Long Division Worksheets

What is long division?

Long division is the written method for dividing a large number by another number one digit at a time. You divide, multiply, subtract and bring the next digit down, then repeat until every digit is used. What is left at the end is the remainder, and it is always smaller than the divisor.

The four moves, in order

Divide, multiply, subtract, bring down. That is the whole algorithm, and it runs once for every digit of the dividend, so a four-digit number under a one-digit divisor takes the loop four times. The quotient digit goes above the line, directly over the digit you just used, and that placement is half the skill: a child who writes the right digits in the wrong columns gets the wrong answer with perfectly good arithmetic.

Two checks catch nearly every mistake. After each subtraction, what is left must be smaller than the divisor, or the quotient digit was too small. At the end, multiply the quotient by the divisor and add the remainder: you should be back at the dividend exactly.

What is on the 84 sheets

The set starts with two-digit dividends and a single-digit divisor and finishes with five-digit dividends under two-digit divisors. Along the way it covers the things that actually go wrong: remainders, a zero landing inside the quotient, a leading digit smaller than the divisor, and the moment a two-digit divisor stops fitting in your head.

Three layouts run through the whole set. Blank pages give open space to work in, grid-guided pages rule faint squares so the columns stay straight, and the boxed pages print one dashed box for every digit the algorithm will produce, which is the scaffold to hand a child who knows what to do but keeps losing the place value. On top of those sit the formats that catch different errors: build the divisor's multiples first, estimate how many digits the quotient will have before dividing, check the answer by multiplying back, find the missing dividend or divisor, decide whether somebody else's quotient is right, carry the division on past the decimal point, and word problems where the remainder has to mean something.

Every PDF is two pages: the worksheet, then its answer key. The key is not a list of quotients, it is the same page worked out, so you can see which line went wrong rather than just that something did.

Choosing a starting point

If the times tables are not fluent, long division will feel impossible for reasons that have nothing to do with division, so start with the multiplication worksheets and the multiplication chart and come back. If short division and the division facts are the gap, the broad division worksheets cover those first.

Otherwise: three-digit dividends with divisors 2 to 5, then 6 to 9, then remainders, then four digits, then the zero-in-the-quotient pages, then two-digit divisors last. The multiples pages belong immediately before the first two-digit divisor sheet, not after it.

Printing and what comes next

Print at 100% (choose "actual size" in the print dialog) on US Letter or A4 paper. Reading the digits of a large dividend correctly is a place value skill, dividing by 10 and 100 in your head sits in the skip counting worksheets, and once division lands inside longer calculations it belongs with the order of operations worksheets. A remainder written as a fraction is the doorway to the fraction worksheets.