Long Division: Why a Child Who Knows Their Tables Still Loses the Answer

7 October 2026 · by Larry

Your child knows the tables. Ask 4 x 6 and the answer is instant. Then the homework says 672 ÷ 4, and a page of neat working ends in 148, or 18, or something that does not look like an answer at all.

That gap is very common and it is rarely about the tables. Long division is the first sum most children meet where the method has four jobs that must go in the right order, and losing the place in the middle is easy.

What the method actually asks for

Take 672 ÷ 4 written in the usual way, with the 4 outside the bracket and 672 inside. Each digit goes through the same four jobs:

• Divide. How many 4s fit into 6? One. Write 1 on top.
• Multiply. 1 × 4 = 4. Write it under the 6.
• Subtract. 6 − 4 = 2.
• Bring down. Bring the 7 down next to the 2, to make 27.

Then round again: 27 ÷ 4 is 6 (6 × 4 = 24), 27 − 24 = 3, bring down the 2 to make 32. And 32 ÷ 4 = 8. The answer is 168.

Notice that the child has to do a division, a multiplication and a subtraction on every round, and remember what is waiting to be brought down. A child with fine tables can still drop one of those. Dropping the “bring down” is the commonest.

Five places it goes wrong

1. The first digit is too small. In 349 ÷ 5, the 3 cannot hold even one 5. A child who divides it anyway writes 0 and carries on, or squeezes in a wrong number. The move they need is to look at the first two digits instead: 34 ÷ 5 = 6, remainder 4, then bring down the 9 to make 49, and 49 ÷ 5 = 9, remainder 4. The answer is 69 remainder 4.

2. The missing zero. In 824 ÷ 4, the first round gives 2 (8 ÷ 4), and then the 2 is brought down. But 2 ÷ 4 is 0, so a 0 has to go on top before the 4 is brought down: 24 ÷ 4 = 6. The answer is 206. Children who do not write the 0 end up with 26, and the working still looks tidy, which is why it is hard to spot. It is the same idea as zeros as placeholders in place value.

3. Forgetting to bring down. The child finishes a round, sees a remainder, and starts the next round with the old number instead of the new one. The tell-tale sign is that the answer has fewer digits than it should.

4. A subtraction slip inside the division. Everything in the division steps is right, but 32 − 28 comes out as 6 instead of 4 and the next round goes wrong. The division is not the problem, the subtraction is. If borrowing is where this happens, carrying and borrowing: why column sums go wrong is the thing to look at.

5. The remainder gets lost. Take 523 ÷ 4. 5 ÷ 4 = 1, remainder 1; bring down the 2 to make 12, and 12 ÷ 4 = 3, remainder 0; bring down the 3, and 3 ÷ 4 = 0, remainder 3. The answer is 130 remainder 3. Children often write 13 and forget both the 0 and the 3. What a remainder means in a word problem is a separate trap, covered in division with remainders: one sum, four different answers.

A five-minute check at the table

Write four sums on a piece of paper and ask your child to do them while you watch, without helping:

• 672 ÷ 4 (the plain case: every digit divides)
• 349 ÷ 5 (first digit too small, and a remainder)
• 824 ÷ 4 (a zero in the answer)
• 523 ÷ 4 (a zero and a remainder together)

Do not mark them yet. Watch which of the four jobs goes wrong. If the first sum fails, the problem is the routine, so go slowly through one sum with the four jobs named out loud. If only the second and fourth fail, it is the too-small first digit. If only the third and fourth fail, it is the zero. A child who gets the divisions right and the subtractions wrong needs a different kind of help.

What helps

• Say the four jobs out loud, in order, every time. Divide, multiply, subtract, bring down. Some children like a small note at the top of the page for a week or two. It can go once the order is automatic.
• Make an estimate first. Before starting 349 ÷ 5, ask: is it nearer 7, 70 or 700? 350 ÷ 5 is 70, so the answer should be a little under 70. That one question catches a missing zero or a dropped digit straight away.
• Check by multiplying back. 69 × 5 = 345, and 345 + 4 = 349. The check takes thirty seconds and tells the child, not you, whether the answer is right. If there was a remainder, add it on after multiplying.
• Keep the working tidy and down the page. The numbers being subtracted should sit directly under each other. Children who work across a messy line lose their place. Squared paper helps for a while.
• Firm up the tables the divisor needs. If 7s and 8s are the shaky ones, every long division by 7 or 8 will be harder. The order in times tables: memorising, understanding, and the order that works is a sensible place to start.

What does not help

• Another page of the same sums. If the routine is shaky, repeating it repeats the slips.
• Teaching a different layout from the one in school. If the workbook uses one layout and you show another, the child has two half-learned methods. See when the school method is not the one you learned.
• Calling it careless. A child who loses the place in a four-step routine is not careless. The routine is simply new.

Which level learns long division, and with what size of numbers, is set by the school and the MOE syllabus, so check the primary mathematics syllabus on moe.gov.sg or ask the class teacher what is expected this term. If the same slip keeps coming back after a couple of weeks of this, show the teacher the page. They can usually tell you quickly whether it is the routine, the tables or the subtraction.

For some low-pressure practice, the free maths practice has a drill builder where you can choose division and the size of the numbers, and it works on a phone. Keep it short, and do the multiply-back check on a few answers together.

Frequently asked questions

Why does my child get long division wrong when they know their times tables?
Long division is several small steps in a fixed order: divide, multiply, subtract, bring down. A child can know every table and still lose track of which step they are on, or forget to bring a digit down. The tables are only one of the four jobs.

Why does my child leave out the zero in answers like 206?
When a digit cannot be divided (2 divided by 4 in 824 divided by 4), the answer for that place is 0 and it has to be written. Children who skip it write 26 instead of 206. Asking whether the answer is nearer 20 or nearer 200 usually shows the problem.

How can my child check a long division answer?
Multiply the answer by the number divided by. 168 x 4 = 672, so 672 divided by 4 is 168. If there was a remainder, add it back on after multiplying. Doing this once per sum is worth more than doing extra sums.

Is long division taught the same way in every school?
Not necessarily. Layouts and the stage at which long division is taught can differ between schools, so follow the layout in your child's workbook and check the MOE primary mathematics syllabus on moe.gov.sg for what each level covers.

What if the working looks right but the answer is still wrong?
Look for a subtraction slip (usually borrowing) inside the working, not a division slip. The division steps can all be right while one small subtraction sends the next step wrong.

Related: if the mistakes feel random, careless mistakes in maths: what they usually are sorts them into kinds. For sums done without a pencil, see mental sums.

Related: the other half of the same four-step habit is long multiplication: where the carry and the zero go missing.