What is ratio?

For example, they might be shown the following diagram and would need to know that the ratio of blue shapes to pink shapes is three to four. They would need to know to write this as 3:4.

(Proportion is not the same thing as ratio, as it tells us about a number in relation to a whole, so in the case above we would say there are 4 pink shapes in every 7 shapes, or 3 blue shapes in every 7 shapes.)

Children then need to be able to move onto solving ratio problems using a quicker method. For example:

There are 48 beads in a jar. For every 2 purple beads there are 6 red beads. How many red beads are there altogether?

A quick way to work this out would be to:

• Add the 2 and 6 together to make 8. If you then divide 48 by 8 you get 6.
• To find out how many purple beads, you would multiply 2 by 6 = 12
• To find out how many red beads, you would multiply 6 by 6 = 36

This can also be demonstrated like this:

Ratio problems can be presented in a number of different ways. These three problems all involve the same set of data:

There are 63 children in a playground. For every 2 children wearing black shoes there are 5 children wearing brown shoes. How many children are wearing black shoes?

There are 45 children in a playground wearing brown shoes. For every 5 children wearing brown shoes there are 2 wearing black shoes. How many children are wearing black shoes?

For every 2 children in a playground wearing black shoes there are 5 children wearing brown shoes. There are 18 children wearing black shoes. How many children are wearing brown shoes?

This data could be represented in the following way: