Subtracting fractions

You can only subtract fractions when the pieces are the same size, so the denominators must match. If they don’t, change them to a common denominator first. With mixed numbers you may need to exchange a whole for fraction pieces.

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 subtract the bottoms: 3/4 − 1/2 is not 2/2.
  • When subtracting mixed numbers you may need to exchange a whole: 4 1/5 = 3 6/5.
  • Check a subtraction by adding: your answer plus the fraction you took away gives the fraction you started with.
  • Simplify the answer at the end.

Worked examples

Example 1

Work out 5/6 − 1/6.

  1. Subtract the numerators. 5 − 1 = 4 → 4/6
  2. Simplify. 4/6 = 2/3

Answer: 2/3

Example 2

Work out 7/9 − 4/9.

  1. The pieces are all ninths, so subtract the numerators. 7 − 4 = 3 → 3/9
  2. Simplify. 3/9 = 1/3

Answer: 1/3

Example 3

A jug is 7/10 full of juice. Sam pours out 3/10 of a jug. How full is the jug now?

  1. Both are tenths, so subtract the numerators. 7/10 − 3/10 = 4/10
  2. Simplify. 4/10 = 2/5

Answer: 2/5 full

Example 4

Work out 3/4 − 3/8.

  1. 8 is a multiple of 4, so change the quarters into eighths. 3/4 = 6/8
  2. Subtract the numerators. 6/8 − 3/8 = 3/8

Answer: 3/8

Example 5

Work out 4/5 − 1/3.

  1. 15 is the lowest common multiple of 5 and 3. 4/5 = 12/15, 1/3 = 5/15
  2. Subtract the numerators. 12/15 − 5/15 = 7/15

Answer: 7/15

Example 6

Sipho earns £12,000 a month. He spends 1/4 of it on rent and 1/3 on food. How much is left?

  1. Fraction spent: 1/4 + 1/3 = 3/12 + 4/12 = 7/12
  2. Fraction left: 1 − 7/12 = 5/12
  3. 5/12 of 12,000: 12,000 ÷ 12 × 5 = 5,000

Answer: £5,000

Example 7

Work out 3 1/4 − 1 2/3.

  1. Change both to improper fractions. 13/4 − 5/3
  2. Use 12 as the common denominator. 39/12 − 20/12 = 19/12
  3. Back to a mixed number. 19/12 = 1 7/12

Answer: 1 7/12

Example 8

Work out 5 1/3 − 2 3/4.

  1. Use twelfths. 5 4/12 − 2 9/12
  2. 4 twelfths is less than 9 twelfths, so exchange 1 whole for 12 twelfths. 5 4/12 = 4 16/12
  3. Subtract the wholes and the fractions. 4 16/12 − 2 9/12 = 2 7/12

Answer: 2 7/12

Example 9

A ribbon is 4 1/2 m long. Mia cuts off 1 5/6 m. How much ribbon is left?

  1. Use sixths. 4 3/6 − 1 5/6
  2. Exchange 1 whole for 6 sixths. 4 3/6 = 3 9/6
  3. Subtract, then simplify. 3 9/6 − 1 5/6 = 2 4/6 = 2 2/3

Answer: 2 2/3 m