Long Multiplication by Two Digits

Long multiplication by two digits

Long multiplication helps you multiply a number by a two-digit number in an organized way. The key idea is to split the two-digit multiplier into tens and ones, then combine the partial results.

Method

1. Write the numbers in column form. Put the larger number on top if that helps you stay organized.
2. Multiply by the ones digit first. Start at the right and work left, carrying any extra tens.
3. Multiply by the tens digit next. This time, shift one place to the left, because you are really multiplying by tens.
4. Add the two partial products. The final answer is the sum of those results.

Example structure

If the multiplier is 34, think of it as:

• 4 ones
• 3 tens, meaning 30

So you compute:

• number × 4
• number × 30
• then add them

Check your work

A good check is to estimate first and see whether your answer is reasonable. You can also reverse the order mentally: the two partial products should both make sense, and the final total should be close to the estimate. Careful alignment of place values is the most important part.