A ratio is used to describe how two quantities are related.
For example, we might say that orange squash is to be mixed with water in a ratio of 1:6.
This means that for every 1 part squash, there will need to be 6 parts of water.
If there was 100ml of squash, there would be 600ml of water.
Another common example of a ratio is a map scale. A particular map scale might be 1:50,000.
In this case it means that 1cm on the map represents 50,000cm in "reallife".
50,000cm = 500m = 0.5km, so 1cm on the map represents half a kilometre. 2cm would therefore represent 1km.
Finding equivalent ratios
The ratio of squash to water in the example above was 1:6, but this could be written as 100:600, or 20:120, or 5:30.
These ratios are equivalent because they have the same meaning  the amount of water is six times the amount of squash.
You can find equivalent ratios by multiplying or dividing both sides by the same number. This is similar to finding equivalent fractions. Some examples of finding equivalent ratios are shown on the right. All the ratios in the diagram are equivalent.
Writing a ratio in its simplest form
To write a ratio in its simplest form, keep dividing both sides by the same number until

Writing a ratio in the form 1 : n or n : 1
Sometimes we need to write a ratio in the form 1 : n or in the form n : 1.
To write a ratio in the form 1 : n, divide both sides by the lefthand number.
For example, with the ratio 4 : 10 you would divide both sides by 4, giving the equivalent ratio 1 : 2.5
To write a ratio in the form n : 1, divide both sides by the righthand number.
For example, with the ratio 8 : 5 you would divide both sides by 5, giving the equivalent ratio 1.6 : 1
Practice Questions
Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) Write the ratio 7 : 14 in its simplest form
(b) Write the ratio 15 : 25 in its simplest form
(c) Write the ratio 10 : 4 in its simplest form
(d) Write the ratio 5 : 13 in the form 1 : n
(e) Write the ratio 12 : 3 in the form n : 1
(f) A map has scale 1:20000. What actual distance is represented by 8cm on the map?
(g) A map has scale 1:100000. What distance on the map would represent 20km in real life?
