# Simplify Ratios

In this worksheet, students will reduce a ratio to its simplest form

Key stage:  KS 3

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Use Ratio Notation

Difficulty level:

#### Worksheet Overview

As you may know by now, mathematicians like to simplify problems in maths as much as they can!

When we see a fraction like:

we immediately want to divide by 2 and write it as

Simplifying it makes it look better and makes it easier to calculate with.

In this activity, we are going to do this with ratio.

So, in the same way that we can simplify the fraction above, we can do this with any ratio given.

We divide by the highest common factor!

Example

Write 6:18 in its simplest form.

The highest common factor of 6 and 18 is 6.

We will divide both by 6.

6 ÷ 6 = 1

18 ÷ 6 = 3

Therefore, we write the answer as 1:3

Here's a useful tip: if you can't think of the highest common factor straight away, divide by something smaller first. This would make it more manageable.

In the example above, we could have divided both 6 and 18 by 2 first to get 3:9 and then by 3 to get 1:3. It doesn't matter if we have to do it several times to get the simplest form!

Are you ready to give it a go?

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