Sometimes a number doesn't share equally. 23 ÷ 5: the most fives that fit is four (4 × 5 = 20), and 3 are left over. We write this as 4 remainder 3, or '4 r 3'. The remainder is always smaller than the divisor — if it isn't, another group fits.
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Equal groups
3 × 4 = 12
12 ÷ 3 = 4
The same picture shows multiplication and division. Each group must have the same number.
Words to know
- remainder
- what is left over after sharing equally
- divisor
- the number you are dividing by
Worked examples
23 ÷ 5
- 1.5 × 4 = 20, the most 5s in 23.
- 2.23 − 20 = 3 left over.
= 4 r 3
17 ÷ 3
- 1.3 × 5 = 15, the most 3s in 17.
- 2.17 − 15 = 2 left over.
= 5 r 2
29 ÷ 4
- 1.4 × 7 = 28, the most 4s in 29.
- 2.29 − 28 = 1 left over.
= 7 r 1
For parents
Method: Bar/counter sharing, then name the leftover.
What to say: Point to the counters that can't be shared — those are the remainder.
Common mistakes:
- Dropping the remainder (23 ÷ 5 → 4).
- Writing the remainder as a decimal (→ 4.3).