Long division method, step by step: the four steps with worked examples, remainders, two-digit divisors and decimals, the UK bus-stop version and the US layout side by side, and the five mistakes that cause most wrong answers

"Long division method" is typed in two countries for two reasons: British parents whose child has moved from the bus-stop method to "proper" long division in Year 6, and American parents whose Grade 4 or 5 child has brought home a layout they do not recognise. This page does the four steps in full on four examples (a simple one, a remainder, a two-digit divisor, decimals), puts the UK and US layouts side by side so parents can help in whichever the school uses, and lists the five mistakes behind most wrong answers, because the method itself is only four steps and the errors are always the same ones.

The four steps

Divide, multiply, subtract, bring down. Then divide again. Children in the UK often learn it as "Dad, Mum, Sister, Brother"; in the US as "Does McDonald's Sell Burgers". When there is nothing left to bring down, what remains is the remainder.

Example 1: 672 ÷ 6.

Answer: 112. Check: 112 × 6 = 672.

Example 2, with a remainder: 925 ÷ 4. 4 into 9 is 2 (write 2), 2 × 4 = 8, 9 - 8 = 1, bring down 2 to make 12; 4 into 12 is 3 (write 3), 3 × 4 = 12, 12 - 12 = 0, bring down 5; 4 into 5 is 1 (write 1), 1 × 4 = 4, 5 - 4 = 1. Nothing to bring down. Answer: 231 remainder 1, or 231¼, or 231.25 if the question wants a decimal (bring down a zero: 4 into 10 is 2, remainder 2; bring down another zero: 4 into 20 is 5). Check: 231 × 4 + 1 = 925.

Two-digit divisors: estimate first

Example 3: 1,368 ÷ 24. The four steps are the same; the new skill is guessing how many times 24 goes into a number, and the trick is to write the first ten multiples of 24 down the margin before starting (24, 48, 72, 96, 120, 144, 168, 192, 216, 240).

24 into 1 does not go; 24 into 13 does not go; 24 into 136: look down the list, 120 is the largest under 136, so 5 (write 5 above the 6). 5 × 24 = 120; 136 - 120 = 16; bring down 8 to make 168. 24 into 168: 168 is on the list, so 7 (write 7 above the 8). 7 × 24 = 168; 168 - 168 = 0. Answer: 57. Check: 57 × 24 = 1,368.

Without the list, children guess 6 (6 × 24 = 144, too big) or 4 (leaves 40, which is more than 24, so the guess was too small). Both are caught by one rule: the number left after subtracting must be smaller than the divisor. If it is not, the guess was too small; if the subtraction goes negative, the guess was too big.

Decimals

Example 4: 7.5 ÷ 6. Divide as if the point were not there but put a point in the answer directly above the point in the dividend. 6 into 7 is 1 (write 1), remainder 1; bring down 5 to make 15; 6 into 15 is 2 (write 2 after the point), remainder 3; bring down a zero to make 30; 6 into 30 is 5. Answer: 1.25.

When the divisor has a decimal: 7.5 ÷ 0.6. Move the point one place in both numbers so the divisor is whole: 75 ÷ 6 = 12.5. Moving both points the same way does not change the answer, because you have multiplied top and bottom of a fraction by the same number.

The UK bus-stop layout and the US layout, side by side

Both put the divisor on the left and the answer on top of a line over the dividend. The difference is what goes underneath.

• Bus-stop (short division), UK Year 4 to 6, one-digit divisors: nothing is written underneath. The remainder at each step is carried as a small digit in front of the next digit: for 672 ÷ 6, the 1 remainder from 7 ÷ 6 is written as a small 1 in front of the 2, making 12. Fast, but it breaks down with two-digit divisors because the mental subtraction gets too big.
• Long division, UK Year 6 and US Grade 4 to 5: the multiply and subtract steps are written out below, one under the other. Slower, but it works for any divisor and shows the working, which is what the marks are for.

A child moving from one to the other is not learning new maths; the four steps are the same. Show them the same problem in both layouts, once, and the fear goes.

Where it sits in each curriculum

The five mistakes behind most wrong answers

1. Skipping a digit. 4 into 5 does not go, so the child moves on and forgets to write a 0 in the answer: 2,020 ÷ 4 written as 55 instead of 505. Rule: every digit brought down gets a digit in the answer, even if it is 0.
2. A remainder bigger than the divisor. The guess was too small; go up one.
3. Subtracting wrongly because the numbers were not lined up. Squared paper, one digit per square, fixes half of all errors.
4. Forgetting the point in a decimal answer. Put it in the answer before you start dividing.
5. Not checking. Multiply the answer by the divisor, add the remainder; it must give the dividend. Ten seconds, and it catches everything above.

Where to get help

A 1-on-1 online maths class with a tutor who holds a master's in mathematics: the layout the school uses, the multiples list, one problem type at a time until it is automatic. For Grade 4 and 5, Year 5 and 6, and Class 4 and 5, in the US, UK, Australian and CBSE orders. The recording and notes after every class, US$10 an hour. The Grade 5 maths page has the year's topics, and the free 30-minute first class is a real lesson, usually on the problem that came home wrong.

Questions parents ask

See how we teach this, 1-on-1 online →