Identity Property of Multiplication: Definition & Example

Identity Property of Multiplication: Definition & Example
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  • 0:00 Identity Property of…
  • 0:38 Examples
  • 1:15 Why Does it Work?
  • 2:42 Lesson Summary
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Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

This lesson will give you the definition of the identity property of multiplication, examples of this property and an explanation of why this property always works. Following the lesson will be a brief quiz to test your knowledge of the material.

Identity Property of Multiplication

The identity property of multiplication simply states that a number equals itself when multiplied by 1. If you multiply 8 and 2, the product is 16, so the factors 8 and 2 have changed their identity to the product 16. But if you multiply 8 by 1, the product is 8, so the factor 8 has been able to keep its identity. So if you have 25,000,000,000 and multiply it by 1, you will get 25,000,000,000. And you thought you couldn't multiply large numbers in your head!

Examples of the Identity Property of Multiplication

Let's look at some examples of the property at work:

1 * 1 = 1

1 * 15 = 15

178 * 1 = 178

The property also applies to negative numbers multiplied by 1 and variables multiplied by 1. For instance:

-7 * 1 = -7

2x * 1 = 2x

It doesn't matter how long the number is that you are multiplying with 1, the product will still be that number. After all, 100,000,000,000,000,000,000 * 1 = 100,000,000,000,000,000,000.

Why Does it Work?

In order to understand why the identity property of multiplication works, we must first look at the definition of multiplication. Multiplication is basically the process of adding an integer to itself a certain number of times.

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