Long division

Long division is a step-by-step method for dividing large numbers by breaking the problem into smaller, easier parts.

Reading is good — doing is better. Practice Long division as an interactive lesson.

Definition

Long division is a way to divide a big number (the dividend) by another number (the divisor) by working through it one digit at a time, from left to right. You repeat four steps — Divide, Multiply, Subtract, Bring down — until you have used every digit of the dividend.

Remember the rule

Divide → Multiply → Subtract → Bring down. Repeat! (Remember: Dad, Mom, Sister, Brother — D, M, S, B)

Key words

Dividend: The big number you are splitting up. It goes inside the division bracket.
Divisor: The number you are dividing by. It goes outside (to the left of) the division bracket.
Quotient: The answer to a division problem. It goes on top of the division bracket.
Remainder: The amount left over when a number cannot be divided evenly.
Bring down: After you subtract, you pull the next digit of the dividend down next to your leftover number so you can keep dividing.
Partial quotient: Each single digit you write on top of the bracket as you work through the problem step by step.
Divisible: A number is divisible by another when it divides evenly with no remainder.
Estimate: A smart guess that helps you figure out how many times the divisor fits into a number.

Worked examples

84 ÷ 4

→ 21 · 4 goes into 8 exactly 2 times (write 2 on top), then 4 goes into 4 exactly 1 time (write 1 on top). No remainder.

96 ÷ 3

→ 32 · 3 goes into 9 three times (write 3), bring down the 6, 3 goes into 6 twice (write 2). Answer is 32.

75 ÷ 5

→ 15 · 5 goes into 7 once (write 1), subtract to get 2, bring down the 5 to make 25, 5 goes into 25 five times (write 5). Answer is 15.

143 ÷ 7

→ 20 remainder 3 · 7 goes into 14 twice (write 2), subtract to get 0, bring down the 3. 7 does not go into 3, so write 0 on top and 3 is the remainder.

256 ÷ 8

→ 32 · 8 goes into 25 three times (3 × 8 = 24), subtract to get 1, bring down 6 to make 16. 8 goes into 16 twice. Answer is 32.

639 ÷ 3

→ 213 · Divide each digit one at a time: 3 into 6 is 2, 3 into 3 is 1, 3 into 9 is 3. Answer is 213 with no remainder.

Common mistakes

Forgetting to bring down the next digit after subtracting, which makes the answer too short.
Writing the quotient digit in the wrong place on top of the bracket — always line each digit up directly above the digit you just divided into.
Subtracting incorrectly — a small subtraction error early on causes every step after it to be wrong.
Choosing a quotient digit that is too big or too small — always check by multiplying back: if the product is bigger than your current number, your digit is too large.
Forgetting to write a 0 in the quotient when the divisor does not fit into the current number (for example, writing 23 instead of 203).

FAQs

What do I do if the divisor is bigger than the first digit of the dividend?

Look at the first two digits together instead of just the first one. For example, in 156 ÷ 6, since 6 does not go into 1, look at 15. 6 goes into 15 twice, so write 2 on top above the 5.

How do I check if my answer is correct?

Multiply your quotient by the divisor, then add any remainder. If you get back the original dividend, your answer is right. For example, 21 × 4 = 84, which checks out.

What does the remainder mean in real life?

It is the leftover amount. If 7 kids share 75 stickers, each kid gets 10 stickers and there are 5 left over that cannot be shared evenly.

Does the remainder ever get bigger than the divisor?

No — if your remainder is bigger than the divisor, that means your quotient digit was too small and you need to go back and make it one bigger.

How many times do I repeat the steps?

You repeat Divide, Multiply, Subtract, Bring down until you have brought down every digit of the dividend and finished dividing.

Is long division the only way to divide big numbers?

No, there are other methods like partial quotients, but long division is the standard method taught in 4th grade and is very useful for dividing even larger numbers later on.

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