Maths · Multiplication & Division
Division with remainders
Divide with remainders, like 25 ÷ 4 = 6 remainder 1.
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What is a remainder?
Sometimes numbers don't divide evenly. The amount left over is called the remainder. Imagine sharing 10 sweets among 3 friends. Each friend gets 3 sweets, and 1 sweet is left. That leftover sweet is the remainder!
Writing division with remainders
We write remainders with an 'r' after the answer. For example, 13 ÷ 4 = 3 r 1. This means 4 goes into 13 three times, with 1 left over.
Checking your answer
You can check if your remainder is correct. Multiply your answer by the divisor, then add the remainder. You should get back to the number you started with! For 13 ÷ 4 = 3 r 1, check: (3 × 4) + 1 = 13. Perfect!
Remainders are always smaller
The remainder must always be smaller than the number you're dividing by. If 17 ÷ 5 = 3 r 2, the remainder 2 is less than 5. If your remainder is bigger, you can divide one more time!
Worked examples
1. 17 ÷ 3 = ?
- How many 3s fit into 17? Count: 3, 6, 9, 12, 15, 18.
- 18 is too big, so 15 is the largest. That's 5 groups of 3.
- 17 minus 15 equals 2. That's the remainder.
- Answer: 17 ÷ 3 = 5 r 2
2. 22 ÷ 5 = ?
- 5 × 4 = 20 and 5 × 5 = 25.
- 20 fits into 22, but 25 is too big. So the answer is 4.
- 22 minus 20 equals 2. That's what's left over.
- Answer: 22 ÷ 5 = 4 r 2
3. 30 ÷ 7 = ?
- 7 × 4 = 28 and 7 × 5 = 35.
- 28 fits into 30, but 35 doesn't. So we have 4 groups of 7.
- 30 minus 28 equals 2.
- Answer: 30 ÷ 7 = 4 r 2
Try it yourself
23 ÷ 4 = ?
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