Divide by a one-digit divisor (short division) - With a remainder
Theory
When short division does not come out evenly, the amount left at the end is the remainder, written after the quotient. Mid-way leftovers are carried; only the last leftover is the remainder, and it is always smaller than the divisor.
Short division does not always come out evenly. The amount left at the end is the remainder.
Work through the digits carrying any leftover on. At the last digit, whatever cannot be shared is the remainder, written after the quotient.
The remainder is always smaller than the divisor.
Only the leftover from the last digit becomes the remainder; earlier leftovers are carried.
| Digit | Divide | Write | Leftover |
|---|---|---|---|
| Hundreds | \(4\div4=1\) | \(1\) | — |
| Tens | \(9\div4=2\) | \(2\) | carry \(1\) |
| Ones | \(14\div4=3\) | \(3\) | remainder \(2\) |
How to divide with a remainder
- Divide each digit in turn, carrying any leftover to the next digit.
- Write each answer digit above the line.
- Stop at the last digit: whatever is left cannot be shared.
- Write that leftover as the remainder after the quotient.
\(14\div4=3\) with \(2\) left.
| \(494 \div 4\) | \(=\) | \(123\) r \(2\) |
\(5\div3=1\) with \(2\) left.
| \(725 \div 3\) | \(=\) | \(241\) r \(2\) |
\(3\div5=0\) with \(3\) left.
| \(853 \div 5\) | \(=\) | \(170\) r \(3\) |
| \(638 \div 7\) | \(=\) | \(91\) r \(1\) |
1 pencil is left over.
Common pitfalls
Frequently asked questions
How do you show a remainder in short division?
Work through the digits carrying leftovers on. The amount left after dividing the last digit is written as the remainder after the quotient, such as \(123\) r \(2\).
Why must the remainder be smaller than the divisor?
If the remainder were as big as the divisor, one more group would fit and the quotient would go up by one. So dividing by \(4\) gives a remainder of \(0\), \(1\), \(2\) or \(3\).
What is the difference between a carry and a remainder?
A carry is a leftover from a middle digit that joins the next digit. A remainder is the leftover from the very last digit, which cannot be divided further.
How do I check a division with a remainder?
Multiply the quotient by the divisor and add the remainder. \(123\times4+2=494\).
What if a digit gives zero in the quotient?
Write \(0\) above that digit and carry the whole amount on, as in \(853\div5\) where the ones give \(0\) with \(3\) left.