What is the Standard Algorithm for Multiplication?

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  • 0:04 What Is a Standard Algorithm?
  • 0:26 How It Works
  • 2:24 Multiplying by a Single Digit
  • 3:02 Multiplying by a Larger Number
  • 4:16 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After reading this lesson, you will know how to multiply any two numbers using the standard algorithm. Learn how it uses both multiplication and addition to help you multiply large numbers.

What Is a Standard Algorithm?

In this lesson, you'll learn how you can use the standard algorithm to help you multiply. The standard algorithm is a way of doing multiplication by using partial products or multiplying in parts. Remember that the word 'product' is another word that also means multiplication. This algorithm is the one that's been used for many decades now. This is probably the way your parents have learned to multiply.

How It Works

This standard algorithm can be used to multiply any two numbers no matter how small or how large. Look at these examples of multiplication using the standard algorithm to multiply.

Multiplication Examples
standard multiplication

You can see that this method of doing multiplication uses both multiplication and addition. What's happening here is that we're multiplying the top number by the bottom number one digit at a time working from right to left, opposite the direction that we read. Notice too, that we write our numbers in columns instead of in one line.

For the 12 multiplied by a 3, we first do 3 * 2, which gives us 6. We write the 6 down under the 3. Then we do 3 * 1. This gives us 3, which we write to the left of the 6. And we're done, with an answer of 36.

For the 49 * 2, we begin by multiplying the 2 * 9. This gives us 18, so we write down the 8 and carry the 1, like you do when you are adding really large numbers. Then, we multiply the 2 * 4. This gives us 8. We have carried a 1, so we add that 1 to the 8: 8 + 1 gives us a 9 that we write down to the left of the 8. And we're done, with an answer of 98.

For the 157 * 23, we do the same process of multiplying from right to left, but we do each digit of the lower number separately. As you can see, we have a line for the 3 (3 * 157 = 471) and a separate line for the 2 (2 * 157 = 314). Notice that the line for the 2 starts directly underneath the 2 and continues to the left. That empty space to the right is treated as a 0. Once we've multiplied all the digits of our bottom number with the top number, then we add up all our lines. We get 471 + 3,140 = 3,611. We follow the rules of adding large numbers and carry where we need to.

Multiplying by a Single Digit

Now, let's look at a couple more examples.

For an example of multiplying by a single digit, multiply 87 * 4.

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