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

Here is an example.

- Share £200 in the ratio 2:3
- This means share the money into 5 equal parts and give one person 2 shares, and the other 3
- So 200/5 = 40, one person gets 2 x £40 = £80 and the other 3 x £40 = £120
- 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?

- Answer
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.

- Answer
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?

- Answer
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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