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How to check long division answers
Every long division answer can be checked with multiplication. Multiply the answer by the divisor, then add the remainder. If you get the number you started with, the answer is right.
It takes less than a minute, and it teaches children that division and multiplication are two sides of the same fact.
Worked examples
- No remainder. For 952 ÷ 4 = 238, check 238 × 4 = 952. It matches.
- With a remainder. For 347 ÷ 6 = 57 R 5, check 6 × 57 + 5 = 347. It matches.
- Catching a mistake. A child writes 428 ÷ 4 as 17. Check: 17 × 4 = 68, nowhere near 428. The right answer is 428 ÷ 4 = 107, and 107 × 4 = 428.
- Quick estimate. 347 ÷ 6 is a bit less than 360 ÷ 6, which is 60. So 57 is reasonable.
6 checks to try: what number did each division start with?
- 7 × 28 + 3 = ?
- 5 × 43 + 2 = ?
- 8 × 64 + 1 = ?
- 9 × 35 + 4 = ?
- 12 × 26 + 9 = ?
- 6 × 108 + 5 = ?
Show answers
- 7 × 28 + 3 = 199
- 5 × 43 + 2 = 217
- 8 × 64 + 1 = 513
- 9 × 35 + 4 = 319
- 12 × 26 + 9 = 321
- 6 × 108 + 5 = 653
Tips for parents
- The remainder must be smaller than the divisor. If it isn't, the answer is too small.
- Estimate before dividing, then check after.
- Let your child find their own mistakes with the check, rather than marking answers wrong.
Questions parents ask
How do you check long division with a remainder?
Multiply the answer by the divisor, then add the remainder. If the result equals the number you divided, the answer is correct.