Dividing

Dividing shares a number into equal groups, or finds how many equal groups fit. For bigger numbers we use short division, and what to do with a remainder depends on the question.

Key facts

  • Dividing shares a number into equal groups, or finds how many groups fit: 12 ÷ 3 = 4.
  • Use the times tables backwards: 56 ÷ 8 = 7 because 7 × 8 = 56.
  • To divide a 2-digit number, split it into parts the divisor goes into: 72 ÷ 3 = 60 ÷ 3 + 12 ÷ 3 = 24.
  • Short division: divide each digit from the left, carrying the remainder to the next digit.
  • Remainders: round up when everything must fit (buses, boxes); round down when only whole ones count (pieces, packs).
  • Check a division by multiplying back: quotient × divisor + remainder = number.

Worked examples

Example 1

Share 20 sweets equally between 4 children. How many does each child get?

  1. Give one to each child, again and again, until none are left.
  2. Each child gets 5. 20 ÷ 4 = 5

Answer: 5

Example 2

15 strawberries are shared equally onto 3 plates. How many strawberries go on each plate?

  1. Put one on each plate in turn until none are left.
  2. Each plate gets 5. 15 ÷ 3 = 5

Answer: 5

Example 3

24 children get into teams of 4. How many teams are there?

  1. Count in 4s until you reach 24. 4, 8, 12, 16, 20, 24
  2. That is 6 jumps, so there are 6 teams.

Answer: 6 teams

Example 4

Use a times table fact to work out 56 ÷ 8.

  1. Which number times 8 makes 56? 7 × 8 = 56
  2. So 56 shared into 8 equal groups is 7. 56 ÷ 8 = 7

Answer: 7

Example 5

Work out 72 ÷ 3.

  1. Split 72 into parts that 3 goes into. 72 = 60 + 12
  2. Divide each part, then add. 60 ÷ 3 + 12 ÷ 3 = 20 + 4 = 24

Answer: 24

Example 6

1,476 ÷ 6

  1. Start with 14 hundreds: 14 ÷ 6 = 2 remainder 2.
  2. Carry the 2 to make 27: 27 ÷ 6 = 4 remainder 3.
  3. Carry the 3 to make 36: 36 ÷ 6 = 6.
  4. Answer: 246

Answer: 246

Example 7

A carton holds 6 eggs. How many cartons are needed for 80 eggs?

  1. Divide the eggs into sixes. 80 ÷ 6 = 13 remainder 2
  2. 13 cartons hold 78 eggs. The last 2 eggs need one more carton.
  3. So 14 cartons.

Answer: 14

Example 8

Work out 43 ÷ 5, and give the remainder.

  1. The biggest multiple of 5 that is not more than 43 is 40. 8 × 5 = 40
  2. 43 − 40 leaves 3. 43 ÷ 5 = 8 remainder 3

Answer: 8 remainder 3

Example 9

A ribbon 250 cm long is cut into pieces 8 cm long. How many whole pieces can be cut?

  1. Divide the length by the length of one piece. 250 ÷ 8 = 31 remainder 2
  2. The 2 cm left over is too short for a piece, so round down: 31 pieces.

Answer: 31 pieces

Example 10

A factory packs 9,630 eggs into boxes of 6. How many boxes does it fill?

  1. 9 ÷ 6 is 1, with 3 left over. Carry the 3.
  2. 36 ÷ 6 is 6.
  3. 3 ÷ 6 is 0, with 3 left over. Write 0 and carry the 3.
  4. 30 ÷ 6 is 5. 9,630 ÷ 6 = 1,605

Answer: 1,605 boxes

Example 11

Work out 6,354 ÷ 9, and check your answer by multiplying.

  1. 9 does not go into 6, so carry the 6: 63 ÷ 9 is 7.
  2. 5 ÷ 9 is 0, with 5 left over. Write 0 and carry the 5.
  3. 54 ÷ 9 is 6. 6,354 ÷ 9 = 706

Answer: 706