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High School Trigonometry: Help and Review30 chapters | 228 lessons

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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.

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.

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.

But what if we use a bigger number? Let's look at 1,000 * 1. What we're dealing with here is one group of 1,000 items. Yes, 1,000 is a big number. But since we only have one group of 1,000 items, the total number of items will still be 1,000.

Therefore, any number multiplied by one gives us that original number because we are only counting one group of that number of items. One group of ten tables is still ten tables. One group of 60 students is still 60 students. And one group of one billion citizens is still one billion citizens.

So, when someone thinks they can stump you with a lot of words and asks, 'What is the **multiplicative identity property**,' you can tell them that any number multiplied by 1 gives a product of that original number, no matter how large that number is!

So, 999,999,999,999 * 1 = 999,999,999,999. Always and forever.

Once you have finished, you should be able to:

- State the multiplicative identity property
- Explain why the multiplicative identity property is always true

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High School Trigonometry: Help and Review30 chapters | 228 lessons

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