Parents helping with homework are often surprised to find two written methods for division. Short division is the "bus stop" layout with little numbers carried between digits. Long division writes out every multiplication and subtraction underneath. They give the same answers and use the same idea. The difference is how much of the working stays in your head.
What short division looks like
Take 936 ÷ 4:
- 9 ÷ 4 = 2 remainder 1. Write 2 above the 9 and carry the 1 to make 13.
- 13 ÷ 4 = 3 remainder 1. Write 3 and carry the 1 to make 16.
- 16 ÷ 4 = 4 exactly. Write 4.
Answer: 234. The remainders are written as small digits next to the next number, and the multiplication (how many 4s make 13?) is done mentally.
What long division looks like
Take 7,896 ÷ 24. The steps are the same (divide, multiply, subtract, bring down) but each one is written out:
- 78 ÷ 24 = 3. Write 3 above. Multiply: 3 × 24 = 72. Subtract: 78 − 72 = 6.
- Bring down the 9 to make 69. 69 ÷ 24 = 2. 2 × 24 = 48. 69 − 48 = 21.
- Bring down the 6 to make 216. 216 ÷ 24 = 9. 9 × 24 = 216. 216 − 216 = 0.
Answer: 329. Writing the subtraction down matters here because few people can work out 216 − 9 × 24 in their head reliably.
Checking either method
The check is the same too: multiply the answer by the divisor and add any remainder. 234 × 4 = 936, and 329 × 24 = 7,896. For long division practice, it also helps to compare each written row with a worked solution. A step-by-step solver such as https://www.longdivisioncalculator.org/ shows every divide, multiply, subtract and bring-down line, so a child can find exactly where their working went wrong rather than just seeing a different answer.
When to use which
| Situation | Better method | Why |
|---|---|---|
| One-digit divisor (÷ 3, ÷ 7) | Short | The mental steps are small times-table facts |
| Divisors like 11, 12, 25 that you know well | Short (if confident) | You can carry the remainders mentally |
| Two-digit divisors you don't know by heart (÷ 24, ÷ 37) | Long | The written subtraction prevents errors |
| Answers needing decimal places | Either | Add a decimal point and zeros, then continue |
In England, the national curriculum introduces short division in Year 5 (up to four digits divided by one digit) and long division in Year 6 (up to four digits divided by a two-digit number). Pupils are also expected to use short division with two-digit divisors where it's sensible. The details are in the mathematics programmes of study.
The same idea underneath
Both methods ask the same question at each step: "How many times does the divisor fit into this part of the number, and what's left over?" Short division keeps the leftover as a carried digit. Long division writes it at the bottom of a subtraction. If a child understands short division, long division is the same process with more writing, not a new topic.
Common mix-ups
- Carrying in long division. Children who learned short division sometimes carry digits in long division too, and then subtract as well, counting the remainder twice.
- Skipping zeros. In 5,838 ÷ 7 = 834, each step has a digit. But in 6,321 ÷ 7 = 903, the middle step gives 0, and forgetting to write it gives 93.
- Misaligned columns. Squared paper keeps each digit of the answer above the right digit of the dividend.
Summary
- Use short division for one-digit divisors and familiar small divisors.
- Use long division when the divisor is two digits or more and the mental steps get hard.
- Check by multiplying back, whatever the method.
