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Multiplicative Identity Property: Definition & Example

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  • 0:02 The Multiplicative…
  • 1:10 Explanation
  • 2:56 Lesson Summary
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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.

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?

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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