Page 139 - Mathematics Coursebook

14.2 Sharing in a ratio

14.2 Sharing in a ratio

You can use ratios to divide things up, or share them.
Look at this example.
Sally and Bob bought a car for $15 000.
Sally paid $10 000 and Bob paid $5000.
You can write the amounts they paid as a ratio.

Sally : Bob
10 000 : 5000 The highest common factor of 10 000
and 5000 is 5000, so divide by 5000 to
÷ 5000 ÷5000 simply the ratio.
2 : 1
So, Sally paid twice as much as Bob.
Five years later they sold the car for $9000.

!ey need to share the money fairly between them.
Sally paid twice as much as Bob, so she should get twice as much as
him.
How do you work out how much each of them gets?
To share in a given ratio

t Add the numbers in the ratio to $nd the total number of parts.
t Divide the amount to be shared by the total number of parts to $nd the value of one part.

t Use multiplication to work out the value of each share.

Worked example 14.2

Share $9000 between Sally and Bob in the ratio 2 : 1.

Total number of parts: 2 + 1 = 3 Add the numbers in the ratio to fi nd the total number of
parts.
Value of one part: $9000 ÷ 3 = $3000 Divide the amount to be shared by the total number of
parts to fi nd the value of one part.
Sally gets: $3000 × 2 = $6000 Multiply by 2 to get Sally’s share.
Bob gets: $3000 × 1 = $3000 Multiply by 1 to get Bob’s share.

) Exercise 14.2

1 Copy and complete the workings to share $45 between Ethan and Julie in the ratio 1 : 4.

Total number of parts: 1 + 4 =
Value of one part: $45 ÷ =

Ethan gets: 1 × =
Julie gets: 4 × =

138 14 Ratio and proportion