# What is Long Multiplication?

Long multiplication is an easy way to multiply two numbers that are difficult to bear. For example, you can find out that 212 x 14 = 2,968. Follow the steps below to learn how to do long multiplication to solve large problems.

It breaks down multiplication into easier steps that can be solved using times table knowledge. Learning to work out expansion at an easier level seems less daunting than long multiplication. However, our resources can make the transition process easier for young learners.

Short multiplication deals with one-digit multiplication problems only. This easier type of multiplication is commonly learned using times tables. These make expansion a breeze to understand and stick with us for life!

How to work out long multiplication:

Take the example 212 x 14.

All long multiplication questions should be laid out as below.

1. First, take the right-most letter in the bottom number and multiply it by each of the top numbers individually. In this case, you would multiply the:

4 x 2 = 8

4 x 1 = 4

4 x 2 = 8

= 848

1. This number would then be written beneath the line.
2. You then do the same with the second number on the bottom – in this case, 1. As it is one position to the left of the number 4, the answer is written one space to the left under the line, like this.
1. Finally, you add the two answers (848 and 212) from right to left using the same method as before to get the final answer. So the sums would be

8 + (blank) = 8

4 + 2 = 6

8 + 1 = 9

(blank) + 2 = 2

2,968

Long Multiplication Examples

Let’s look at a few examples to solidify your understanding of long multiplication:

Example 1: What is 112 × 28?

First, let’s lay it out in the proper long multiplication format. This gives us the following:

112

x28

Step 1: Take the right-most letter in the bottom number and multiply it by each of the top numbers individually.

8 × 2 = 16

Now, we have to carry the one from the 16. So, our next sum will look like this:

8 × 1 = 8 + 1 = 9

8 × 1 = 8

= 896

Step 2: Write the number below the line.

112

x28

_______

896

Step 3: We’ve got to do the same thing with the second number on the bottom. Remember, the answer must be written one space to the left under the line because it is one position to the left.

2 × 2 = 4

2 × 1 = 2

2 × 1 = 2

= 224

So, this means that:

112

x28

_______

896

224

Step 4: The final step in long multiplication is adding the two answers from right to left.

112

x28

_______

896

224 +

The sums are as follows:

6 + (blank) = 6

9 + 4 = 13

Now, we must carry the one from the 13 to the 8. So, this will give us the following:

8 + 2 = 10 + 1 = 11

Again, we have to carry the one from the 11.

2 + 1 = 3

This gives us the final answer, which is:

3,136

Example 2: What is 431 × 15?

First, let’s lay it out in the proper long multiplication format. This gives us the following:

431

x15

Step 1: Take the right-most letter in the bottom number and multiply it by each of the top numbers individually.

5 × 1 = 5

5 × 3 = 15

Now, we have to carry the one from the 15.

4 × 5 = 20 + 1 = 21

= 2155

Step 2: Write the number below the line.

431

x15

_______

2155

Step 3: We’ve got to do the same thing with the second number on the bottom.

1 × 1 = 1

3 × 1 = 3

4 × 1 = 4

= 431

431

x15

_______

2155

431

Step 4: The final step in long multiplication is adding the two answers from right to left.

431

x15

_______

2155

431 +

The sums are as follows:

5 + 0 = 5

5 + 1 = 6

1 + 3 = 4

2 + 4 = 6

This gives us the final answer, which is:

6,465