What’s left over
Not every number shares out evenly. Share 17 cookies among 5 friends: each gets 3, and 2 are left. Those 2 cookies are the remainder.
We write: 17 ÷ 5 = 3 R2
| Part | Value |
|---|---|
| Dividend | 17 |
| Divisor | 5 |
| Quotient | 3 |
| Remainder | 2 |
The check
Quotient × divisor + remainder = dividend
3 × 5 + 2 = 17 ✓
The golden rule
The remainder must always be smaller than the divisor. If you have a remainder of 6 when dividing by 5, you could have made another group of 5.
Finding remainders
Example: 43 ÷ 6
- What multiple of 6 is just below 43? 6 × 7 = 42.
- 43 − 42 = 1.
- Answer: 7 R1.
What to do with the remainder
In word problems, you must interpret the remainder. It depends on the question.
| Situation | What to do | Example |
|---|---|---|
| Leftovers don’t matter | Ignore it | 26 apples, 4 per bag: how many full bags? 26 ÷ 4 = 6 R2 → 6 bags |
| Everyone/everything must fit | Round up | 26 people, 4 per car: how many cars? → 7 cars |
| The question asks about leftovers | Give the remainder | How many apples are left? → 2 |
| Things can be split | Write it as a fraction or decimal | 26 pizzas ÷ 4 people = 6½ each |
Remainders as fractions and decimals
The remainder can become a fraction: the remainder over the divisor.
- 17 ÷ 5 = 3 R2 = 3 and 2/5 = 3.4
- 26 ÷ 4 = 6 R2 = 6 and 2/4 = 6½ = 6.5
Worked examples
Example 1: 29 ÷ 4
4 × 7 = 28. 29 − 28 = 1. 7 R1.
Example 2: 50 students go on a trip. Each van holds 8. How many vans?
50 ÷ 8 = 6 R2. The 2 extra students still need a ride: 7 vans.
Example 3: A 100 cm ribbon is cut into 30 cm pieces. How many full pieces, and how much is left?
100 ÷ 30 = 3 R10. 3 pieces with 10 cm left over.
Common mistakes
- A remainder bigger than the divisor. Divide again.
- Ignoring the remainder when it should round up (leaving people behind!).
- Writing the remainder as a decimal directly: 17 ÷ 5 = 3 R2 is 3.4, not 3.2.
Try it yourself
- 38 ÷ 5
- 61 ÷ 7
- 45 eggs go in cartons of 12. How many full cartons?
- 45 eggs: how many cartons are needed to hold them all?
- Write 23 ÷ 4 as a mixed number.
Answers: 1) 7 R3 2) 8 R5 3) 3 4) 4 5) 5¾
Quick recap
- The remainder is what’s left over; it must be smaller than the divisor.
- Check: quotient × divisor + remainder = dividend.
- Interpret it: ignore it, round up, report it, or write a fraction.