Equivalent ratios

As with fractions, there are equivalent ways to write ratios.

So if we agree that each person will get 2 slices of pizza, we can say that the ratios of slices to people is 2:1, but we could also say that it is 4:2 as 2 people get 4 slices, or that it is 8:4 as 4 people get 8 slices. These are all equivalent ratios.

Exercise 1

Simplifying Ratios

As with fractions, the preferred form of a ratio is the one where there are no common factors to the two sides of the ratio. We call this simplest form. We can get to this form either by dividing both sides by their HCF or just continuously dividing them by any common factors we identify until there are no more.

Worked Example

Simplify the ratio 9:108

What is the simplest form of the ratio 100:30

Exercise 2

Ratios that have fractions in can also be simplified. It is easiest to do this by replacing them with equivalent fractions that have a common denominator.

Worked examples

Simplify 2/3 : 5/6

Simplify 3/4 : 2/3

Exercise 3

Answers to all 3 exercises