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Long Division Made Simple: A Step-by-Step Method

By John Cabardo 3 min read Math Grade 5

Divide, multiply, subtract, bring down. A clear walkthrough of long division with worked examples, plus the mistakes to watch for.

A long division problem written on paper

Long division is often the most dreaded topic of the upper elementary years. It has a lot of steps, and one small slip early on carries through to a wrong answer. The good news is that the steps repeat in exactly the same order every time. Once a child has the routine, it is just practice.

Before starting: check the foundations

Long division uses three skills over and over: multiplication facts, subtraction and place value. If a child has to count on their fingers to find 7 × 8, every division problem becomes exhausting. Spend a week or two on facts first if needed, with our multiplication worksheets or simple division fact worksheets, before tackling the long method.

The four steps

Many classrooms teach a memory phrase for the repeating cycle:

  1. Divide: how many times does the divisor go into this part of the number?
  2. Multiply: multiply that answer by the divisor.
  3. Subtract: subtract to find what’s left over.
  4. Bring down: bring down the next digit and start again.

A popular way to remember the order is “Does McDonald’s Sell Burgers?”, or invent your own family version.

Worked example: 852 ÷ 4

  1. Divide: 4 goes into 8 exactly 2 times. Write 2 above the 8.
  2. Multiply: 2 × 4 = 8. Write 8 under the 8.
  3. Subtract: 8 − 8 = 0.
  4. Bring down the 5. Now we have 5.
  5. Divide: 4 goes into 5 once. Write 1 above the 5. Multiply: 1 × 4 = 4. Subtract: 5 − 4 = 1. Bring down the 2, making 12.
  6. Divide: 4 goes into 12 three times. Write 3 above the 2. Multiply: 3 × 4 = 12. Subtract: 12 − 12 = 0. Nothing left to bring down.

The answer is 213. Check it: 213 × 4 = 852. ✔

Worked example with a remainder: 947 ÷ 6

  1. 6 into 9 goes once. 1 × 6 = 6. 9 − 6 = 3. Bring down the 4: 34.
  2. 6 into 34 goes 5 times. 5 × 6 = 30. 34 − 30 = 4. Bring down the 7: 47.
  3. 6 into 47 goes 7 times. 7 × 6 = 42. 47 − 42 = 5. Nothing left to bring down.

The answer is 157 remainder 5. Check: 157 × 6 = 942, plus 5 = 947. ✔

The mistakes to watch for

  • A remainder bigger than the divisor. If you subtract and get a number equal to or larger than the divisor, the estimate in the divide step was too small. Go back and try one more.
  • Forgetting a zero in the answer. In 624 ÷ 3, after dividing 6, you bring down the 2, and 3 doesn’t go into 2. Many children skip ahead and get 28 instead of 208. Every time you bring a digit down, a digit must go in the answer, even if it is 0.
  • Misaligned columns. Use squared paper, or turn lined paper sideways so the lines become columns. Keeping digits lined up prevents a lot of errors.
  • Skipping the check. Multiplying the answer by the divisor (and adding the remainder) takes thirty seconds and catches almost every mistake.

Estimating first

Before starting, ask: roughly what should the answer be? For 947 ÷ 6, 900 ÷ 6 is 150, so the answer should be a little over 150. If a child ends up with 15 or 1,570, they will notice straight away that something went wrong.

Practice that works

Three or four long division problems done carefully, with checking, are worth more than twenty done in a rush. Start with one-digit divisors and no remainders, then add remainders, then zeros in the quotient. Two-digit divisors come later and are much easier once this routine is automatic.

If frustration builds, stop and play a quick round of the times table quiz instead. Fast facts are the engine that makes long division feel manageable.

Put it into practice