Long division

Long division divides by bigger numbers one step at a time: divide, multiply, subtract, bring down. It’s like short division but writing every step so nothing gets lost.

Key facts

  • Divide, multiply, subtract, bring down: repeat.
  • Writing out multiples of the divisor first helps.
  • A remainder can be written as r, as a fraction, or as a decimal by carrying on after the point.

Worked examples

Example 1

Work out 672 ÷ 16.

  1. Multiples of 16: 16, 32, 48, 64, 80…
  2. 16 into 67 goes 4 times. 4 × 16 = 64, 67 − 64 = 3
  3. Bring down the 2 to make 32. 16 into 32 goes 2 times. 672 ÷ 16 = 42

Answer: 42

Example 2

130 children go on a trip in minibuses of 15. How many minibuses?

  1. 130 ÷ 15 = 8 remainder 10.
  2. The 10 children left over need a bus too. 8 + 1 = 9

Answer: 9