# Multiplicative Identity Property: Definition & Example

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• 0:02 The Multiplicative…
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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.

## Explanation

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.

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?

So, if we look at 6 * 1, what we're really saying is that we have one group of six items. Well, since we have only one group, the total number of items is going to be six.

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