Long Division with Remainders Worksheets

After a demonstration, let students work the twelve problems on their own while you walk the room. Each remainder must be at least 1 and smaller than the divisor, so tell children to check that rule before moving on. The answer key prints each quotient with its R. Have students verify by multiplying the quotient by the divisor and adding the remainder, which should give back the dividend. Switching Remainders off in the controls gives the exact-division sheet for comparison.

A remainder is what is left when the divisor no longer fits. The idea is easy to say and hard to feel, so many children think the remainder can be as large as the divisor. Here the rule becomes checkable: dividing by 7, a remainder of 7 or more means the quotient digit was too small. The page assumes division facts and the long division steps are known. After it, students move to fractions or decimals as the way to write what is left.

Use twelve problems for steady learning. If a student keeps writing remainders that are too large, slow down and write the divisor beside each remainder to compare. Thirty problems works as a timed review for confident children. Remainders is already on for this page, and turning it off gives exact division when you need an easier warm-up. Missing number mode is optional for extension.

Can a remainder ever be zero here?

No. With the switch on, every problem leaves a remainder of at least 1. If a student gets R0, there is a calculation slip somewhere in the steps, so it is a built-in check.

How do I check a long division answer with a remainder?

Multiply the quotient by the divisor, add the remainder, and the sum should equal the dividend. Having students do this check on the page teaches more than reading the answer key.

Should remainders be written as R or as fractions?

The key uses R, the form third and fourth grade programs teach first. Later the same problems work with fractional remainders, where only the final line changes.