Dividing by unit fractions

Home learning focus

In this lesson you will learn how to divide by a unit fraction.

This lesson includes:

  • one slideshow lesson
  • one downloadable activity

Learn

Key vocabulary

A unit fraction is a fraction where the numerator is 1.

What does it mean to divide by a fraction?

You can think of 20 ÷ 10 as asking how many 10s are there in 20.

The same thing applies when you are dividing by fractions, so for example you can think of 4 ÷ ½ as asking how many halves are there in 4.

You can see that the 4 whole circles below are made up of 8 halves.

This shows that 4 ÷ ½ = 8.

Now let's think about this sum. You need to work out how many quarters there are in 3 halves.

Here you have 3 halves of a whole circle.

Splitting this into quarters of the whole circle, you can see there are 6 quarters in 3 halves.

So the answer to the calculation is 6!

Example 1

How many eighths are there in three eighths?

As you can see, the answer to the calculation is:

3/8 ÷ 1/8 = 3

Example 2

How many eighths are there in one quarter?

How many eighths are there in three quarters?

As you can see, the answers to these calculations are:

1/4 ÷ 1/8 = 2 and

3/4 ÷ 1/8 = 6

What other method can you use?

The following slides from Numerise will show you a method for dividing by fractions without relying on images:

  1. keep the first value the same
  2. change the ÷ for a ×
  3. flip the second fraction
Dividing by a unit fraction

Dividing by a unit fraction

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Practise

Activity 1

Dividing fractions

Download the activity below from White Rose Maths on dividing fractions. You can print it out, or use a pen and paper to answer the questions.

Dividing fractions

Click here to download the answer sheet.

There's more to learn

Have a look at these other resources around the BBC and the web.

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