Divide by a one-digit divisor (short division) - Exact
Theory
Short division (the “bus stop” method) divides one digit at a time from the left. Any remainder is carried to the next digit, and a zero is written in the answer when the divisor does not fit. This Year 5 maths page shows how to divide three- and four-digit numbers exactly and check the answer by multiplying.
In short division the number being divided (the dividend) goes under the bus-stop line, the divisor outside, and the answer (the quotient) on top.
Divide from the left. If a digit does not divide exactly, write the quotient digit on top and carry the remainder in front of the next digit, making a two-digit number.
If the divisor does not fit into a digit at all, write \(0\) in the quotient (except at the very start) and carry the digit across.
Exact means the final remainder is \(0\). Check by multiplying: quotient \(\times\) divisor \(=\) dividend.
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 and its check:
Short division
- Set out the dividend under the line and the divisor outside.
- Divide the first digit (or first two, if the first is too small). Write the answer on top.
- Carry the remainder to the front of the next digit.
- Repeat until the last digit, then check by multiplying.
| \(\text{H: }8 \div 2\) | \(=\) | \(4\) |
| \(\text{T: }4 \div 2\) | \(=\) | \(2\) |
| \(\text{O: }6 \div 2\) | \(=\) | \(3\) |
The answer is \(423\).
| \(\text{H: }9 \div 4\) | \(=\) | \(2 \text{ r } 1\) |
| \(\text{T: }18 \div 4\) | \(=\) | \(4 \text{ r } 2\) |
| \(\text{O: }24 \div 4\) | \(=\) | \(6\) |
The answer is \(246\).
| \(\text{H: }7 \div 5\) | \(=\) | \(1 \text{ r } 2\) |
| \(\text{T: }23 \div 5\) | \(=\) | \(4 \text{ r } 3\) |
| \(\text{O: }35 \div 5\) | \(=\) | \(7\) |
The answer is \(147\).
| \(\text{H: }15 \div 6\) | \(=\) | \(2 \text{ r } 3\) |
| \(\text{T: }37 \div 6\) | \(=\) | \(6 \text{ r } 1\) |
| \(\text{O: }12 \div 6\) | \(=\) | \(2\) |
Start with \(15\) because \(1\) is smaller than \(6\). The answer is \(262\).
| \(\text{Th: }6 \div 6\) | \(=\) | \(1\) |
| \(\text{H: }3 \div 6\) | \(=\) | \(0 \text{ r } 3\) |
| \(\text{T: }32 \div 6\) | \(=\) | \(5 \text{ r } 2\) |
| \(\text{O: }24 \div 6\) | \(=\) | \(4\) |
The \(3\) hundreds do not make a group of \(6\), so write \(0\). The answer is \(1054\).
| \(\text{H: }34 \div 8\) | \(=\) | \(4 \text{ r } 2\) |
| \(\text{T: }25 \div 8\) | \(=\) | \(3 \text{ r } 1\) |
| \(\text{O: }16 \div 8\) | \(=\) | \(2\) |
Each class gets \(432\) stickers. To check, multiply: \(432 \times 8 = 3456\).
| \(\text{H: }28 \div 7\) | \(=\) | \(4\) |
| \(\text{T: }5 \div 7\) | \(=\) | \(0 \text{ r } 5\) |
| \(\text{O: }56 \div 7\) | \(=\) | \(8\) |
Ty left out the zero in the tens. The answer is \(408\). Check: \(408 \times 7 = 2856\).
Common pitfalls
Frequently asked questions
How do you do short division?
Divide each digit from the left. Write the answer above, and carry any remainder to the next digit. \(984 \div 4 = 246\).
What do you do when the divisor does not fit into a digit?
Write \(0\) in the quotient and carry the digit to the next place, as in \(6324 \div 6 = 1054\).
What if the first digit is smaller than the divisor?
Use the first two digits together. In \(1572 \div 6\), start with \(15 \div 6\).
How do you check a division?
Multiply the answer by the divisor. \(246 \times 4 = 984\).
Why is it called the bus stop method?
The line over the dividend with the divisor outside looks like a bus shelter.