LEARN · PRACTISE · DISCOVER
Division with Remainders
Sometimes things do not share out perfectly. If you share 13 marbles between 4 friends, each friend gets 3 marbles, but 1 marble is left over. The amount left over is called the remainder. In this lesson you will learn to find remainders and decide what to do with them.
What is a remainder?
A remainder is what is left over after you make as many equal groups as possible. The remainder must always be smaller than the divisor. If it is not, you can make another group.
Example
Share 13 marbles among 4 friends:
- Each friend gets 3 marbles, using 4 × 3 = 12 marbles.
- 13 − 12 = 1 marble is left over.
We write: 13 ÷ 4 = 3 r 1 (read “3 remainder 1”).
If there is nothing left over, the remainder is 0, and we say the number divides exactly. For example, 12 ÷ 4 = 3 with nothing left over.
How to find a remainder
- Find the biggest multiple of the divisor that is not more than the total.
- That gives you the quotient.
- Subtract to find what is left over.
| Problem | Biggest multiple that fits | Quotient | Remainder | Answer |
|---|---|---|---|---|
| 17 ÷ 5 | 5 × 3 = 15 | 3 | 17 − 15 = 2 | 3 r 2 |
| 26 ÷ 4 | 4 × 6 = 24 | 6 | 26 − 24 = 2 | 6 r 2 |
| 50 ÷ 7 | 7 × 7 = 49 | 7 | 50 − 49 = 1 | 7 r 1 |
Check your answer
Multiply the quotient by the divisor, then add the remainder. You should get the total. For 17 ÷ 5 = 3 r 2: 3 × 5 = 15, and 15 + 2 = 17. Correct!
What does the remainder mean?
In real life, we must think about what to do with the remainder. There are three common choices.
Round up
29 children are going on a trip. Each car holds 4 children. 29 ÷ 4 = 7 r 1. Seven cars carry 28 children, but one child still needs a seat! We need 8 cars.
Ignore it
You have 20 sweets and want to make bags of 6. 20 ÷ 6 = 3 r 2. You can make 3 full bags. The 2 extra sweets cannot fill a bag.
Share it
3 friends share 7 pizzas. 7 ÷ 3 = 2 r 1. Each friend gets 2 pizzas, and they can cut the last pizza into 3 equal slices to share. (You will learn about these parts, called fractions, later.)
Key takeaways
- The remainder is what is left over after making equal groups.
- The remainder must be smaller than the divisor.
- Check: quotient × divisor + remainder = total.
- In word problems, decide whether to round up, ignore or share the remainder.
Practice
- 23 ÷ 5
- 38 ÷ 6
- 30 people want to ride a boat. Each boat holds 8 people. How many boats are needed?
Answers: 1 is 4 r 3. 2 is 6 r 2. 3 is 30 ÷ 8 = 3 r 6, so 4 boats are needed (round up).