Long division is the paper method for dividing a big number by another number when you can't do it in your head. It repeats four small moves, divide, multiply, subtract, bring down, until the digits run out.
Try it with your own problem ↓
The steps
- Write the number being divided (the dividend) under the bracket and the number you are dividing by (the divisor) outside it.
- Start at the left of the dividend and take just enough digits to make a number that is at least as big as the divisor.
- Divide: ask how many times the divisor fits into that number without going over. Write that digit above the last digit you used.
- Multiply: multiply that digit by the divisor and write the answer underneath.
- Subtract it. The result must be smaller than the divisor. If it isn't, your digit was too small.
- Bring down the next digit of the dividend, next to the result, and repeat from the divide step.
- When there are no digits left, what is at the bottom is the remainder. Write the answer as the top number, then R and the remainder.
A worked example
Work out 847 ÷ 12.
7 0 R 7
-------
12 ) 8 4 7
8 4
---
0 7
0 0
---
7
- 12 does not go into 8, so take two digits: 84.
- Divide: 12 goes into 84 seven times (12 × 7 = 84). Write 7 above the 4.
- Multiply and subtract: 12 × 7 = 84, and 84 − 84 = 0.
- Bring down the 7. You now have 07, which is 7.
- 12 goes into 7 zero times. Write 0 above the 7. Then 12 × 0 = 0 and 7 − 0 = 7.
- No digits are left, so the remainder is 7.
847 ÷ 12 = 70 R 7. Check: 12 × 70 + 7 = 840 + 7 = 847. ✓
Common mistakes
- Skipping the zero. When the divisor doesn't fit, you still write 0 in the answer. Leaving it out turns 70 into 7.
- Subtraction slips. Most wrong answers come from the subtract step, so check each one by adding back.
- A leftover that is too big. If the number at the bottom is as big as the divisor (or bigger), go back and use a larger digit.
- Misaligned digits. Each digit of the answer sits right above the digit of the dividend you just used.
Questions people ask
What do I do with the remainder?
Write it with an R, as in 70 R 7, or turn it into a fraction over the divisor: 70 7/12. For a decimal answer, add a decimal point and zeros to the dividend and keep going.
How do I check a long division answer?
Multiply the answer by the divisor, then add the remainder. You should get the dividend back: 12 × 70 + 7 = 847.
What if I can't tell how many times the divisor fits?
Estimate with round numbers (12 is about 10), try a digit, and fix it if the product is too big or the remainder is too big.
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