Simplify Ratios with Mixed Units

In this worksheet, students will reduce a ratio to its simplest form when the units are not the same

Key stage:  KS 3

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Use Ratio Notation

Difficulty level:

Worksheet Overview

Here's a quick reminder of how to simplify ratios by dividing by the HCF (highest common factor).

For example:

In this activity, we will practise simplifying ratios, but  with an extra challenge!

If the units are different, we will first have to convert one to the other.

Sound scary? Let's take a look at an example.

Example

Write 40p:£2.00 in its simplest form.

Before we look for the HCF, we need to convert one to the other.

If we convert both to £'s, then we would have to deal with decimals.

So, let's convert both to pence.

£2.00 = 200p

We can now rewrite the ratio as 40:200

It looks much better to deal with now!

The highest common factor is 40.

We can divide both by 40 and we get 1:5

or

if we don't see 40 straight away, we can divide by 10 first to give us

4:20

then divide by 4

= 1:5

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.

Do you feel happier about that now?

Let's get started!

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