NumberKey Stage 3

Adding mixed numbers

Add mixed numbers by working with improper fractions.

  • Convert both mixed numbers to improper fractions.
  • Find a common denominator, then add the numerators.
  • Simplify if needed, then convert an improper answer back to a mixed number.

Example 1

Convert, then add

Calculate. Give your answer as a mixed number.

Convert both mixed numbers to improper fractions.Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.48 parts make 4 wholes; 5 parts remain.

Example 2

Convert back to a mixed number

Work out the result. Give your answer as a mixed number.

Convert both mixed numbers to improper fractions.Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.24 parts make 4 wholes; 1 part remains.

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

Your turn

Question 1

Calculate. Give your answer as a mixed number.

Check answer
Convert both mixed numbers to improper fractions.Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.12 parts make 3 wholes; 3 parts remain.
Question 2

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

Check answer
Convert both mixed numbers to improper fractions.Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.Highest common factor: 3.Cancel the common factor from top and bottom.8 parts make 4 wholes; 1 part remains.
Question 3

Calculate. Give your answer as a mixed number.

Check answer
Convert both mixed numbers to improper fractions.Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.120 parts make 6 wholes; 3 parts remain.
Question 4

Calculate. Give your answer as a mixed number.

Check answer
Convert both mixed numbers to improper fractions.Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.120 parts make 5 wholes; 5 parts remain.
Question 5

Calculate. Give your answer as a mixed number.

Check answer
Convert both mixed numbers to improper fractions.Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.108 parts make 6 wholes; 13 parts remain.
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