Divide by a one-digit divisor (short division) - Exact
Theory
Short division works through the dividend one digit at a time from the left, writing each answer above the line and carrying any leftover. When nothing is left over at the end, the division is exact.
Short division works through the dividend one digit at a time, from the left, writing each answer above the line.
The number being divided is the dividend; the number dividing it is the divisor; the answer is the quotient.
When the last digit divides with nothing left over, the division is exact — there is no remainder.
Divide each digit in turn, carrying any leftover to the next digit.
| Digit | Divide | Write | Carry |
|---|---|---|---|
| Hundreds | \(6\div6=1\) | \(1\) | — |
| Tens | \(4\div6=0\) | \(0\) | \(4\) |
| Ones | \(48\div6=8\) | \(8\) | — |
How to divide with short division
- Divide the divisor into the first digit and write the answer above it.
- Carry any leftover to the next digit as a small number.
- Write a zero above if the divisor does not fit that digit.
- Continue to the last digit; nothing left over means an exact answer.
\(9\div3=3\), \(3\div3=1\), \(6\div3=2\).
| \(936 \div 3\) | \(=\) | \(312\) |
\(4\div6=0\), carry \(4\); \(48\div6=8\).
| \(648 \div 6\) | \(=\) | \(108\) |
\(9\div5=1\), carry \(4\); \(42\div5=8\), carry \(2\); \(25\div5=5\).
| \(925 \div 5\) | \(=\) | \(185\) |
| \(7256 \div 8\) | \(=\) | \(907\) |
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Common pitfalls
Frequently asked questions
How does short division work?
Divide the divisor into each digit of the dividend from the left, writing each answer above the line and carrying any leftover to the next digit. \(648\div6=108\).
What does an exact division mean?
It means the last digit divides with nothing left over, so there is no remainder. The answer is a whole number.
What if the divisor does not fit a digit?
Write \(0\) in the quotient above that digit and carry the digit on to join the next one, like \(4\div6=0\) carry \(4\).
How do I check a division answer?
Multiply the quotient by the divisor. If you get back the dividend, the answer is correct. \(108\times6=648\).
Where do I start?
Always start at the left-most digit of the dividend and work to the right, one digit at a time.