year 8 maths

5B
Simplifying ratios
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■ The quantities in ratios must be expressed using the same unit .
For example, 20 minutes : 1 hour = 20 minutes : 60 minutes
= 20 : 60
■ Simplifying ratios
A ratio is simplified by dividing all numbers in the ratio by their highest common factor (HCF).
For example, the ratio 15 : 25 can be simplified to 3 : 5 .
Key ideas
15 : 25
÷5 ÷5
3 : 5
■ Ratios in simplest form use whole numbers only.
■ In the following list of equivalent ratios, 2 : 3 is expressed in simplest form.
2 : 3 = 1 : 1 1 = 5 : 7.5 = 4 : 6 = 20 : 30
2
Example 3
Simplifying ratios
Simplify the following ratios.
a 7 : 21 b 450 : 200
SOLUTION
a 7 : 21
÷7 ÷7
1 : 3
b 450 : 200
÷50 ÷50
9 : 4
EXPLANATION
HCF of 7 and 21 is 7 .
Divide both quantities by 7 .
HCF of 450 and 200 is 50 .
Divide both quantities by 50 .
Example 4
Simplifying ratios involving fractions
Simplify the following ratios.
3
a
5 : 1
2
SOLUTION
a 3
5 : 1
2
×10 ×10
6 : 5
Alternatively, 3 5 : 1
2 = 6
10 : 5
b 7
3 : 5
4
×12 ×12
28 : 15
b 2 1 3 : 1 1
4
EXPLANATION
10 = 6 : 5. LCD of 5 and 2 is 10 .
Multiply both quantities by 10 .
Convert mixed numerals to improper fractions.
LCD of 3 and 4 is 12 .
Multiply both quantities by 12 .
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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