35

8. percentage multiplier
Percentages
You will notice that whatever the percentage you are finding the
first step is always the percentage ÷ 100
This calculation can be done in your head to gain the
percentage multiplier
e.g. to find 6.4% of we first calculate 6.4 ÷ 100
6.4 ÷ 100 = 0.064
This means that we can calculate 6.4% of by pressing the
following calculator buttons:
0.064 ×
15.95 =
1.0208
percentage multiplier

9. The percentage multiplier is the percentage ÷ 100
Percentages
The percentage multiplier is the percentage ÷ 100
Now do these just using the percentage multiplier:
1. Find 31.6% of
2. Find 73% of 56
3. Find 23% of 84
4. Find 42.3% of £240
5. Find 12% of 325cm
40.88
19.32
£101.52
39cm