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Maths

Ratios

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# Dividing in a ratio

Ratios are also used when dividing up amounts. The basic method is quite easy.

Here is an example.

1. Share £200 in the ratio 2:3
2. This means share the money into 5 equal parts and give one person 2 shares, and the other 3
3. So 200/5 = 40, one person gets 2 x £40 = £80 and the other 3 x £40 = £120
4. Check that this adds up to the total, in this case £200
Question

Amit is 12 years old. His brother, Arun, is 9.

Their grandfather gives them £140, which is to be divided between them in the ratio of their ages. How much does each of them get?

The ratio of their ages is 12:9.

We can simplify this. Dividing by 3 gives 4:3.

So Amit gets 4 parts, and Arun gets 3.

This means that the money has to be divided into 7 parts (4 + 3).

£140 ÷ 7 = £20, so 1 part is £20.

• Amit gets 4 parts: 4 × £20 = £80.
• Arun gets 3 parts: 3 × £20 = £60.

Check that they add to make the total amount: £80 + £60 = £140.

A ratio can have more than 2 numbers in it. Here is another typical question.

Question

The angles in a triangle are in the ratio 1:2:9. Find the size of the largest angle.

1 + 2 + 9 = 12 so in total, there are 12 parts.

The angles in a triangle add up to 180 degrees.

So 1 part is 180 ÷ 12 = 15.

The largest angle in the ratio is the 9.

9 × 15 = 135 degrees.

Try this one.

Question

In a certain town, the ratio of left-handed people to right-handed people is 2:9. How many right-handed people would you expect to find in a group of 132 people?

Did you get the answer 108?

You divide 132 by 11, and multiply by 9.

If you did not get the correct answer, see if you can fill in the blanks here:

2 + 9 = 11

132 ÷ 11 = ?

9 × ? = 108 people.

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