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Long Division Steps: Divide, Multiply, Subtract, Bring Down

In one line: Long division splits a big number into equal parts one digit at a time by repeating four steps: divide, multiply, subtract, bring down.

Why it works

Long division lets you divide numbers that are too big to work out in your head, such as 936 ÷ 12. It breaks one hard problem into lots of small, easy ones. The same four steps are used later for decimals, fractions and algebra, so learning them well now saves trouble later. The number being divided is called the dividend, the number you divide by is the divisor, the answer is the quotient, and anything left over is the remainder.

Think of it like: Imagine sharing money between friends using £100 notes, £10 notes and £1 coins. You share out the biggest notes first. Any £100 notes you cannot share fairly get swapped for £10 notes and added to the £10 pile. Then you share the £10 notes, swap the leftovers for £1 coins, and share those. Each 'swap and add to the next pile' is exactly the 'bring down' step in long division. (Where this breaks: The money picture stops at £1 coins, but long division can keep going past the ones into decimals by adding zeros. It also only shows sharing, while division can also mean 'how many groups of this size fit?', which is often a better way to think about a two-digit divisor like 12.)

Worked example

Work out 936 ÷ 12 using long division.

  1. Divide: 12 does not go into 9, so look at 93. 12 goes into 93 seven times (12 × 7 = 84, and 12 × 8 = 96 is too big). Write 7 above the 3.
  2. Multiply and subtract: 7 × 12 = 84. Then 93 − 84 = 9. The 9 is smaller than 12, so the 7 was right.
  3. Bring down: bring the next digit, 6, down next to the 9 to make 96.
  4. Divide again: 12 goes into 96 exactly eight times (12 × 8 = 96). Write 8 above the 6.
  5. Multiply and subtract: 8 × 12 = 96, and 96 − 96 = 0. There are no digits left to bring down, so the remainder is 0.
  6. Check: 78 × 12 = 936, so the answer is correct.

Answer: 936 ÷ 12 = 78

Common mistakes

  • Forgetting to write a 0 in the answer when the divisor does not fit (for example writing 13 instead of 103 for 618 ÷ 6), so always write a digit above every digit you bring down, even if it is 0.
  • Leaving a remainder that is bigger than or equal to the divisor, which means you chose too small a number, so go back and make that digit of the answer one bigger.
  • Forgetting to bring down a digit or bringing down two at once, so tick each digit of the dividend as you bring it down.
  • Writing digits in the wrong columns so the subtraction goes wrong, so use squared paper and keep each digit lined up under its place value.

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Questions parents ask

What year do kids learn long division?

In the UK, children usually learn short division in Year 5 and formal long division with two-digit divisors in Year 6. In Australia it is typically built up across Years 5 to 7, and in the US children start with one-digit divisors in 4th grade, move to two-digit divisors in 5th grade and are expected to be fluent by 6th grade.

How can I help my child with long division at home?

Teach the four steps as a chant, such as 'Divide, Multiply, Subtract, Bring down', and have them say each step aloud as they work. Squared paper keeps columns neat, and checking every answer by multiplying back builds confidence and catches mistakes.

What should my child know before starting long division?

They should know their times tables up to 12 × 12 quickly and be confident with column subtraction. Understanding place value (hundreds, tens and ones) also helps them see why the 'bring down' step works.

What is the difference between short division and long division?

Both use the same idea, but in short division the remainders are written as small digits and the multiplying and subtracting are done in your head. Long division writes every step out in full, which makes it easier to follow and check, especially with two-digit divisors.