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## Definition of Identity Properties of Addition and Multiplication

• Identity property of addition states that the sum of zero and any number or variable is the number or variable itself.

For example, 4 + 0 = 4, - 11 + 0 = - 11, y + 0 = y are few examples illustrating the identity property of addition.

• Identity property of multiplication 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 few examples illustrating the identity property of multiplication.

### 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

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.

Related Terms for Identity Properties of Addition and Multiplication

• Multiplication
• Sum
• Product