Simplifying ratios is pretty much the same as simplifying fractions – we just look for the highest common factor and divide both sides of the ratio by it. But a ratio is different to a fraction. Instead of telling us a part of a whole, it relates different parts. So 2:3 for instance relates 2 parts of one thing to 3 parts of another. Another way of expressing that is to say that the first part is 2/5 of the whole and the second part is 3/5 of the whole.

We can write a relationship between two measurements in a ratio, but in order to write it without any units, we first need to make sure both parts are in the same units. For instance 1km:10m we would have to write as 1000m:10m, and then we don’t need the units and can just say that it is a ratio of 1000:10 or (better) 100:1

Example

Exercise

Let’s complete exercises 16B and 16C from pages 253-254 of the textbook:

The answers are below: