Short multiplication: the column method, step by step

What is short multiplication?

Short multiplication is a written method for multiplying any number by a one-digit number, set out in columns. It's often called the column method, because each digit stays in its own place value column: ones, tens, hundreds, thousands. It's one of the formal written methods in the national curriculum, alongside column addition and column subtraction.

You write the bigger number on top, the one-digit number underneath on the right, and a line below. The answer goes under the line, and any carried digits are written small, just under the answer line.

How to do short multiplication

To do short multiplication, start with the ones. Multiply the ones digit, write the ones of that answer in the ones column, and carry any tens into the tens column. Then multiply the tens digit and add the carried number. Keep going left until every digit is done.

Government guidance suggests starting with a calculation that needs no carrying, so here is 43 × 2.

1. Ones: 3 × 2 = 6. Write 6 in the ones column.
2. Tens: 4 × 2 = 8. Write 8.

Children often say it in place value words at first: "2 times 3 ones is 6 ones, 2 times 4 tens is 8 tens." That helps them see that the 4 is really 40.

Short multiplication with carrying

When a column gives an answer of 10 or more, write the ones and carry the rest into the next column. Carrying in the column method is the same as exchanging 10 ones for a ten. Here is a three-digit number, 258 × 6.

1. Ones: 8 × 6 = 48. Write 8 in the ones column and carry 4 into the tens column.
2. Tens: 5 × 6 = 30, plus the 4 carried makes 34. Write 4 in the tens column and carry 3 into the hundreds column.
3. Hundreds: 2 × 6 = 12, plus the 3 carried makes 15. Write 15.

The carried digit is added after multiplying, never before. In the tens column, 5 × 6 = 30 comes first, then the 4 carried is added to make 34.

Short multiplication with a four-digit number

Four-digit numbers work in exactly the same way: there is just one more column. Here is 2,435 × 3.

1. Ones: 5 × 3 = 15. Write 5 in the ones column and carry 1 into the tens column.
2. Tens: 3 × 3 = 9, plus the 1 carried makes 10. Write 0 in the tens column and carry 1 into the hundreds column.
3. Hundreds: 4 × 3 = 12, plus the 1 carried makes 13. Write 3 in the hundreds column and carry 1 into the thousands column.
4. Thousands: 2 × 3 = 6, plus the 1 carried makes 7. Write 7.

How short multiplication links to the grid method

Short multiplication is the grid method squashed into one line. Here is 46 × 7 both ways.

46 × 7 with the grid method

×	40	6
7	280	42

1. Partition 46 into 40 and 6.
2. 40 × 7 = 280.
3. 6 × 7 = 42.
4. Add the answers in the grid: 280 + 42 = 322.

1. Ones: 6 × 7 = 42. Write 2 in the ones column and carry 4 into the tens column.
2. Tens: 4 × 7 = 28, plus the 4 carried makes 32. Write 32.

In the grid, 6 × 7 = 42 sits in its own box. In short multiplication, the 2 of that 42 goes in the ones column and the 4 tens are carried. Then 4 tens × 7 is 28 tens, and the 4 tens carried make 32 tens, which is 320. 320 + 2 = 322, the same answer as the grid. The adding that the grid does at the end, the column method does as it goes.

This is why schools teach the grid method and partitioning first. A child who knows where each digit comes from is far less likely to slip up with the carrying.

Estimate first

Before working it out, round the bigger number and multiply in your head. 46 × 7 is about 50 × 7 = 350, so 322 is sensible. 258 × 6 is about 250 × 6 = 1,500, so 1,548 is sensible too. The national curriculum asks children to use estimation to check answers from Year 3 onwards. A quick estimate catches a missed carry or a digit in the wrong column.

Which year is short multiplication taught?

Short multiplication starts in Year 4. The national curriculum says Year 4 children multiply two-digit and three-digit numbers by a one-digit number using formal written layout, and practise until they are fluent in short multiplication. In Year 5, they multiply numbers up to 4 digits by a one-digit number, and start multiplying by two-digit numbers with long multiplication.

Government guidance for teachers expects children to master short multiplication in Year 5. It says children who leave Year 4 fluent in their times tables have the best chance of doing so, because every column needs a fact from the times tables. The multiplication tables check in Year 4 looks at those same facts.

Common mistakes with short multiplication

• Adding the carry before multiplying. In 46 × 7, adding the 4 carried to the 4 tens first makes 8, then 8 × 7 = 56, giving 562. Multiply first, then add the carry.
• Forgetting the carry. In 46 × 7, writing 28 in the tens without the 4 carried gives 282. Ask your child to cross out each carried digit once it's used.
• Writing the whole answer in one column. 6 × 7 = 42, but only the 2 goes in the ones column.
• Starting from the left. The method only works from the ones, so the carries can move left.
• Untidy columns. Digits that drift out of line end up in the wrong place. Squared paper helps.
• A times tables slip. A secure 7 times table and 8 times table prevent most wrong answers.

Short multiplication isn't always the best way, either. Government guidance gives the example of 201 × 4: it's quicker to do 200 × 4 = 800 in your head and add 4 more. If your child is searching for the column method for division, that's short division, also known as the bus stop method.

How to help at home

• Estimate together. Before your child starts, ask "about how big will the answer be?"
• Keep the times tables fresh. The facts to 9 × 9 are the ones short multiplication uses most.
• Talk it through. Ask your child to explain one column out loud: what they multiplied, what they wrote and what they carried.
• Check with the inverse. Once they know the bus stop method, dividing the answer by the one-digit number should give back the number you started with.

Short multiplication questions to try

1. 32 × 3
2. 57 × 6
3. 184 × 5
4. 609 × 7
5. 3,148 × 4
6. 2,756 × 8

Answers

1. 96 (no carrying)
2. 342 (7 × 6 = 42, write 2 and carry 4; 5 × 6 = 30, plus 4 is 34)
3. 920
4. 4,263 (the 0 tens still get the 6 carried from 9 × 7 = 63)
5. 12,592
6. 22,048

For everything else in these years, see the Year 4 maths and Year 5 maths guides, or the KS2 maths hub.