Long Multiplication: Where the Carry and the Zero Go Missing

8 October 2026 · by Larry

Your child knows the tables. Ask 6 × 4 and the answer is there before you finish the question. Then the homework says 34 × 6, and the answer comes back as 1824, or 24, or 184.

That is very common and it is rarely a tables problem. Long multiplication is the first time a multiplication has to be done one digit at a time, with a carry, and the answer has to be put back together in the right places.

What the method actually asks for

Take 34 × 6, with the 6 under the 4. Work from the right, the ones first:

• Multiply the ones. 4 × 6 = 24. Write the 4 in the ones place and carry the 2.
• Multiply the tens. 3 × 6 = 18.
• Add the carry. 18 + 2 = 20. Write 20 in front of the 4.

The answer is 204. The same sum can be seen another way: 30 × 6 = 180, 4 × 6 = 24, and 180 + 24 = 204. The column method is that sum, written short.

Notice that on every digit the child has to multiply, remember the carry, add it, and decide what to write and what to carry. A child with perfect tables can still drop one of those, and the carry is the one that goes first.

Five places it goes wrong

1. Writing both digits of the product. In 34 × 6 the first step gives 24. A child who writes all of 24 in the answer, and then writes 18 beside it, gets 1824. The tell-tale sign is an answer that is far too big. The idea they are missing is that only the ones digit stays and the tens digit travels on.

2. The carry is forgotten or added to the wrong thing. In 47 × 5, the first step is 7 × 5 = 35: write 5, carry 3. Then 4 × 5 = 20, and the carried 3 makes 23. The answer is 235. A child who forgets the 3 writes 205. Another common slip is adding the carry before multiplying, which gives (4 + 3) × 5 = 35 and a wrong answer of 355.

3. A zero in the middle of the number. In 306 × 4, the first step is 6 × 4 = 24: write 4, carry 2. The next digit is 0, and 0 × 4 = 0, but the carried 2 still has to go somewhere, so the tens place is 2. Then 3 × 4 = 12. The answer is 1224. A child who sees 0 × 4 = 0 and writes 0 in the tens place, forgetting to add the carry, gets 1204. It is the same trap as the missing zero in long division, in reverse.

4. The placeholder zero. This is the one parents ask about most. In 23 × 14, the child multiplies 23 by the 4 first: 23 × 4 = 92. Then they multiply 23 by the 1, but that 1 is really a 10, so it is 23 × 10 = 230, and the line is written as 230. The zero in the ones place is a placeholder: it keeps the other digits in the tens and hundreds where they belong. Add the two lines, 92 + 230 = 322. Without the zero the second line is 23, and 92 + 23 = 115, a neat answer that is far too small. Where a child has never been shown why the zero is there, it is an arbitrary rule that is easy to forget. It is the same idea as zeros as placeholders in place value.

5. Slips in the final addition. The multiplying is all correct, then the two lines are added with the places not lined up, or a carry inside the addition is lost. The working looks tidy and the answer is wrong, so it is easy to blame the multiplication. If the addition is where it keeps happening, carrying and borrowing: why column sums go wrong is the place to look.

A five-minute check at the table

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

• 34 × 6 (a carry into the tens)
• 47 × 5 (a carry that has to be added on)
• 306 × 4 (a zero in the middle, with a carry)
• 23 × 14 (the placeholder zero)
• 58 × 27 (everything together)

Do not mark them yet. Watch where it goes wrong. If the first sum fails, it is the carry, so go slowly through one sum and say what is written and what is carried. If only the third fails, it is the zero with a carry. If only the fourth and fifth fail, the carry is fine and the problem is the placeholder zero or the final addition. A child who gets every multiplication right and still loses marks needs help with the adding, not the tables.

What helps

• Estimate first. Before starting 58 × 27, ask: is it about 150, 1,500 or 15,000? Rounding to 60 × 30 gives 1,800, so the answer should be somewhere near that. One question catches a missing zero or a doubled digit straight away.
• Show where the numbers come from. Split the sum: 58 × 20 = 1,160 and 58 × 7 = 406, and 1,160 + 406 = 1,566. Once a child has seen that the second line is “times 20”, the placeholder zero stops being a rule and becomes obvious.
• Write the carry small, above the next digit, and cross it out when it has been used. Children who keep carries in their heads lose them.
• Keep the places in columns. Squared paper, or lined paper turned sideways, keeps the ones under the ones. Misaligned lines cause a lot of wrong answers in the final addition.
• Firm up the shaky tables. If the 7s and 8s are slow, every long multiplication using them will be slow and error-prone. 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. Some workbooks use the column method and some use a box layout, and a child with two half-learned methods does worse than a child with one. See when the school method is not the one you learned.
• Calling it careless. A child who loses a carry in a routine with several moving parts is not careless. The routine is simply new.

Which level learns long multiplication, and with how many digits, 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 carry, the zero or the adding.

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

Frequently asked questions

Why does my child get multiplication sums wrong when they know their times tables?
Long multiplication asks for the tables plus carrying, adding and place value in the right order. A child can know every table and still drop the carried digit or lose track of which place they are in. The tables are only one of the jobs.

Why do we put a zero in the second line of 23 x 14?
The second line is 23 times 10, not 23 times 1, so the answer is 230. The zero holds the ones place empty so the other digits sit in the tens place where they belong. Leaving it out gives 115 instead of 322.

How can my child check a long multiplication answer?
Round the numbers first and see whether the answer is about the right size: 58 x 27 is close to 60 x 30, so the answer should be near 1,800. Then split one number and add: 58 x 20 = 1,160 and 58 x 7 = 406, which makes 1,566.

Is long multiplication taught the same way in every school?
Not necessarily. Some workbooks use the column layout and some use a box or area layout, and the stage at which it is taught differs. 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 neat but the answer is still wrong?
Check the carried digit first, then the addition at the end. In most neat-but-wrong sums the multiplying is fine and one carry was forgotten, or two lines were added without lining up the places.

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.