Page 113 - MAT KS3 Y8 Cambridge CheckPoint

11.1 Calculating percentages

11.1 Calculating percentages

Percentage means ‘out of 100’, so a percentage is just a fraction with
100 as the denominator. 50% = 1 25% = 1 75% = 3
2 4 4
You need to be able to write percentages as fractions. There are some
1
simple percentages, with the equivalent fractions, in the box. 10% = 10 20% = 1
5
1
2
33 % = 1 66 % = 2
Can you work out a percentage of an amount? 3 3 3 3
If the percentage is a simple fraction you should be able to work it out
mentally. For other percentages you could use a calculator.

Worked example 11.1

a Lynn has 600 dollars ($600) and decided to give 40% to charity. How much was that?
b Chris earns $723 and had to pay 27% in tax. How much was that?

a 40% = 2 20% = 1 so 40% is 2 because 40 is double 20.
5 5 5
2 of $600 = $240 1 of 600 = 600 ÷ 5 = 120, so 2 of 600 is 120 × 2 = 240.
5 5 5

b 27% = 0.27 27% is not a simple fraction so write it as a decimal.
27% of 723 = 0.27 × 723 Use a calculator to multiply the decimal by the amount.
= $195.21

✦ Exercise 11.1 5% 30% 37 % 45% 50% 60%
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2
1 Here are some decimals and some fractions. 1 3 3 1 3 9
Match each percentage to the corresponding fraction. 2 5 8 20 10 20
2 Write each percentage as a decimal.
a 15% b 5% c 90% d 6.5% e 150%
3 Calculate these amounts. Do not use a calculator. Start by changing the percentages to
fractions and simplifying them as much as possible.
a 25% of 60 kg b 75% of 1000 litres c 40% of $300 d 70% of 120 g
4 Find the following amounts. Do not use a calculator.
1
1
a 10% of 45 cm b 60% of 60 people c 33 % of 2400 d 12 % of 40
3 2
5 Use a calculator to find these amounts.
a 27% of $43 b 57% of 280 c 93% of 3700 d 6% of 9.200
6 a Which of these would be easy to find without using a calculator?
2
A 66 % of 90 B 82% of 200 C 60% of 55 D 3% of 2100 E 23% of 50
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b Find the values of each percentage in part a.
7 Find:
a 7% of 30 b 17% of 30 c 107% of 30 d 117% of 30.

11 Percentages 111