What is a remainder?
When a number doesn’t divide exactly, the amount left over is the remainder.
17 ÷ 5 = 3 r 2, because 5 × 3 = 15, and 17 − 15 = 2 left over.
- The remainder is always smaller than the number you divide by.
- Check it: 5 × 3 + 2 = 17 ✔
What do I do with the remainder?
In a word problem, the remainder tells you what to do next:
| The question asks… | Do this | Example |
|---|---|---|
| how many are needed to fit everyone or everything | round up | 30 children, 4 per car → 7 r 2 → 8 cars |
| how many full groups, or how many you can afford | round down | 45 eggs, boxes of 6 → 7 r 3 → 7 full boxes |
| how many are left over | the remainder is the answer | 50 sweets shared by 6 → 2 left over |
Watch out! “7 r 2 cars” is never an answer: you can’t have part of a car. Always ask: does the leftover need a place of its own?
Top tip: if the question has money in pounds and pence, change it all to pence first. £2 = 200p.
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