year 8 maths

5C
Dividing a quantity in a given ratio
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5C Dividing a quantity in a given ratio
When two people share an amount of money they usually split it evenly. This is a 1 : 1 ratio or a 50–50
split. Each person gets half the money.
Sometimes one person deserves a larger share than the other. The diagram below shows $20 being divided
in the ratio 3 : 2 . Gia’s share is $12 and Ben’s is $8 .
Gia’s share Ben’s share
$1 $1 $1 $1 $1
$1 $1 $1 $1 $1
$1 $1 $1 $1 $1
$1 $1 $1 $1 $1
Gia and Ben divided $20 in the ratio 3 : 2.
Let’s start: Is there a shortcut?
Take 15 counters or blocks and use them to represent $1 each.
Working with a partner:
• Share the $15 evenly. How much did each person get?
• Start again. This time share $15 in the ratio 2 : 1 , like this: ‘ 2 for me, 1 for you; 2 for me, 1 for you…’.
How much did each person get?
• Start again. This time share $15 in the ratio 3 : 2 , like this: ‘ 3 for me, 2 for you; 3 for me, 2 for you…’.
How much did each person get?
• Is there a shortcut? Without using the counters, can you work out how to share $15 in the ratio 4 : 1 ?
• Does your shortcut work correctly for the example at the top of this page?
• Have a class discussion about different shortcuts.
• Use your favourite shortcut (and a calculator) to divide $80 in the ratio 3 : 2 . Write down the steps you
used.
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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