Parent guide · 5 min read
Long division for kids: the four steps, and where they go wrong
Long division is the first written method in primary maths that asks a child to hold several small jobs in their head at once: work out a fact, write it in the right column, subtract, and carry on. A child who copes fine with times tables can still lose the thread halfway down the page, and the answer they end up with looks wrong for reasons that are hard to spot. The method is a loop of four short steps, and nearly every mistake comes from one of them, not from the whole thing.
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4 things you can do at home
Check the times tables the problem needs, before starting
For 2,184 ÷ 7, the child needs the sevens table. Ask two or three quick questions first: "how many sevens in 21? in 8? in 14?" If those come slowly, the long division will feel impossible for a reason that has nothing to do with the method itself.
Write the four steps at the top of the page
Put "divide, multiply, subtract, bring down" on a sticky note, with a small arrow from the last back to the first. Children who lose their place mid-problem usually skipped a step, and the note gives them something to check against instead of starting again.
Use squared paper, or turn lined paper sideways
Keeping each digit in its own column stops the quotient (the answer on top) drifting out of line with the number underneath. Misaligned digits are behind a surprising number of wrong answers that look like they are arithmetic slips.
Check by multiplying back
The answer times the divisor, plus any remainder, must give the starting number. 312 × 7 = 2,184. It takes a minute, and it teaches a child that division can be checked rather than just hoped for.
The four-step loop, in plain terms
Divide: how many times does the divisor fit into the first digit or two of the number? Multiply: write that many times the divisor underneath. Subtract: take it away to see what is left over. Bring down: drop the next digit beside the leftover, and start again with that new number.
Each pass through the loop produces one digit of the answer. A four-digit number can take four passes, which is why a single slip early on spoils everything that follows.
A worked example: 2,184 ÷ 7
Start with the first digits. 2 is too small for 7, so use 21. Divide: 7 goes into 21 three times, so write 3 on top. Multiply: 3 × 7 = 21. Subtract: 21 − 21 = 0. Bring down the 8 to make 08.
Next pass: 7 goes into 8 once, so write 1. Multiply: 1 × 7 = 7. Subtract: 8 − 7 = 1. Bring down the 4 to make 14. Last pass: 7 goes into 14 twice, so write 2. Multiply: 2 × 7 = 14. Subtract: 0. The answer is 312, and checking 312 × 7 = 2,184 confirms it.
The traps: the missing zero, and what to do with a remainder
In 618 ÷ 3, the first pass gives 2 (6 ÷ 3), leaving 0. Bring down the 1: 3 does not go into 1, so the answer digit for this pass is 0. Many children skip it and write 26 instead of 206. The rule is that every digit brought down gets an answer digit above it, even when that digit is zero.
When the last subtraction leaves something over, that is the remainder. In 95 ÷ 4, the first pass gives 2 (4 × 2 = 8), leaving 1; bring down the 5 to make 15; 4 goes into 15 three times (12), leaving 3. The answer is 23 remainder 3. A remainder must always be smaller than the divisor, so if it is 4 or more, the answer digit above was too small.
Signs it’s time for outside help
When home help has done what it can
- Knows the method in class but gets lost after the first digit of the answer.
- Regularly leaves out zeros in the answer, such as writing 26 for 206.
- Gets a remainder larger than the divisor and does not notice.
- Is slow on the times table facts the problem needs, so each pass takes a long time.
- Avoids or gives up on division homework that has more than two digits.
Questions parents ask
FAQ
What age do children usually learn long division?
It is usually introduced around ages 9–11 (US Grades 4–5, England Years 5–6, Australian Years 5–6), starting with one-digit divisors and moving on to two-digit divisors later.
Should my child use the "short" method or the long one?
Follow the method the school teaches, since mixing methods causes more confusion than either method does. Short division suits one-digit divisors and long division suits larger ones, and both use the same divide, multiply, subtract, bring-down thinking.
Why does my child get the right digits in the wrong order?
This usually means the answer digits are not lined up above the digits of the number being divided. Squared paper, or writing each answer digit directly above the last digit used, usually fixes it.
Do we really need to do this by hand when calculators exist?
The written method builds understanding of place value and of how division and multiplication undo each other, and that understanding is needed later for fractions, decimals and algebra. Most curricula still ask for it.
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