Adding fractions

You can only add fractions when the pieces are the same size, so the denominators must match. If they don’t, change the fractions to equivalent fractions with a common denominator first, then add the numerators.

Key facts

  • Same denominator: add or subtract the tops. The bottom stays the same.
  • Different denominators: first change both to a common denominator (the lowest common multiple is easiest). Then add or subtract.
  • Never add the bottoms: 1/2 + 1/3 is not 2/5.
  • Mixed numbers: add the wholes and the fractions separately, or turn both into improper fractions.
  • If the answer is an improper fraction, you can write it as a mixed number: 19/12 = 1 7/12.
  • Simplify the answer at the end.

Worked examples

Example 1

Work out 2/7 + 3/7.

  1. The denominators are the same, so add the numerators. 2 + 3 = 5
  2. The denominator stays 7. 5/7

Answer: 5/7

Example 2

Work out 1/5 + 2/5.

  1. The pieces are all fifths, so add the numerators. 1 + 2 = 3
  2. The denominator stays the same. 1/5 + 2/5 = 3/5

Answer: 3/5

Example 3

Work out 3/8 + 1/8.

  1. Same denominator, so add the numerators. 3/8 + 1/8 = 4/8
  2. Simplify. 4/8 = 1/2

Answer: 1/2

Example 4

Leo eats 2/8 of a pizza and Amy eats 3/8 of the same pizza. How much of the pizza do they eat altogether?

  1. Both are eighths, so add the numerators. 2/8 + 3/8 = 5/8

Answer: 5/8 of the pizza

Example 5

Work out 1/2 + 3/8.

  1. 8 is a multiple of 2, so change the halves into eighths. 1/2 = 4/8
  2. Add the numerators. 4/8 + 3/8 = 7/8

Answer: 7/8

Example 6

Work out 2/3 + 1/4.

  1. 12 is in both the 3 and the 4 times tables.
  2. Change 2/3 to twelfths. 2/3 = 8/12
  3. Change 1/4 to twelfths. 1/4 = 3/12
  4. Add the tops. 8/12 + 3/12 = 11/12

Answer: 11/12

Example 7

Work out 3/4 + 5/6.

  1. 12 is the lowest common multiple of 4 and 6. 3/4 = 9/12, 5/6 = 10/12
  2. Add the numerators. 9/12 + 10/12 = 19/12
  3. Write the improper fraction as a mixed number. 19/12 = 1 7/12

Answer: 1 7/12

Example 8

Work out 1 3/5 + 2 2/3.

  1. Add the whole numbers. 1 + 2 = 3
  2. Add the fractions with a common denominator. 3/5 + 2/3 = 9/15 + 10/15 = 19/15 = 1 4/15
  3. Put them together. 3 + 1 4/15 = 4 4/15

Answer: 4 4/15

Example 9

Work out 1 5/6 + 2 3/4.

  1. Add the whole numbers. 1 + 2 = 3
  2. Add the fractions using twelfths. 10/12 + 9/12 = 19/12 = 1 7/12
  3. Put them together. 3 + 1 7/12 = 4 7/12

Answer: 4 7/12

Example 10

A path is 2 3/4 km long. Ana walks the path, then another 1 2/3 km to the shop. How far does she walk altogether?

  1. Add the whole numbers. 2 + 1 = 3
  2. Add the fractions using twelfths. 9/12 + 8/12 = 17/12 = 1 5/12
  3. Put them together. 3 + 1 5/12 = 4 5/12

Answer: 4 5/12 km