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High School Trigonometry: Help and Review30 chapters | 228 lessons

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Lesson Transcript

Instructor:
*Karin Gonzalez*

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

This lesson will give you the definition of the identity property of addition. You will be shown examples to clearly illustrate the material. Following the lesson will be a brief quiz to test your knowledge.

When you think of the word **identity**, you may think about who or what a person or thing is. You may think about an identification card, like a driver's license, that has your picture and some basic description information. You may also think of things like identity theft, where others can steal all of your information and thus, your identity.

But in mathematical addition, an identity takes on a different meaning. In math, an **identity** is a number, *n*, that when added to other numbers, gives the same number, *n*. The **additive identity** is always zero. This brings us to the **identity property of addition**, which simply states that when you add zero to any number, it equals the number itself.

Before getting into more about this property, let's first go over some vocabulary related to addition. When you add two or more numbers together, those numbers are called **addends**. A **sum** is what you get when you add two or more addends together.

Okay, now that we know those vocabulary terms, let's look at a quick example of how the property works. If you add the numbers, or addends, 8 + 0, the sum is 8. The addend 8 did not have to change his identity when added with 0; it stayed the same. But, if we used any other number to add to 8, we would get a different sum. Let's take a look:

8 + 1= 9 (not 8)

8 + 2 = 10 (not 8)

8 + -5 = 3 (not 8)

I think you get the point by now!

In the identity property of addition, a number is always being added to zero. The sum is always that number. Let's look at some examples:

10 + 0 = 10

0 + 24 = 24

175 + 0 = 175

-6 + 0 = -6

As you can see, the property even applies to zero added to negative numbers: -6 + 0 = -6

100,000,000,000,000,000,000 + 0 = 100,000,000,000,000,000,000

One incredibly huge number plus zero equals one incredibly huge number. It doesn't matter how long the number is that you are adding to zero; the sum will still be that number.

Why does the identity property of addition always work? Well, think about a real life example:

If you had a $100 bill and didn't spend it or make any other money that day (zero money), then you would still have $100 at the end of the day, right? The numeric expression would be written like this:

$100 + 0 = $100

The identity property of addition does not just work with numbers. It also works when we use **variables** in arithmetic expressions. Variables, like *x* or *y* are letters used to represent an unknown number. Let's look at some examples of the identity property of addition using variables:

*x* + 0 = *x**y* + 0 = *y**xy* + 0 = *xy*

Take a look at a few more expressions:

5*x* + 0 = 5*x*

65*x* + 0 = 65*x*

(4*x* +5) + 0 = (4*x* + 5)

Even an expression using parentheses will follow the identity property for addition if one of the addends is zero.

An **identity** in addition is a number, *n*, that when added to other numbers, gives the same number *n*. The **additive identity** is zero. The **identity property of addition** simply states that when you add zero to any number, it equals the number itself. Remember that **addends** are simply the numbers that are being added. The **sum** is the result of the numbers being added. No matter what the number is, if it is added to the additive identity, zero, it will stay the same. For example:

5,471 + 0 = 5, 471

7*x* + 0 = 7*x*

Once you've completed the lesson, you should be able to:

- Define identity as it's defined in mathematics
- Recall what addends, the sum and the additive identity are
- Explain the identity property of addition

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High School Trigonometry: Help and Review30 chapters | 228 lessons

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