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 onedigit 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.
 First, take the rightmost 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
 This number would then be written beneath the line.
 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.

 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 rightmost 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 rightmost 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
Five Facts About Multiplication:
 The answer to multiplication can also be called a product.
 Anytime there is a zero in expansion, the answer is always zero.
 The 10s and one digit of a nine multiplication fact always add up to 9. For example, 9 x 4 = 36, meaning the answer is 36 when broken down to 3+6 = 9.
 When you multiply an even number by six, the product always ends in the same number. So, for example, 6×4= 24 or 6×2=12.
 Multiplying a number is another way of repeatedly adding it, so basically, it’s like repeated addition.