year 8 maths

238 Chapter 4 Fractions, decimals, percentages and financial mathematics
Example 23
Converting units before expressing as a percentage
Express:
a 60 cents as a percentage of $5 b 2 km as a percentage of 800 m
SOLUTION
a
b
60
500 × 100
1 % = 60 5 %
= 12%
2000
800 × 100
1 % = 2000
8 %
= 250%
EXPLANATION
Convert $5 to 500 cents.
Write quantities as a fraction and multiply by 100% .
Cancel and simplify.
60
Alternatively,
500 = 6 50 = 12
100 = 12%.
Convert 2 km to 2000 m .
Write quantities as a fraction and multiply by 100% .
Cancel and simplify.
2000
Alternatively,
800 = 200
8 = 50 2 = 25
10 = 250
100 = 250% .
Example 24
Finding a certain percentage of a quantity
Find:
a 25% of 128 b 155% of 60
SOLUTION
EXPLANATION
a 25% of 128 = 25
100 × 128
Write the percentage as a fraction over 100 .
1
= 1 4 × 128
1 = 32 Cancel and simplify.
Alternatively, 25% of 128 = 1 of 128 = 128 ÷ 4 = 32 .
4
b 155% of 60 = 155
100 × 60 Write the percentage as a fraction over 100 .
1
= 155
5 × 3 Cancel and simplify.
1
= 31 1 × 3 1 = 93
Exercise 4G
UNDERSTANDING AND FLUENCY
1, 2, 3(½), 6, 9–10(½) 3–10(½)
6–11(½)
1 The correct working line to express 42 as a percentage of 65 is:
42
A
100 × 65% B 65
42 × 100% C 100
42 × 65% D 42
65 × 100%
2 The correct working line to find 42% of 65 is:
42
A
100 × 65 B 65
42 × 100 C 100
42 × 65 D 42
65 × 100
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.