How to Do Long Multiplication

What Is Long Multiplication?

Long multiplication is a method for multiplying numbers.

Long multiplication involves writing the numbers to be multiplied one underneath another, so the digits are in columns.

Many numbers of any length (including decimals) can be multiplied in this way.

A Real Example of How to Do Long Multiplication

Doing long multiplication is easy.

Question

Multiply the numbers below.

Step-by-Step:

1

Write the numbers you wish to multiply, one underneath the other.

2

Find the right most digit of the bottom number (in the units column).

3

Find the right most digit of the top number (in the units column).

4

Multiply the bottom digit (4) with the top digit (5).

5 × 4 = 20

5

Check if the answer from Step 4 is 9 or less:

No. 20 is not 9 or less.

  • If No, the answer will have two digits.

  • Write the digit on the right underneath the column (beneath the line).

  • Carry the left digit to the column to the left.

6

Move a digit to the left in the top number.

7

  • Multiply the bottom digit (4) with the top digit (2).

    2 × 4 = 8

  • Add any carried numbers to the answer.

    8 + 2 = 10

8

Check if the answer from Step 7 is 9 or less:

No. 10 is not 9 or less.

  • If No, the answer will have two digits.

  • Write the digit on the right underneath the column (beneath the line).

  • Carry the left digit to the column to the left.

9

Move a digit to the left in the top number.

There are no more digits to the left.

10

Write the carried digit underneath the line.

11

Write a 0 on the right in a new row underneath the line.

12

Move a digit to the left in the bottom number (in the tens column).

13

Find the right most digit of the top number (in the units column).

14

Multiply the bottom digit (1) with the top digit (5).

5 × 1 = 5

15

Check if the answer from Step 4 is 9 or less:

Yes. 5 is 9 or less.

  • If Yes, write the number beneath the line, to the left of the 0.

16

Move a digit to the left in the top number.

17

Multiply the bottom digit (1) with the top digit (2).

2 × 1 = 2

18

Check if the answer from Step 17 is 9 or less:

Yes. 2 is 9 or less.

  • If Yes, write the number below beneath the line.

19

Move a digit to the left in the top number.

There are no more digits to the left.

20

Use long addition to add the two numbers beneath the line.

Answer:

The solution to 25 × 14 is 350.

Slider

It is possible to multiply decimals together.

The slider below shows another example of how to do long multiplication.

Open the slider in a new tab

See Also

How to multiply How to do long addition What is place value? Try a long multiplication ( interactive widget)