Divide by a one-digit divisor (short division) - With a remainder
Theory
Short division does not always come out exactly. The amount left after the last digit is the remainder, written after the quotient: \(587 \div 4 = 146 \text{ r } 3\). This Year 5 maths page shows how to find it, check it with multiplication, and decide in a problem whether the answer should be rounded up.
Use short division as usual. After the last digit, whatever is left is the remainder. Write it as r: \(587 \div 4 = 146 \text{ r } 3\).
The remainder must be less than the divisor. A remainder of \(4\) or more when dividing by \(4\) means a quotient digit is too small.
Check: quotient \(\times\) divisor \(+\) remainder \(=\) dividend. \(146 \times 4 + 3 = 587\).
In the working, O, T, H, Th, TTh, HTh and M stand for ones, tens, hundreds, thousands, ten thousands, hundred thousands and millions.
Short division with a remainder and its check:
Short division with a remainder
- Divide each digit from the left, carrying remainders.
- After the last digit, the amount left is the remainder.
- Write the answer as quotient r remainder.
- Check: quotient \(\times\) divisor \(+\) remainder.
| \(\text{H: }5 \div 4\) | \(=\) | \(1 \text{ r } 1\) |
| \(\text{T: }18 \div 4\) | \(=\) | \(4 \text{ r } 2\) |
| \(\text{O: }27 \div 4\) | \(=\) | \(6 \text{ r } 3\) |
The answer is \(146 \text{ r } 3\).
| \(\text{H: }9 \div 6\) | \(=\) | \(1 \text{ r } 3\) |
| \(\text{T: }31 \div 6\) | \(=\) | \(5 \text{ r } 1\) |
| \(\text{O: }13 \div 6\) | \(=\) | \(2 \text{ r } 1\) |
The answer is \(152 \text{ r } 1\).
| \(\text{H: }23 \div 7\) | \(=\) | \(3 \text{ r } 2\) |
| \(\text{T: }24 \div 7\) | \(=\) | \(3 \text{ r } 3\) |
| \(\text{O: }37 \div 7\) | \(=\) | \(5 \text{ r } 2\) |
The answer is \(335 \text{ r } 2\).
| \(\text{H: }61 \div 8\) | \(=\) | \(7 \text{ r } 5\) |
| \(\text{T: }52 \div 8\) | \(=\) | \(6 \text{ r } 4\) |
| \(\text{O: }43 \div 8\) | \(=\) | \(5 \text{ r } 3\) |
The answer is \(765 \text{ r } 3\).
| \(\text{H: }48 \div 6\) | \(=\) | \(8\) |
| \(\text{T: }3 \div 6\) | \(=\) | \(0 \text{ r } 3\) |
| \(\text{O: }31 \div 6\) | \(=\) | \(5 \text{ r } 1\) |
The \(3\) tens do not make a group of \(6\), so write \(0\). The answer is \(805 \text{ r } 1\).
| \(152 \times 6\) | \(=\) | \(912\) |
| \(912 + 1\) | \(=\) | \(913\) |
The check gives \(913\), so the answer is correct.
| \(\text{T: }35 \div 8\) | \(=\) | \(4 \text{ r } 3\) |
| \(\text{O: }35 \div 8\) | \(=\) | \(4 \text{ r } 3\) |
\(355 \div 8 = 44 \text{ r } 3\). The \(3\) people left need a van too, so \(45\) vans are needed.
Common pitfalls
Frequently asked questions
How do you show a remainder in short division?
Write it after the quotient with r. \(587 \div 4 = 146 \text{ r } 3\).
How do you check a division with a remainder?
Multiply the quotient by the divisor, then add the remainder: \(146 \times 4 + 3 = 587\).
What is the largest remainder when dividing by 8?
\(7\). The remainder is always less than the divisor.
When do you round up the answer?
When everything must be included, such as vans for all the people. \(355 \div 8 = 44 \text{ r } 3\), so \(45\) vans.
What if the divisor does not fit into a digit?
Write \(0\) in the quotient and carry the digit, as in \(4831 \div 6 = 805 \text{ r } 1\).