How to Teach Long Division Step by Step

Long division has a reputation as the hardest thing in primary maths, and plenty of parents remember struggling with it. The good news is that it's really one short routine repeated over and over. Once your child knows the four steps (and their times tables), it becomes very mechanical. Here's how to teach it.

What are the four steps of long division?

1. Divide: how many times does the divisor go into the current number?
2. Multiply: multiply the divisor by that answer.
3. Subtract: take it away to find what's left.
4. Bring down: bring the next digit down next to the remainder.

Then repeat from step 1. A popular memory aid is Does McDonald's Sell Burgers? for Divide, Multiply, Subtract, Bring down.

Can you show a simple worked example?

84 ÷ 7

1. Divide: 7 into 8 goes 1 time. Write 1 above the 8.
2. Multiply: 1 × 7 = 7. Write 7 under the 8.
3. Subtract: 8 − 7 = 1.
4. Bring down: the 4, making 14.
5. Divide: 7 into 14 goes 2 times. Write 2 above the 4.
6. Multiply and subtract: 2 × 7 = 14, 14 − 14 = 0. Nothing left to bring down.
7. Answer: 12.

What about a bigger example with a remainder?

1,000 ÷ 12

1. 12 into 1? No. 12 into 10? No. 12 into 100: 8 (8 × 12 = 96). 100 − 96 = 4.
2. Bring down 0 to make 40. 12 into 40: 3 (3 × 12 = 36). 40 − 36 = 4.
3. No digits left. Answer: 83 r 4. Check: 83 × 12 = 996, plus 4 = 1,000. ✓

This is where long division earns its keep: with a divisor like 12 or 24, writing the multiplication and subtraction down is much safer than doing it in your head as in short division.

What should a child know before long division?

• Times tables: every "divide" step is a times tables question. See how to learn times tables.
• Column subtraction: see subtraction with borrowing.
• Place value: knowing that the 4 in 84 means 4 ones and the 8 means 8 tens.

What mistakes should you watch for?

• Forgetting to write a 0 in the middle of the answer when the divisor doesn't go in: 612 ÷ 6 is 102, not 12.
• A subtraction result bigger than the divisor, a sign the "divide" step was too small.
• Bringing down two digits at once.
• Misaligned columns. Squared paper helps enormously.

How do you teach it at home without tears?

1. Start with 2-digit ÷ 1-digit numbers that divide exactly.
2. Say the four steps aloud each time until they're automatic.
3. Always check by multiplying back. It catches mistakes and builds trust in the method.
4. Use step-by-step division practice, which checks each step, offers a hint after a mistake, and doesn't mark the whole problem wrong.
5. Keep sessions short, and finish with something your child can do. More on this in maths anxiety in children.

Where does long division lead?

Long division is used for converting fractions to decimals (see fractions, decimals and percentages) and for checking long multiplication answers. For paper practice, the worksheet generator makes division sheets with answer keys, and smart practice keeps the times tables behind every step fresh.