Long Multiplication

What is long multiplication? 

Long multiplication is a method used to solve multiplication problems with large numbers. One thing that can really help you in long multiplication is if you know the multiplication table by heart. This will speed up your work and make it more accurate. 

First Step 

The first step in long multiplication is to write down the numbers on top of each other. You align the numbers on the right. Don't worry about the decimal points when lining up the numbers; just write them down and line up the right-most number. 

Examples: 

469 x 32 87.2 x 19.5 113.05 x 47

Second Step 

Now we are going to start multiplying. We'll use the numbers from the first example above: 469 x 32. We begin with the ones place in the bottom number. This is the 2 in 32. We multiply 2x469 and write it down under the line. 
 

Adding a Zero for the Tens Space 

Now we need to multiply by the next number to the left of the 2. This is the 3 in 32. Because the 3 is in the tens place we need to hold the tens place by placing a zero in the 1's place before we start multiplying. 
 

Finish multiplying 

Multiply the 3 by the top number (469) and write this number next to the zero. 


If there were more numbers we would add more rows and continue to add more zeros. For example, if there were a 4 in the hundreds spot (i.e. the number on the bottom was 432) we would add two zeros in the next row and then multiply 469 by 4. 

Third Step 

After we have multiplied all the numbers on the bottom, we add up the rows of numbers to get the answer. In this case there are two rows, but there would be more if the number we were multiplying by on the bottom (the 32) had more digits. 
 

Another Long Multiplication Example 

Below is an example long multiplication problem where the added zeros are shown in red and the carry numbers for each step are shown in blue.