The bus stop method: how to do short division

How to do the bus stop method

To do the bus stop method, divide each digit in turn, starting from the left, and write each answer on top of the bus stop. Division is the only written method that starts with the biggest place value rather than the ones.

Here are the steps:

1. Write the number you're dividing inside the bus stop, and the number you're dividing by outside it, on the left.
2. Start with the first digit on the left. How many times does the divisor go into it? Write that above.
3. If anything is left over, carry it to the next digit. Write it small, in front of that digit.
4. Repeat for each digit until you reach the ones.

Government guidance for teachers suggests starting with an example where nothing is left over at any step, such as 84 ÷ 4, and saying what each digit is worth: "8 tens divided by 4 is 2 tens. 4 ones divided by 4 is 1 one."

1. 8 ÷ 4 = 2. Write 2 above.
2. 4 ÷ 4 = 1. Write 1 above.

The answer is 21. You can check it with short multiplication, the inverse: 21 × 4 = 84.

Short division with carrying

When a digit doesn't divide exactly, the amount left over is carried to the next digit. Schools may call this exchanging: 2 hundreds left over are exchanged for 20 tens. This example, 612 ÷ 4, is the one government guidance uses.

1. How many 4s in 6? 1, because 1 × 4 = 4, with 2 left over. Write 1 above and carry the 2 to the next digit.
2. The 2 hundreds carried make 21 tens. How many 4s in 21? 5, because 5 × 4 = 20, with 1 left over. Write 5 above and carry the 1 to the next digit.
3. The 1 ten carried makes 12 ones. 12 ÷ 4 = 3. Write 3 above.

The small coral digits are the carries. The carried 2 in front of the 1 turns 1 ten into 21 tens, and the carried 1 in front of the 2 turns 2 ones into 12 ones. If your child understands place value, the carrying makes sense rather than being a rule to remember.

When there's a zero in the answer

If the divisor doesn't go into a digit, write 0 above it and carry the whole digit on. Children often skip this 0, and the answer comes out wrong. Here is 824 ÷ 4:

1. 8 ÷ 4 = 2. Write 2 above.
2. 4 doesn't go into 2, so write 0 above and carry the 2 to the next digit.
3. The 2 tens carried make 24 ones. 24 ÷ 4 = 6. Write 6 above.

Without the 0 in the tens place, the answer would read 26 instead of 206. A quick estimate catches it: 800 ÷ 4 = 200, so the answer must be about 200.

Short division with remainders

A remainder is what's left over when the number can't be shared out exactly. In the bus stop method, the remainder is whatever is left after dividing the ones. It's written after the answer with "r" or "remainder".

1. 4 doesn't go into 1, so write 0 above (some schools leave this space blank) and carry the 1 to the next digit.
2. The 1 hundred carried makes 10 tens. How many 4s in 10? 2, because 2 × 4 = 8, with 2 left over. Write 2 above and carry the 2 to the next digit.
3. The 2 tens carried make 29 ones. How many 4s in 29? 7, because 7 × 4 = 28, with 1 left over. Write 7 above.
4. There are 1 left over at the end, so the answer is 27 remainder 1.

The first digit, 1, is smaller than 4, so it's carried straight on. 109 ÷ 4 = 27 remainder 1.

Government guidance points out that the remainder must always be smaller than the divisor. If it isn't, there was room for one more group.

What to do with the remainder

What the remainder means depends on the question, and children are asked to decide. The national curriculum describes these ways of writing it:

Way	98 ÷ 4	When it fits
As a whole number remainder	24 remainder 2	Counting things that can't be split, such as sweets
As a fraction	24 and a half	Sharing things that can be split, such as pizzas
As a decimal	24.5	Money and measures
By rounding	about 25	When the context needs a whole number

Rounding can go either way. Four scouts fit in a tent, so how many tents do 30 scouts need? 30 ÷ 4 = 7 remainder 2, but "7 remainder 2 tents" doesn't answer the question. The 2 left over still need a tent, so the answer is 8. If tickets cost £4 and you have £30, you can buy 7 tickets, and the £2 left over doesn't buy another.

Working out a remainder as a decimal is a Year 6 skill. If 4 friends share a £109 meal, £27 remainder £1 isn't helpful. Writing 109 as 109.00 and carrying on gives £27.25 each.

The bus stop method with 2 digits

In Year 6, children also use short division to divide by a two-digit number, where it works well. The steps are the same, but the times tables facts aren't there to lean on, so it helps to write out the multiples of the divisor first. For 372 ÷ 12, that's 12, 24, 36, 48 and so on.

1. 12 doesn't go into 3, so write 0 above (some schools leave this space blank) and carry the 3 to the next digit.
2. The 3 hundreds carried make 37 tens. How many 12s in 37? 3, because 3 × 12 = 36, with 1 left over. Write 3 above and carry the 1 to the next digit.
3. The 1 ten carried makes 12 ones. 12 ÷ 12 = 1. Write 1 above.

For harder two-digit divisions, many children write out the working in full instead. That is long division, which is the same idea with each subtraction written down.

When do children learn short division?

The national curriculum lists short division as a Year 5 method, for dividing numbers up to 4 digits by a one-digit number. The Year 4 notes say children should start becoming fluent with it for divisions that come out exactly. In Year 6 they divide by two-digit numbers too, and the remainder work goes further. The Year 5 maths and Year 6 maths guides show where it fits.

Short division depends on division facts. If 56 ÷ 8 takes a while to work out, the method will feel hard, so practise the times tables, especially the 7 times table and 8 times table, with their division facts.

Common mistakes to watch for

• Starting from the right. Every other written method starts with the ones. Short division starts on the left.
• Leaving out a zero. In 824 ÷ 4, writing 26 instead of 206. Estimate first to catch it.
• Not taking the most groups. Government guidance gives the example of writing 3 remainder 5 for 17 divided by 4. A remainder of 5 means there's room for another 4, so the answer is 4 remainder 1. The remainder must be less than the divisor.
• Carrying to the wrong place. The carry goes in front of the next digit, not above the bus stop.
• Stopping at "r". In a word problem, ask what the remainder means: round up, round down, or split it.
• Using it when a mental method is quicker. 804 ÷ 4 is 200 plus 1, so 201, with no bus stop needed.

How to help at home

• Check with multiplication. Multiply the answer by the divisor and add the remainder. You should get back to the starting number.
• Use the right words. Say "8 hundreds divided by 4 is 2 hundreds" rather than "4 into 8 goes 2", at least at first.
• Ask what the remainder means. Make up sharing problems with sweets, money or cars and talk about what to do with what's left.
• Keep division facts sharp. A few minutes on mixed times tables and division facts most days makes every step quicker.

Bus stop method questions to try

1. 96 ÷ 3
2. 738 ÷ 6
3. 927 ÷ 9
4. 541 ÷ 7
5. 3,164 ÷ 4
6. 6 eggs fit in a box. How many boxes do 75 eggs need?

Answers

1. 32
2. 123 (7 ÷ 6 is 1 with 1 left over, 13 ÷ 6 is 2 with 1 left over, 18 ÷ 6 is 3)
3. 103 (9 doesn't go into 2, so there's a 0 in the tens)
4. 77 remainder 2
5. 791
6. 13 boxes. 75 ÷ 6 = 12 remainder 3, and the 3 eggs left over need a box too.

For the rest of what children learn in these years, see the KS2 maths guide. The bar model can help children decide when a word problem needs division.