mathsA ratio is a way of comparing one amount to another. Recipes are a good example of this. For instance, to cook rice you should normally add 1 cup (or part) of rice to 2 cups (or parts) of water. The ratio of water to rice is 2:1.

In this example there are 3 parts altogether: 2 part water and 1 part rice.

As with fractions, it’s possible to simplify a ratio by dividing both sides by the highest common factor.

For example, if there are 10 blackbirds and 8 robins in a park what is the ration of blackbirds to robins?

The ratio of blackbirds to robins is 10:8.

Both sides are divisible by 2 so this ration can be simplified to 5:4.

So, to every 5 blackbirds there are 4 robins

We probably won’t get such a simple question in your exam so here’s another harder example:

A magazine is made up of 10 pages worth of adverts and 14 of articles. What is the ratio of adverts to articles? Give your answer in its simplest form.

articles:adverts = 14:10 = 7:5


Using 1:n or n:1

In the examples you’ve just read the numbers used were all whole numbers.

However, sometimes it can be easier to write a ratio as 1:n or n:1. Here, n could be any kind of number, no necessarily a whole one.

For example, in your exam you might get the following kind of question:

Write the ratio 2:5 in the form of:

a) 1:n

b) n:1

First of all you need to make the left hand side of the ration equal to 1. You do this by dividing it by 2. This means you also need to divide the right hand side by 3:

a) 2:5 = 2/2:5/2 = 1:2.5

Similarly, to get n:1 you divide both side by the right hand side number:

b) 2:5 = 2/5:5/5 = 0.4:


Ways to use ratios

There are a number of ways in which you can use ratios and they can be used to figure out a number of problems.

Example 1: Max decides to draw out a scale drawing of his bathroom. He uses the scale 1:100. When he measures the width of the bathroom he gets 3.5 metres. What width should he use on his scale drawing? Give your final answer in mm

First of you need to consider what measurement your final answer should be in: mm. So, convert 3.5m into mm: 3500mm

Then divide your answer by the scale of the drawing: 3500 100 = 35mm

Example 2: Fiona wants to make chocolate chip cookies. She needs 300 grams of chocolate to make 15 cookies. How many grams of chocolate would she need to make 21 cookies?

So, 15 cookies need 300 grams of chocolate.

This means that 1 cookie needs 300 15 = 20g

So, 21 cookies need 20 x 21 = 420g