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Long Division

In one line: Long division is a way to divide a big number by working one digit at a time, from left to right, using four repeating steps: divide, multiply, subtract, bring down.

Why it works

When numbers are too big to divide in your head, long division breaks the job into small, easy pieces. It helps with real tasks like sharing costs, working out how many boxes you need, or splitting a distance into equal parts. It also builds the skills you need later for dividing decimals, working with fractions and dividing in algebra. A few words first: the dividend is the number being divided, the divisor is the number you divide by, the quotient is the answer, and the remainder is what is left over when it does not divide exactly.

Think of it like: Imagine sharing £875 equally between 6 friends, using £100 notes, £10 notes and £1 coins. First you share the £100 notes: each friend gets one, and 2 are left over. You swap those 2 leftover £100 notes for twenty £10 notes, so you now have 27 tens to share. Each friend gets 4 tens, with 3 tens left over. You swap those for 30 coins, making 35 coins. Each friend gets 5, and 5 coins are left over. Each friend gets £145, with £5 left over. That swapping of leftovers into the next smaller place is exactly the 'bring down' step. (Where this breaks: The money picture works well for small divisors, but it gets clumsy when you divide by a two-digit number like 15, because you have to estimate how many fit rather than hand things out one by one. It also does not show what to do with a remainder when you want a decimal or fraction answer instead.)

Worked example

Work out 875 ÷ 6 using long division.

  1. Divide the first digit: 8 ÷ 6 = 1, so write 1 above the 8. Multiply 1 × 6 = 6, then subtract: 8 − 6 = 2.
  2. Bring down the next digit (7) next to the 2 to make 27.
  3. Divide: 27 ÷ 6 = 4, so write 4 above the 7. Multiply 4 × 6 = 24, then subtract: 27 − 24 = 3.
  4. Bring down the last digit (5) to make 35. Divide: 35 ÷ 6 = 5, so write 5 above the 5. Multiply 5 × 6 = 30, then subtract: 35 − 30 = 5.
  5. There are no digits left to bring down, so 5 is the remainder. Check: 145 × 6 = 870, and 870 + 5 = 875.

Answer: 875 ÷ 6 = 145 remainder 5 (written 145 r 5)

Common mistakes

  • Forgetting to write a 0 in the answer when the divisor does not fit into a step (for example getting 12 instead of 102 for 612 ÷ 6); fix it by always writing a digit above every digit you bring down, even if it is 0.
  • Leaving a remainder at a step that is equal to or bigger than the divisor; fix it by checking after each subtraction that what is left is smaller than the divisor, and if not, make your answer digit one bigger.
  • Bringing down two digits at once or skipping a digit; fix it by bringing down exactly one digit each time and ticking it off as you go.
  • Not checking the answer; fix it by multiplying the quotient by the divisor and adding the remainder, which should give back the original number.

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Questions parents ask

What year do kids learn long division?

In the UK, children are expected to use formal long division to divide by two-digit numbers in Year 6, after learning short division in Year 5. In Australia it is usually taught across Years 5 to 7, and in the US students divide by two-digit numbers in Grade 5 and are expected to be fluent with the standard method by Grade 6.

What is the difference between short division and long division?

Both follow the same idea, but in short division you do the multiplying and subtracting in your head and write small carried digits. In long division you write every step out in full, which makes it easier to divide by bigger numbers like 15 or 24 and to spot mistakes.

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

Make sure they know their times tables well, since every step depends on them. Teach a memory aid for the four steps (divide, multiply, subtract, bring down), and encourage them to check each answer by multiplying back. Using squared paper helps keep the digits lined up neatly.

Why does my child keep getting long division wrong?

The most common causes are shaky times tables, digits that are not lined up in columns, and forgetting to write a zero in the answer. Ask your child to talk through one question out loud so you can spot which step is going wrong, then practise just that step.