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Additive Identity: Definition & Examples

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  • 0:02 Properties of Numbers
  • 1:17 Additive Identity for…
  • 2:11 Additive Identity for…
  • 3:05 Additive Identity for Sets
  • 4:27 Lesson Summary
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Lesson Transcript
Instructor: Neelam Mehta

Neelam has taught variety of math and science subjects. She has masters' degrees in Chemical Engineering and Instructional Technology.

In this lesson, you will learn the definition of the additive identity property and its meaning when applied to various kinds of numbers such as real, imaginary and complex numbers. We will also look at the application of the additive property for sets of numbers.

Properties of Numbers

Solving math problems requires us to work with different kinds of numbers. Often, we need to perform different types of operations on numbers, such as addition, subtraction, multiplication, division, exponents and so on. Before attempting to solve problems involving number operations, we should be aware of the properties of different types of numbers and the rules of arithmetic operations.

In this lesson, we'll focus on learning about one particular property of numbers known as the identity property. We will learn the definition of this property with respect to the addition of numbers. Before we jump into the definition let's review our number system.

Number System

There are three major categories of numbers: real, imaginary and complex. Real numbers are all the numbers that you can plot on a real-number line. The types of real numbers include natural, whole, integers, rational and irrational. Imaginary are the numbers that you cannot plot on a real number line. Imaginary numbers result when you try to take a square root of a negative number. Complex numbers are combinations of real and imaginary numbers. Now that we have reviewed the number system, let's look at how the additive property is applied to these numbers.

Additive Identity for Real Numbers

When performing arithmetic operations you have to work with various properties of numbers, such as the commutative property, the associative property, the distributive property, the inverse property and so on. One of these properties is known as the identity property. The additive identity property says that if you add a real number to zero or add zero to a real number, then you get the same real number back. The number zero is known as the identity element, or the additive identity.

Additive Identity for Real Numbers

Here are some examples of the additive identity with real numbers:

Additive Property Examples for Real Numbers

Here is an illustration of the additive identity property for 18 + 0= 18.

Additive Property on a Number Line

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