How to Teach Long Division: Short Division First, Then Long

By the Success Tutoring team · 5 October 2026

Long division has a reputation as the hardest thing in primary maths, but it is really one simple idea repeated: “how many groups of this number fit?” The trick is to build up in the right order. Start with sharing using place value, then learn short division (often called the bus stop method), and only then write out the full steps of long division. Each stage uses the one before, so nothing feels like a sudden jump.

What your child needs first

• Division facts, such as 42 ÷ 6 = 7, which come straight from times tables. Our guide on how to teach division covers the early stages.
• Place value: knowing that 84 is 8 tens and 4 ones, and that 1 ten can be exchanged for 10 ones.
• Subtraction of 2- and 3-digit numbers.

The words that go with division

Step 1: Share using place value

Use base-ten blocks, or bundles of 10 straws and single straws. For 84 ÷ 4, share 8 tens between 4 groups (2 tens each), then share 4 ones (1 each). Each group has 2 tens and 1 one, so 84 ÷ 4 = 21. This shows that we divide the biggest place value first, which is exactly what the written methods do.

Step 2: Exchange when it doesn't share evenly

Now try 72 ÷ 3. Share 7 tens into 3 groups: 2 tens each, with 1 ten left over. Exchange that ten for 10 ones, so there are now 12 ones. Share 12 ones into 3 groups: 4 each. The answer is 24. Check it: 24 × 3 = 72.

This “left over ten becomes ones” step is the heart of both short and long division, so spend time on it with real objects.

Step 3: Short division (the bus stop method)

Short division writes the same thinking in a compact layout. The number being divided sits inside the “bus stop”, the divisor waits outside, and the answer goes on top. Here is 852 ÷ 6:

1. Hundreds: 8 ÷ 6 = 1 remainder 2. Write 1 on top and carry the 2 to make 25.
2. Tens: 25 ÷ 6 = 4 remainder 1. Write 4 on top and carry the 1 to make 12.
3. Ones: 12 ÷ 6 = 2. Write 2 on top.

So 852 ÷ 6 = 142. Check by multiplying: 142 × 6 = 852. The short division worksheet gives plenty of 3-digit practice.

Step 4: Remainders

Some divisions don't come out exactly. Here is 157 ÷ 4:

1. 1 ÷ 4 = 0 remainder 1, so carry the 1 to make 15.
2. 15 ÷ 4 = 3 remainder 3, so write 3 and carry the 3 to make 37.
3. 37 ÷ 4 = 9 remainder 1, so write 9. There is nothing left to carry into, so 1 is the remainder.

The answer is 39 remainder 1 (written 39 r 1). Check: 39 × 4 = 156, and 156 + 1 = 157. A remainder must always be smaller than the divisor. If it isn't, another group would have fitted.

Older children learn other ways to write a remainder:

• As a fraction: 39 ¼, because 1 is left out of a group of 4.
• As a decimal: 39.25, by carrying on past the decimal point.

Word problems decide what to do with the remainder. If 157 eggs go into boxes of 4, you fill 39 boxes. If 157 people need tables that seat 4, you need 40 tables. The division with remainders worksheet is good practice.

Step 5: Long division

Long division is used when dividing by a 2-digit number, where carrying a remainder in your head gets hard. Instead of carrying, you write every step down. Each step follows the same cycle, which many children remember as Dad, Mum, Sister, Brother:

• Divide: how many times does the divisor fit?
• Multiply: multiply the divisor by that number.
• Subtract: take it away to find what's left.
• Bring down: bring down the next digit, then start again.

Before starting, write a quick list of multiples of the divisor. For 16 that is 16, 32, 48, 64, 80, 96, 112, 128, 144. It turns each “divide” step into a look-up.

Here is 672 ÷ 16:

1. Divide: 16 doesn't fit into 6, so look at 67. 16 fits 4 times (64). Write 4 above the 7.
2. Multiply and subtract: 16 × 4 = 64, and 67 − 64 = 3.
3. Bring down the 2 to make 32.
4. Divide again: 16 fits into 32 exactly 2 times. Write 2 above the 2. 32 − 32 = 0.

So 672 ÷ 16 = 42. Check: 42 × 16 = 672.

A long division with a remainder

Try 905 ÷ 23. Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207.

23 fits into 90 three times (69), leaving 21. Bring down the 5 to make 215. 23 fits into 215 nine times (207), leaving 8. The answer is 39 r 8. Check: 39 × 23 = 897, and 897 + 8 = 905.

Common mistakes and how to fix them

• Missing a zero in the answer. 612 ÷ 6 is 102, not 12. When the divisor doesn't fit (1 ÷ 6), write 0 in the answer and carry. Estimating first helps: 612 ÷ 6 must be about 100.
• A remainder bigger than the divisor. This means the divide step was too small. Look at the multiples list again.
• Digits out of line. Use squared paper and write each answer digit directly above the digit it belongs to.
• Losing track of the steps. Say “divide, multiply, subtract, bring down” aloud each time round.
• Not checking. Multiply the answer by the divisor and add any remainder. You should get back to the starting number.

When do children learn long division?

Children usually learn short division with a 1-digit divisor around 4th Class to 5th Class, and long division by 2-digit numbers around 6th Class or the first year of secondary school. Plenty of practice with division facts along the way makes every stage easier. Long division also uses multiplication skills, so our guide on how to teach long multiplication is a useful companion.

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