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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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Instructor
Karin Gonzalez

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

Expert Contributor
Kathryn Boddie

Kathryn earned her Ph.D. in Mathematics from UW-Milwaukee in 2019. She has over 10 years of teaching experience at high school and university level.

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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Additional Activities

Additional Examples

In the following examples, students will be asked to demonstrate their knowledge on the Identity Property of Multiplication. The examples include multiplication by large numbers, variables, decimals, and fractions. The variety of problems emphasizes the Identity Property of Multiplication, that 1*x = x*1 = x for any real number x.

Examples

Evaluate the following products using the Identity Property of Multiplication.

1) 5*1

2) 1*999,999,999,999

3) p*1

4) 2.5x*1

5) 1*(3/4)

6) 927xyz*(57 - 56)

Solutions

1) 5*1 = 5. This can be thought of as the number 5 added to itself 1 time, resulting in 5.

2) 1*999,999,999,999 = 999,999,999,999 since it does not matter how large the number is, the Identity Property of Multiplication says that 1 multiplied by any real number results in that same real number.

3) p*1 = p. We do not know what the variable p is, but we know that when multiplying by 1, the result does not change.

4) 2.5x*1 = 2.5x. Even with decimals and variables together in a problem, multiplying by 1 does not change the result due to the Identity Property of Multiplication.

5) 1*(3/4) = 3/4. Multiplying fractions can be intimidating, but multiplying a fraction by 1 results in the same fraction as before.

6) This problem does not appear to be an Identity Property of Multiplication problem at first, but if we simplify inside the parentheses first, we have

927xyz*(57-56) = 927xyz*(1) = 927xyz by the Identity Property of Multiplication.

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