Identity Property Definition Examples

Author: nitin.p070

In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set. It leaves other elements unchanged when combined with them. This is used for groups and related concepts.

Let (S,*) be a set S with a binary operation * on it. Then an element e of S is called a left identity if e * a = a for all a in S, and a right identity if a * e = a for all a in S. If e is both a left identity and a right identity, then it is called a two-sided identity, or simply an identity.(Source: Wikipedia)
Definition of Addition and Multiplication Identity Properties:
In the identity properties are mainly two parts they are,
(i) Addition identity property.

(ii) Multiplication identity property

Definition of addition identity property:
Addition identity property is states that the sum of zero and any real number or variable is the number or variable itself.
For example,
4 + 0 = 4,
-11 + 0 = - 11,
y + 0 = y are the examples of addition identity property.

Definition of Additive identity property:
Operation of addition performed with the set ‘a' and zero then the yield is ‘a'.

Example of Additive identity property:
The number 9 has to be adding with zero then according to the additive identity property the yield will be the number itself.
`9+0=0+9=9`

Problem 1:
In the below mentioned five expressions, which of the following satisfies the properties of additive identity properties.
Options: A) 8 + 0 = 8
B) -6 + 0 = 0
C) – 7× 0 = 0
D) 5 - 4 = 1

Solution :
Here option A i.e,8+0=8 satisfied the properties of additive identity. Adding 8 with 0 give us the yield of 8 so it satisfies the properties of additive identity.
Solved Example on Identity Properties of Addition and Multiplication
Which of the following equations illustrate identity property of addition?

Choices:
A. xy = yx
B. x + 0 = x
C. (x + y) + z = x + (y + z)
D. x + 1 = 1 + x

Correct Answer: B
Step 1: According to identity property of addition, the sum of a number and 0 is the number itself.
Step 2: Among the choices, the equation x + 0 = x illustrates identity property of addition.

Definition of multiplication identity property:
Multiplication identity property is states that the product of 1 and any number or variable is the number or variable itself.
For example,
4 × 1 = 4,
-11 × 1 = - 11,
y × 1 = y are the examples of multiplication identity property.

Examples for Addition and Multiplication Identity Properties Definition:
Example of addition identity property:
Find the Addition identity property for the given
positive numbers
Negative numbers
algebraic notation
decimals
fraction numbers

Solution:
For positive numbers
6 + 0 = 6
For negative numbers
- 5 + 0 = -5
For algebraic notation
y + 0 = y
For decimal numbers
87.3 + 0 = 87.3
For fraction numbers
(1/3) + 0 = (1/3)

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Example of multiplication identity property:
Find the Multiplication identity property for the given
positive numbers
Negative numbers
algebraic notation
decimals
fraction numbers

Solution:
For positive numbers
9 × 1 = 9
For negative numbers
- 8 × 1 = -8
For fraction numbers
(2/4) × 1 = (2/4)
For decimal numbers
2.1 × 1 = 2.1
For algebraic notation
y × 1 = y

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