Division With Remainders
Practise division that doesn’t come out evenly — here you find the remainder, the amount left over.
Practice now
What a remainder is
Not every division is tidy. When a number can’t be split into equal whole groups, the bit left over is the remainder. Sharing 17 among 5 gives 3 each, with 2 left over — we write 17 ÷ 5 = 3 r2. On this page you practise finding that left-over amount.
- Find the largest multiple of the divisor that fits inside the number.
- Subtract it from the number.
- What is left is the remainder — always smaller than the divisor.
Worked examples
Tips & common mistakes
The key check: a remainder is always smaller than the divisor. If your remainder is bigger than (or equal to) the number you divided by, the divisor went in at least one more time. Finding the right multiple quickly is, again, a times-tables skill.
- Giving a remainder that is bigger than the divisor — it should always be smaller.
- Choosing too small a multiple, leaving more than one group still possible.
- Confusing the quotient (the groups) with the remainder (the leftover) — here we want the leftover.
Frequently asked questions
What is a remainder?
The amount left over when a number cannot be divided into equal whole groups. 17÷5 = 3 remainder 2, because 2 is left after making three groups of 5.
Why is this page asking only for the remainder?
To practise that one idea cleanly. The full quotient-and-remainder answer is built on long division, which is practised separately.
How big can a remainder be?
Always smaller than the divisor. Divide by 5 and the remainder can only be 0, 1, 2, 3 or 4.
What grade is this?
Division with remainders is a grade 4 skill.
How does this connect to long division?
Long division produces a quotient and, when it does not divide evenly, a remainder — the same leftover idea, just inside the bigger method.