year 8 maths

5C
Dividing a quantity in a given ratio
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Example 7 Dividing a quantity in a ratio with three terms
Divide $300 in the ratio 2 : 1 : 3 .
SOLUTION
Unitary method
Total number of parts = 6
÷6 6 parts = $300 ÷6
1 part = $50
×2 ×2 ×3 1 part = $50 ×3
2 parts = $100 3 parts = $150
$300 divided in the ratio 2 : 1 : 3 is
$100, $50 and $150 .
Fractions method
2
6 of 300 = 2 6 × 300
1 = 100
EXPLANATION
Total number of parts = 2 + 1 + 3 = 6
Value of 1 part = $300 ÷ 6 = $50
Check numbers add to total:
$100 + $50 + $150 = $300
Fraction =
number in ratio
total number of parts
1
6 of 300 = 1 6 × 300
1 = 50
3
6 of 300 = 3 6 × 300
1 = 150
$300 divided in the ratio 2 : 1 : 3 is
$100, $50 and $150 .
Check numbers add to total:
$100 + $50 + $150 = $300
Example 8 Finding a total quantity from a given ratio
The ratio of boys to girls at Birdsville College is 2 : 3 . If there are 246 boys at the school, how many
students attend Birdsville College?
SOLUTION
Unitary method
2 parts = 246
÷2
÷2
1 part = 123
×5
5 parts = 615 ×5
615 students attend Birdsville College.
Equivalent ratios method
boys : girls
×123 = 2 : 3 ×123
= 246 : 369
615 students attend Birdsville College.
EXPLANATION
Ratio of boys : girls is 2 : 3 .
Boys have ‘ 2 parts’ = 246
Value of 1 part = 246 ÷ 2 = 123
Total parts = 2 + 3 = 5 parts
Check: 5 parts = 5 × 123 = 615
Use equivalent ratios.
Multiply each quantity by 123 .
Total number of students
= 246 boys + 369 girls = 615
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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