Ross MackellUK-qualified primary teacher · 9 min read

If you learnt long multiplication at school, you probably remember the rules. "Times by the units. Put a zero in. Times by the tens. Add them up."

What most of us were never told is why. And when your child gets stuck, the rules on their own are not much help. You end up saying "just put the zero in" and they ask "but why?" and nobody enjoys the next ten minutes.

Here is the most common long multiplication mistake I see in Year 5 and Year 6. The question is 34 × 26.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll walk you through long multiplication step by step, explain the zero so it finally makes sense, and show you the mistakes to look for. You don't need to be good at maths to help. You just need to know what to check.

What is long multiplication?

Long multiplication is the formal written method for multiplying a number by a two-digit number. It is sometimes called column multiplication. You set the numbers out in columns, work out two rows of answers, then add them.

• Short multiplication is multiplying by a one-digit number, like 247 × 6. It is one row. Children use it from Year 4.
• Long multiplication is multiplying by a two-digit number, like 247 × 36. It is two rows plus an addition. The national curriculum introduces it in Year 5, and by Year 6 children multiply numbers up to four digits by a two-digit number.

It comes up on the Year 6 SATs arithmetic paper every year, usually towards the end. Those questions are worth 2 marks, and children can often pick up a mark for a correct method even with one slip. That's one reason teachers insist on a neat, set-out method. I explain how the paper works in my Year 6 SATs arithmetic guide.

What your child needs first

Long multiplication isn't really one skill. It's four skills stacked on top of each other. If any of them is wobbly, the whole thing falls over.

1. Times tables. Every single step is a times table fact. If your child is counting on their fingers for 7 × 8, they'll lose track of where they are. My guide on how to learn times tables fast shows the quickest route.
2. Place value. Knowing that the 2 in 26 is worth 20, not 2. This is the bit behind the zero. If it's shaky, read my guide to place value first.
3. Short multiplication. One row, with carrying. Long multiplication is just this, done twice.
4. Column addition. The last step is adding the two rows, often with carrying. My column addition and subtraction guide covers it.

This is why I always say arithmetic comes before problem solving. A child who is stuck on long multiplication is very rarely stuck on long multiplication. They're stuck on one of the four skills underneath it.

Long multiplication step by step: 34 × 26

Let's do the same question properly. Write the bigger number on top and line the digits up in their columns: ones under ones, tens under tens.

Row 1: multiply by the ones (34 × 6)

1. 6 × 4 = 24. Write 4 in the ones column. Carry the 2 into the tens.
2. 6 × 3 = 18, plus the carried 2 makes 20. Write 0 in the tens and 2 in the hundreds.
3. Row 1 is 204. Cross out the little carried 2 so it can't confuse the next row.

Row 2: multiply by the tens (34 × 20)

1. Put a zero in the ones column first. We're multiplying by 20, not 2. More on this below.
2. 2 × 4 = 8. Write 8 in the tens column.
3. 2 × 3 = 6. Write 6 in the hundreds column.
4. Row 2 is 680.

Add the two rows

204 + 680 = 884. That's the answer.

Then do a quick sense check. 34 × 26 is close to 30 × 30, which is 900. Our answer is 884, nice and close. If your child had written 272 or 8,840, the estimate would tell them straight away that something's gone wrong.

Why do you put a zero in long multiplication?

This is the question every parent gets asked, so here's an answer you can give.

The 2 in 26 is not really 2. It's in the tens column, so it's worth 20. That means the second row isn't 34 × 2. It's 34 × 20.

Multiplying by 20 is the same as multiplying by 2 and then by 10. And when you multiply by 10, every digit moves one place to the left. The zero is simply holding the ones column empty, so the digits land in the right place.

Some schools call it a "placeholder". Some teachers draw a little star or dot instead of a zero to stop children treating it as a digit they worked out. Either is fine. What matters is that your child can say why it's there.

A bigger one: 247 × 36

Three digits by two digits is where Year 6 lives. Exactly the same steps, just one more digit in each row.

Row 1 (× 6): 6 × 7 = 42, write 2, carry 4. 6 × 4 = 24, plus 4 is 28, write 8, carry 2. 6 × 2 = 12, plus 2 is 14, write 14. That gives 1,482.

Row 2 (× 30): zero in the ones first. 3 × 7 = 21, write 1, carry 2. 3 × 4 = 12, plus 2 is 14, write 4, carry 1. 3 × 2 = 6, plus 1 is 7. That gives 7,410.

Add: 1,482 + 7,410 = 8,892. Estimate: 250 × 40 = 10,000, and we rounded both numbers up, so a bit under 10,000 makes sense.

Four digits by two digits, like 1,254 × 18, works the same way again. Each row just gets one digit longer.

The grid method (and why schools use it first)

If your child's book has boxes in it instead of columns, that's the grid method. Many schools teach it before long multiplication because it shows what's really going on. Here's 34 × 26 as a grid.

Add the four boxes: 600 + 80 + 180 + 24 = 884. Same answer.

Look at the grid and you can see long multiplication hiding inside it. The bottom row (180 + 24 = 204) is row 1 of long multiplication. The top row (600 + 80 = 680) is row 2. Long multiplication is just a faster, tidier way to write the grid.

So if your child understands the grid but finds long multiplication confusing, show them this link. It's often the moment it clicks. If you want to know why schools teach so many methods, I explain it in why maths is taught differently now.

3 long multiplication mistakes and how to fix them

Mistake 1: Forgetting the zero

• What it looks like: 272 for 34 × 26. The second row is ten times too small.
• The fix: Before they multiply anything in row 2, they write the zero. Make it a habit, not a decision. Then check with an estimate.

Mistake 2: Using the old carries

• What it looks like: Row 1 is right, but row 2 is a little too big because a carried digit from row 1 got added in again.
• The fix: Cross out each carry as soon as it's been used, and cross out all of row 1's carries before starting row 2. Your child's school may write carries in a particular place. Follow the school, but always cross them out.

Mistake 3: Columns drifting

• What it looks like: The working is right, but the final addition is wrong because digits weren't lined up.
• The fix: Use squared paper, one digit per square. It sounds small, but it fixes this mistake almost completely.

One check catches nearly everything: estimate first. Round both numbers, multiply, and compare. If the answer is miles away, look for the zero first.

A 10-minute long multiplication practice routine

I use the same three steps for every written method: watch, copy, practise.

1. Watch: you do one, saying each step out loud. "6 times 4 is 24. Write the 4, carry the 2." Don't skip the zero line: "Now the tens. Zero first, because it's 20."
2. Copy: your child does a very similar one, saying the steps out loud too.
3. Practise: three on their own. Estimate first, then work it out, then compare.

Start with two digits by two digits with no carrying, and only move on when they get three in a row right. Here's a set that builds up slowly.

A few minutes, four or five times a week, will do far more than one long session at the weekend. For SATs-style practice, the government publishes free KS2 past papers.

Once long multiplication is secure, long division is the natural next step. It uses the same carrying and the same times tables, just in reverse. Start with my guide to the bus stop method, which is short division.

Frequently asked questions

What year do children learn long multiplication?

The national curriculum introduces long multiplication in Year 5, when children multiply numbers up to four digits by a two-digit number using a formal written method. In Year 6 they're expected to use long multiplication confidently for numbers up to four digits by a two-digit whole number.

What is the difference between short and long multiplication?

Short multiplication is multiplying by a one-digit number, so there's only one row of working. Long multiplication is multiplying by a two-digit number, so there are two rows (one for the ones digit, one for the tens digit) which are then added together.

Why do you put a zero in long multiplication?

Because the second row multiplies by the tens digit, which is worth ten times as much. In 34 × 26, the 2 is really 20. Multiplying by 20 shifts every digit one place to the left, and the zero holds the ones column so the answer is 680, not 68.

Is the grid method the same as long multiplication?

They give the same answer and use the same idea: splitting numbers into tens and ones. The grid method writes every part in a separate box. Long multiplication combines them into two rows, which is quicker. Many schools teach the grid first, then move to long multiplication.

How can I help my child with long multiplication at home?

Check their times tables first, because every step depends on them. Then use watch, copy, practise: you model one out loud, they copy a similar one, then they try three alone. Use squared paper, cross out carries, and always estimate the answer first.