A ratio is a way to compare amounts of something. Recipes, for example, are sometimes given as ratios. To make pastry you may need to mix 2 parts flour to 1 part fat. This means the ratio of flour to fat is 2:1.

If pastry is 2 parts flour to 1 part fat, then there are 3 parts (2 + 1) altogether. Two thirds of the pastry is flour; one third fat.

Ratios are similar to fractions; they can both be simplified by finding common factors. Always try to divide by the highest common factor. Have a look at this question.

- Question
There are 15 girls and 12 boys in a class. What is the ratio of girls to boys? Give your answer in its simplest form.

- Answer
The ratio of girls to boys is 15:12

However, both sides of this ratio are divisible by 3

Dividing by 3 gives 5:4

5 and 4 have no common factors (apart from 1).

So the

**simplest form**of the ratio is 5:4This means there are 5 girls in the class for every 4 boys.

Now practise ratios for yourself in this activity.

Now try some more difficult questions below.

- Question
A newspaper includes 12 pages of sport and 8 pages of TV. What is the ratio of sport to TV? Give your answer in its simplest form.

- Answer
The answer is

**3:2**You can divide both sides of 12:8 by 4.

If your answer was incorrect, try to fill in the blanks here:

The ratio is 12:8.

Both of these numbers are divisible by 4.

Dividing by 4 gives 3:2.

You have to be sure that the things you are comparing are measured in the same units. Look at the following problem:

- Question
Anna has 75p.

Fiona has £1.20.

What is the ratio of Anna's money to Fiona's money, in its simplest form?

- Answer
One amount is in pence, the other in pounds. We have to convert Fiona's amount into pence first:

£1.20 = 120p.

Now the ratio is 75:120. Both sides are divisible by 15.

Dividing both sides by 15 gives 5:8

So the ratio is

**5:8**.

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