NumberKS3 / GCSE

Dividing mixed numbers

Divide mixed numbers by working with improper fractions.

  • Convert both mixed numbers to improper fractions.
  • Multiply the first fraction by the reciprocal of the second.
  • Simplify if needed, then convert an improper answer back to a mixed number.

Example 1

Convert, then divide

Calculate. Give your answer as a mixed number in its simplest form.

Convert both mixed numbers to improper fractions.Keep the first fraction and multiply by the reciprocal of the second.Highest common factor: 6.Cancel the common factor from top and bottom.2 parts make 1 whole; 1 part remains.

Example 2

Simplify the result

Work out the result and simplify fully.

Convert both mixed numbers to improper fractions.Keep the first fraction and multiply by the reciprocal of the second.Highest common factor: 30.Cancel the common factor from top and bottom.

Remember
A mixed number represents the whole number plus its fraction part.

Your turn

Question 1

Calculate. Give your answer in its simplest form.

Check answer
Convert both mixed numbers to improper fractions.Keep the first fraction and multiply by the reciprocal of the second.Highest common factor: 10.Cancel the common factor from top and bottom.
Question 2

Calculate. Give your answer as a mixed number in its simplest form.

Check answer
Convert both mixed numbers to improper fractions.Keep the first fraction and multiply by the reciprocal of the second.Highest common factor: 6.Cancel the common factor from top and bottom.4 parts make 2 wholes; 1 part remains.
Question 3

Calculate. Give your answer in its simplest form.

Check answer
Convert both mixed numbers to improper fractions.Keep the first fraction and multiply by the reciprocal of the second.Highest common factor: 22.Cancel the common factor from top and bottom.
Question 4

Calculate. Give your answer in its simplest form.

Check answer
Convert both mixed numbers to improper fractions.Keep the first fraction and multiply by the reciprocal of the second.Highest common factor: 21.Cancel the common factor from top and bottom.
Question 5

Calculate. Give your answer as a mixed number in its simplest form.

Check answer
Convert both mixed numbers to improper fractions.Keep the first fraction and multiply by the reciprocal of the second.Highest common factor: 20.Cancel the common factor from top and bottom.2 parts make 1 whole; 1 part remains.