Multiplicative Inverse: Definition, Property & Examples Video

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: What is a Linear Equation?

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:02 What is the…
  • 0:28 Examples
  • 2:10 Multiplicative Inverse…
  • 2:56 Multiplicative Inverse…
  • 3:20 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Karin Gonzalez

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

In this lesson, we will cover the definition of the multiplicative inverse, as well as its property. We will review some examples of the property so that we can gain a better understanding of the material. Following the lesson will be a brief quiz.

What Is the Multiplicative Inverse?

A multiplicative inverse is a reciprocal. What is a reciprocal? A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1. For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1!

Examples

Let's look at a couple examples before proceeding with the lesson.

Example 1:

What is the multiplicative inverse of 15? In other words, which number when multiplied with 15 would give us the number 1 as a result? Let's solve this in an algebraic way, with x being the unknown multiplicative inverse.

15 * x = 1
x = 1/15

That's it! It was really that simple! The multiplicative inverse of a number is that number as the denominator and 1 as the numerator. When we multiply 15 and 1/15, we get 1.

Example 2:

What is the multiplicative inverse of 1/4? Now this example is a little different because we are beginning with a fraction. Let's again solve this algebraically, with x being the unknown multiplicative inverse of 1/4.

1/4 * x = 1
x = 1 / (1/4)
(1/1) / (1/4) = (1/1) * (4/1) = 4

Remember that when you divide fractions, you must flip the numerator and denominator of the second fraction and then multiply. We got 4 as the multiplicative inverse of 1/4. Makes sense, right?

So, the conclusion that we can draw from these two examples is that when you have a whole number, the multiplicative inverse of that number will be that number in fraction form with the whole number as the denominator and 1 as the numerator. When you have a fraction with 1 as the numerator, the multiplicative inverse of that fraction will simply be the denominator of the fraction.

Multiplicative Inverse of More Complicated Fractions

You may be thinking, that's just way too easy! What about when we have a fraction like 4/5? What would be the multiplicative inverse of that? Well, let's solve it algebraically, with x being the unknown multiplicative inverse.

4/5 * x = 1
1 / (4/5) = x
(1/1) * (5/4) = x
5/4= x

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support