Divide fractions and mixed numbers

Home learning focus

Learn how to divide fractions and mixed numbers.

This lesson includes:

  • two videos
  • a learning summary
  • two activity worksheets with answers

Learn

Dividing fractions

When you divide 10 by 2, you are working out how many 2s there are in 10.

10 ÷ 2 = 5, so there are five 2s in 10.

In a similar way, when dividing 2 by ¹/₂, you are working out how many ¹/₂s there are in 2.

There are four ¹/₂s in 2, so:

2 ÷ ¹/₂ = 4

If you divide 1¹/₂ by ¼ you are working out how many ¼s there are in 1¹/₂.

There are six ¼s in 1¹/₂, so:

1¹/₂ ÷ ¼ = 6

Can you see a pattern forming? Look at those calculations written out in a different way.

  • 2 ÷ ¹/₂ = 4 and 2 × 2 = 4, so 2 ÷ ¹/₂ is the same as 2 × 2

  • 1¹/₂ ÷ ¼ = 3/2 ÷ ¼ = 6, so 3/2 ÷ ¼ is the same as 3/2 × 4 = 12/2 = 6

So, '÷ ¹/₂' is the same as ‘ × 2’.

and '÷ ¼' is the same as ‘ × 4’.

Top tip - To divide fractions, turn the second fraction upside down, then multiply.

Have a look at the Class Clip below from BBC Teach to learn more about dividing fractions - the section from 02:25 to the end looks at this topic so will help you especially.

Find out more on how to divide fractions

Division with mixed numbers

Remember, a mixed number is made up of a whole number and a fraction, such as 1²/₃.

Now, watch this short video from Pearson to see a demonstration on how to divide fractions when using mixed numbers.

Learn more about dividing fractions and mixed numbers

Practise

Activity 1

Dividing fractions, mixed numbers and problem solving

Test your skills in dividing fractions and working with mixed numbers by having a go at these worksheets from Hodder Education, also attempting the problem solving section at the end. Write your answers on a piece of paper.

Dividing fractions, mixed numbers skills and problem solving

Click here to see the correct answers to the questions.

Activity 2

Fractions and mixed numbers - all skills

Now put all the skills to the test that you have learned in working with fractions and mixed numbers this week with this worksheet of assorted activities from Collins. Write your answers on a piece of paper.

Fractions and mixed numbers - skills

Click here to see the correct answers to the questions.

There's more to learn

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