Long Multiplication

Write the larger number above the smaller one and line the digits up to the right. Multiply every digit of the top number by each digit of the bottom number, one digit at a time. Carry where needed. This gives a partial product for each bottom digit. Finally, add the partial products together.

Use long multiplication when a calculation is too hard to work out in your head. This often means multiplying two larger numbers. For example, 24 times 352 is tricky to do mentally. The method breaks it into smaller digit-by-digit steps that are each easy to handle.

A partial product is the answer you get from multiplying the top number by one digit of the bottom number. Each digit of the bottom number produces its own partial product. You then add all the partial products together to reach the final answer.

You carry whenever multiplying two digits gives ten or more, because only one digit can sit in each column. You write the units digit in the current column. Then carry the tens digit into the next column and add it to the next result. For example, 4 times 5 is 20. Write 0 and carry 2.

The second digit of the bottom number stands for tens, not units. So its partial product shifts one place to the left, keeping each digit in its correct column. You can leave that end space empty or fill it with a zero as a placeholder.