# What is ratio?

## What is ratio?

A ratio compares values, telling us **how much of one thing there is compared to another thing**.

Children will start to learn about proportion and ratio in Year 6.

## Solving ratio problems in KS2

Children in Year 6 may be asked to solve **problems involving ratio**. For example:

*There are 20 children in a playground. The ratio of boys to girls is 2:8. How many boys are there in the playground?*

The long way to work this out would be to **draw a diagram** of the 20 children, with one symbol (X) for boys and one symbol (0) for girls, for example:

X X 0 0 0 0 0 0 0 0

X X 0 0 0 0 0 0 0 0

They would be able to see from this diagram that there were four boys altogether.

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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: