Multiplicative Identity Property: Definition & Example

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Multiplicative Inverse: Definition, Property & Examples

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

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:02 The Multiplicative…
  • 1:10 Explanation
  • 2:56 Lesson Summary
Add to Add to Add to

Want to watch this again later?

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

Login or Sign up


Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Joseph Vigil
In this lesson, discover what the multiplicative identity property is and view examples of the property in action. You'll also find out why this property is always true.

The Multiplicative Identity Property

For a property with such a long name, it's really a simple math law. The multiplicative identity property states that any time you multiply a number by 1, the result, or product, is that original number.

To write out this property using variables, we can say that n * 1 = n. It doesn't matter if n equals one, one million or 3.566879. The property always hold true. Therefore:

  • 2 * 1 = 2
  • 56 * 1 = 56
  • 100,000,000,000 * 1 = 100,000,000,000
  • 57,687.758943768579875986754890 * 1 = 57,687.758943768579875986754890

You get the picture.


But why is this property always true? Well, let's go back, and think of what multiplication really is. It's a way of adding a list of numbers together quickly. For example, if we're solving the multiplication problem 2 * 6, we're really adding 2 to itself six times. In other words, we can rewrite that multiplication sentence as a long addition problem: 2 + 2 + 2 + 2 + 2 + 2. It would take a lot of paper to write really long addition problems that way, so multiplication gives us a shorter way of doing it.

Another, more visual, way to think of multiplication is as a form of grouping items, as we've just done. Let's consider the same multiplication problem differently, 2 * 6. If we were to visualize it, we can think of two groups of six items.

Six groups of two items

This is simply a visual representation of the addition problem we wrote out above. Of course, when we count all the images, we have a total of 12. So, when we write 2 * 6, we're saying that we're finding the total of two groups of six items. Simple, right?

To unlock this lesson you must be a 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

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

Earning College Credit

Did you know… We have over 160 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? 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