What is long multiplication?
Long multiplication is a written calculation technique. Rather than doing everything in your head, you set out the operation: you write one number above the other, then multiply digit by digit. It is the method used whenever you multiply fairly large numbers, such as 47 × 6 or 34 × 26.
To do it well, only one thing is essential: knowing your times tables. The rest is just a method to apply in order.
How to set out a multiplication
Three rules are enough:
- Write the larger number on top, the second one just below.
- Align the digits to the right: units under units.
- Put the × sign on the left and draw a line under the two numbers.
Then calculate always starting from the units (the right-hand column), working left.
Multiplication without carrying
Let's start with the simplest case: when each product stays below 10, there is no carry. Take 132 × 3.
132 × 3 = 396
- Units: 2 × 3 = 6. Write 6.
- Tens: 3 × 3 = 9. Write 9.
- Hundreds: 1 × 3 = 3. Write 3. Result: 396.
Multiplication with carrying
As soon as a product is more than 9, you use a carry: you write the units digit and keep the tens digit to add it at the next step. Example with 47 × 6.
47 × 6 = 282 — the carry 4 is written above the tens
- Units: 7 × 6 = 42. Write 2 and carry 4 (noted above the tens).
- Tens: 4 × 6 = 24, then add the carry: 24 + 4 = 28. Write 28.
- Result: 282.
Multiplying by a two-digit number
When the bottom number has two digits, you do two multiplications, then add them. The trick: for the 2nd product, you shift one place to the left by writing a 0. Example with 34 × 26.
34 × 26 = 884 — carry 2 for 34 × 6, and the 0 marks the shift
- 34 × 6 (the units digit of 26) = 204.
- Move to the tens digit (the 2). First write a 0 in the units column (the shift), then 34 × 2 = 68 → you get 680.
- Add the two lines: 204 + 680 = 884.
Tips & mistakes to avoid
- Line up on the right: a shifted column throws off the whole calculation.
- Don't forget to add the carry at the next step.
- Don't forget the shift 0 when multiplying by a two-digit number.
- Check the order of magnitude: 34 × 26 is "roughly 30 × 25 = 750". A result of 88 or 8,800 would clearly be wrong.
- If in doubt, revise the relevant table before setting out the operation.
Worked exercises
Set out and calculate, then check the solution.
213 × 3
58 × 7
46 × 23
125 × 14
Now it's your turn!
On EasyMaths, your child practises long multiplication with exercises that never repeat, instant marking and progress tracking. The first exercises are free.
Start the exercises →Frequently asked questions
How do you set out a multiplication?
Write the larger number on top, the second below, aligned to the right (units under units). Draw a line, then multiply each digit of the bottom number by the top number, always starting with the units.
What is a carry?
When the product of two digits is more than 9, you write the units digit and keep the tens digit: that is the carry. You add it to the next product.
How do you multiply by a two-digit number?
First multiply by the units digit, then by the tens digit, shifting the result one place to the left (add a 0). Finally, add the two results.
At what age do children learn long multiplication?
Multiplication by a single digit is usually learned around age 8, then by a two-digit number around ages 9 to 11.