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Ratio

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Division in a given ratio

Question

Dave and Lisa win £500 between them. They agree to divide the money in the ratio 2:3.
How much does each person receive?

Answer

The ratio 2:3 tells us that for every 2 parts Dave receives, Lisa will receive 3 parts. There are 5 parts in total.

£500 represents 5 parts. Therefore, £100 represents 1 part.

Dave receives 2 parts: 2 × £100 = £200
Lisa receives 3 parts: 3 × £100 = £300

Order

It's important to notice what order the parts of the ratio are written in. 2:3 is not the same as 3:2.

In the example, the ratio of Dave's money to Lisa's was 2:3. If we swap the order to 3:2 then Dave would get more than Lisa.

To keep it the same as in the example we could say that the ratio of Lisa's money to Dave's would be 3:2

Question

Q1. Amelia and Shabana win a sum of money, which they agree to share in the ratio 5:3.
If Amelia receives £150, how much will Shabana receive?

Q2. A necklace is made using gold and silver beads in the ratio 3:2. If there are 80 beads in the necklace:
a) How many are gold?
b) How many are silver?

12 gold and 8 white
Answer

A1. Amelia receives 5 parts, which is equivalent to £150. Therefore, £150 represents 5 parts.
£150 ÷ 5 represents one part.
So one part is £30
Shabana receives 3 parts: 3 × £30 = £90.

A2. Gold : Silver = 3:2, so there are 5 parts altogether.
80 ÷ 5 = 16, so 1 part represents 16 beads.
a) Gold = 3 × 16 = 48 beads
b) Silver = 2 × 16 = 32 beads

Activity

Ratio activity

Problems with proportion? Try this activity.

Play

Questionaut

Join Questionaut's quest to find his friend's hat.

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