Back To Course

High School Trigonometry: Help and Review30 chapters | 228 lessons

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

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

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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

Not sure what college you want to attend yet? Study.com 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.

You are viewing lesson
Lesson
10 in chapter 1 of the course:

Back To Course

High School Trigonometry: Help and Review30 chapters | 228 lessons

- What are the Different Types of Numbers? 6:56
- Graphing Rational Numbers on a Number Line 5:02
- Notation for Rational Numbers, Fractions & Decimals 6:16
- The Order of Real Numbers: Inequalities 4:36
- Finding the Absolute Value of a Real Number 3:11
- The Commutative Property: Definition and Examples 3:53
- The Associative Property: Definition and Examples 4:28
- The Multiplication Property of Zero: Definition & Examples 2:40
- Algebraic Numbers and Transcendental Numbers 6:23
- Identity Property of Addition: Definition & Example 4:02
- Identity Property: Definition & Examples 5:59
- Multiplicative Identity Property: Definition & Example 3:36
- Multiplicative Inverse: Definition, Property & Examples 4:09
- Go to Real Numbers - Types and Properties: Help and Review

- FTCE ESOL K-12 (047): Practice & Study Guide
- GACE Media Specialist Test II: Practice & Study Guide
- GACE Media Specialist Test I: Practice & Study Guide
- GACE Political Science Test II: Practice & Study Guide
- NES Essential Components of Elementary Reading Instruction: Test Practice & Study Guide
- 20th Century Spanish Literature
- Sun, Moon & Stars Lesson Plans
- Direct Action & Desegregation from 1960-1963
- Civil Rights Movement from the Civil War to the 1920s
- Civil Rights in the New Deal & World War II Era
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks
- Preview Personal Finance
- California School Emergency Planning & Safety Resources
- Popsicle Stick Bridge Lesson Plan
- California Code of Regulations for Schools
- WV Next Generation Standards for Math

- The Chorus in Antigone
- Where is Mount Everest Located? - Lesson for Kids
- Sperm Cell Facts: Lesson for Kids
- The Motivational Cycle: Definition, Stages & Examples
- Bolivian President Evo Morales: Biography & Quotes
- Labor Unions for Physicians: Benefits & Factors
- Positive Attitude & Call Center Performance
- Chicken Facts: Lesson for Kids
- Quiz & Worksheet - Converting English Measurement Units
- Quiz & Worksheet - What Is Felony Murder?
- Quiz & Worksheet - Characteristics of Agile Companies
- Quiz & Worksheet - A Bend in the River
- Quiz & Worksheet - Sentence Fluency
- Growth & Opportunity for Entrepreneurs Flashcards
- Understanding Customers as a New Business Flashcards

- AP Music Theory: Homeschool Curriculum
- Prentice Hall World History Connections to Today, The Modern Era: Online Textbook Help
- Quantitative Analysis: Skills Development & Training
- GACE Middle Grades Language Arts: Practice & Study Guide
- AP Comparative Government and Politics: Exam Prep
- ACT Math: Inequalities
- Acids, Bases and Reactions in Chemistry
- Quiz & Worksheet - Agents to Promote Bowel Elimination
- Quiz & Worksheet - Quarter Notes, Eighth Notes, Rests & Other Rhythms
- Quiz & Worksheet - Finding the Least Common Multiples with Prime Factorizations
- Quiz & Worksheet - Add & Subtract Like Fractions & Mixed Numbers
- Quiz & Worksheet - Make Estimates and Predictions from Categorical Data

- Practice with Fraction and Mixed Number Arithmetic
- Backwards Planning Tips for Teachers
- Activities of Daily Living Lesson Plan
- Figurative Language Lesson Plan
- Free LSAT Prep
- GED Test Registration Form
- Veterans Day Lesson Plan
- Glorious Revolution Lesson Plan
- How to Ace a Panel Interview
- How to Sign Up for the ACT
- Speculative Writing Prompts
- 9th Grade Writing Prompts

Browse by subject