How do you check a long division answer?

The quickest way to check a long division answer is to reverse the operation. Multiply the quotient by the divisor, then add the remainder if there is one. The result should equal the dividend. This works because dividend = divisor × quotient + remainder.

For example, suppose 965 is divided by 8 and the written answer is 120 remainder 5. Multiply 120 by 8 to get 960, then add 5. The total is 965, so the answer passes the basic check. The remainder must also be smaller than the divisor. A remainder of 8 or more means another whole unit should have been included in the quotient.

When the answer is a decimal, multiply the divisor by the entire decimal quotient. If the calculation stopped at a chosen number of places, the product may be close rather than exact because the quotient was rounded or truncated. I keep extra decimal places during the check and round only at the end. A fraction can be checked by multiplying the quotient fraction by the divisor and simplifying.

Estimation catches a different kind of mistake. If 965 is close to 960 and 8 goes into 960 about 120 times, a quotient near 120 is reasonable. An answer near 12 or 1,200 suggests that a place value was lost or added. I also scan each long-division row to make sure every brought-down digit was used once and that the subtraction signs were aligned.

For a second arithmetic check, longdivisioncalculator.org can show the quotient and remainder. I compare that output with my own multiplication rather than copying it without review. Reverse-checking is valuable in homework, invoices, measurements, and any calculation where a single misplaced digit could change the result. The original dividend, divisor, quotient, and remainder should remain visible in my notes. Keeping the remainder visible makes the reverse check much less likely to be overlooked.