year 8 maths

4G
Finding a percentage and expressing as a percentage
237
■ To express one quantity as a percentage of another
1 Write a fraction with the ‘part amount’ as the numerator and the ‘whole amount’ as the
denominator.
2 Convert the fraction to a percentage by multiplying by 100% .
For example: Express a test score of 14 out of 20 as a percentage.
14 is the ‘part amount’ that you want to express as a percentage out of 20 , which is the
‘whole amount’.
×5
Key ideas
14
14
× 100% =
20 20 × 5 100
1
1 % = 70% Alternatively,
∴ 14
20 = 70%
■ To find a certain percentage of a quantity
1 Express the required percentage as a fraction.
2 Change the ‘of’ to a multiplication sign.
3 Express the number as a fraction.
4 Follow the rules for multiplication of fractions.
For example: Find 20% of 80 .
14
20 = 70
100 = 70%.
20% of 80 = 20
100 × 80 1 = 4 20
× 4 80
5100 1 = 16 Alternatively, 20% of 80 = 1 5 × 80
1
×5
= 80 ÷ 5
= 16
Example 22
Expressing one quantity as a percentage of another
Express each of the following as a percentage.
a 34 out of 40 b 13 out of 30
SOLUTION
a
b
34
40 × 100
1 % = 17
20 × 100
1 %
= 17 1 × 5 1 %
= 85%
13
30 × 100
1 % = 13 3 × 10 1 %
= 130
3 %
= 43 1 3 % or 43.3. %
EXPLANATION
Write as a fraction, with the first quantity as the
numerator and second quantity as the denominator.
Multiply by 100% .
Cancel and simplify.
Write quantities as a fraction and multiply by 100% .
Cancel and simplify.
Express the percentage as a mixed numeral or a
recurring decimal.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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