Writing a ratio in the form 1:n or n:1

We have already covered that to write a ratio in its simplest form we divide both sides by their highest common factor (just as we divide the top and bottom of a fraction).

For example, 12:15 becomes 4:5, and 4:8 becomes 1:2.

When a ratio is in its simplest form, all the numbers are whole numbers.

However, it is sometimes useful to write a ratio in the form 1:n or n:1 (where n is any number, possibly a fraction or decimal). This means we will not necessarily be dealing with whole numbers.

For example, if we are asked to write the ratio 2:5 in the form 1:n, we need to make the left-hand side of the ratio equal to 1. We do this by dividing both sides of the ratio by 2.

2:5 = ²/₂ : ⁵/₂

= 1 : 2.5

If we were asked to write 2:5 in the form n:1, we would need to make the right-hand side equal to 1. So we would divide both sides by 5:

2:5 = ²/₅ : ⁵/₅= 0.4 : 1