Division with remainders
You learn division with a remainder: how many times does the number go in, and what is left over?
How to work it out
- Recite the times table of the divisor.
- Stop at the largest multiple that fits into the number.
- What remains is the remainder.
4 × 4
remainder 2
A worked example
18 ÷ 4
- Count in 4s: 4, 8, 12, 16, 20.
- 20 is too big, but 16 fits: 4 × 4 = 16.
- Left over: 18 − 16 = 2.
- So 4 remainder 2.
More examples
22 ÷ 3
- The biggest number in the 3 times table that fits into 22 is 21: 7 × 3 = 21.
- Left over: 22 − 21 = 1.
- So 7 remainder 1.
29 ÷ 5
- The biggest number in the 5 times table that fits into 29 is 25: 5 × 5 = 25.
- Left over: 29 − 25 = 4.
- So 5 remainder 4.
Try it yourself
35 ÷ 6 =
31 ÷ 6 =
Watch out
You stop too soon and the remainder is too big: for 18 ÷ 4 you say 3 remainder 6.
If the number still goes into the remainder, it goes in one more time. The remainder must be smaller than 4.
You forget to write the remainder: for 18 ÷ 4 you say 4.
After dividing, check whether anything is left over, and write it as the remainder.
Tips
- The remainder is always smaller than the number you divide by.
- Check with multiplication and addition: 4 × 4 = 16 and 16 + 2 = 18.
Exceptions
- If the division comes out exactly, like 20 ÷ 4, the remainder is 0 and you do not write one.
Why it works
Not every division comes out exactly. If you share 18 marbles between 4 children, each child gets 4 and there are 2 left over. The times table tells you how many times it goes in, and what is left is the remainder. The remainder is always smaller than the number you divide by.