Maths
What is a remainder?
Quick answer
A remainder is what is left over when one number does not divide exactly into another. In 17 ÷ 5 = 3 remainder 2, the 2 is left over after making three groups of 5.
In one sentence
A remainder is the amount left over when you divide a number into equal groups and some does not fit.
Explained
Imagine you have 17 biscuits to share between 5 friends. Each friend gets 3, which uses 15 biscuits. Two biscuits are left over, and you cannot share them out equally. We write this as
17 ÷ 5 = 3 remainder 2, or 3 r 2.
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To find a remainder, use your times tables. Find the biggest multiple of the divisor that does not go over your number, and subtract. For 17 ÷ 5: the multiples of 5 are 5, 10, 15, 20. The biggest that fits is 15, which is 5 × 3. Then 17 − 15 = 2.
You can check by multiplying back: (divisor × answer) + remainder = the number you started with. Here 5 × 3 + 2 = 17. Correct.
The remainder is always smaller than the divisor. If it is as big or bigger, you can fit in another group. When the remainder is 0, the division is exact, and the number is a multiple of the divisor.
What you do with a remainder depends on the question. If 30 children travel in cars that hold 4 each, 30 ÷ 4 = 7 remainder 2. Seven cars are not enough; the two extra children need an eighth car, so round up. If you are making bags of 4 sweets from 30 sweets, you can make 7 bags and ignore the 2 left over, so you round down. Sometimes you share the remainder as a fraction: 17 ÷ 5 = 3 2/5, or as a decimal, 3.4.
For bigger numbers, you use long division. The basic idea is in division.
Examples
| Sum | Answer | Check |
|---|---|---|
| 17 ÷ 5 | 3 r 2 | 5 × 3 + 2 = 17 |
| 23 ÷ 4 | 5 r 3 | 4 × 5 + 3 = 23 |
| 40 ÷ 8 | 5 r 0 | 8 × 5 = 40 |
| 29 ÷ 6 | 4 r 5 | 6 × 4 + 5 = 29 |
Common mistakes
- A remainder that is too big. In 29 ÷ 6, 4 r 5 is right but 3 r 11 is not.
- Forgetting what the question asks. For the number of cars needed, round up.
- Forgetting the remainder. Say "3 remainder 2", not just "3".
Quick quiz
Remainders
Check what you know with 4 quick questions.
Question 1 of 4
What is 17 ÷ 5?
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Related topics
Division
Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.
Times tables
Times tables are lists of the multiplication facts for a number, such as 3 × 1 = 3 up to 3 × 12 = 36. Knowing them by heart speeds up almost all later maths.
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Long division splits a big number into equal groups by repeating four steps: divide, multiply, subtract, bring down. Work from the left, one digit at a time.
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2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
3D shapes
3D shapes are solid shapes with length, width and height, like cubes, spheres, cylinders and pyramids. They have faces, edges and vertices.