year 8 maths

232 Chapter 4 Fractions, decimals, percentages and financial mathematics
Example 20
Converting fractions to percentages
Convert the following fractions and mixed numerals to percentages.
3
7
a
b
c 2 1 5
40
4
SOLUTION
a
b
EXPLANATION
3
5 × 100% = 3
5 × 20 100
1 % Multiply by 100% .
1
Simplify by cancelling the HCF.
= 60%
Alternatively:
3
5 = 6 10 = 60
100 = 60%
7
40 × 100% = 7
40 × 5 100
1 % Multiply by 100% .
2
= 35 2 % = 17 1 Simplify by cancelling the HCF.
2 % Write the answer as a mixed numeral.
d
2
3
c 2 1 4 × 100% = 9
4 × 25 100
1 %
1
= 225%
Alternatively:
Convert mixed numeral to improper fraction.
Cancel and simplify.
2 = 200% and 1 4 = 25%.
So 2 1 4 = 225%.
d
2
3 × 100% = 2 3 × 100
1 % Multiply by 100% .
= 200
3 % = 66 2 3 %
Multiply numerators and denominators.
Write answer as a mixed numeral.
Alternatively:
1
3 = 331 3 %
2
So
3 = 662 3 %.
Example 21
Converting decimals to percentages
Convert the following decimals to percentages.
a 0.458 b 17.5
SOLUTION
EXPLANATION
a 0.458 = 45.8% 0.458 × 100 0.458
The decimal point appears to move two places to the right.
b 17.5 = 1750% 17.5 × 100 17.50
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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