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Ratios

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# Ratios

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.

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 5:4

This means there are 5 girls in the class for every 4 boys.

## Activity

Now practise ratios for yourself in this activity.

Ratios activity

## More questions

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.

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?

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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