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# Identity Property â€“ Explanation with Examples

## What is Identity Property?

Real numbers are an ordered set of numbers that possess unique properties. The basic properties are commutative, associative, distributive, and identity. An identity property is a property that applies to a group of numbers in the form of a set. It cannot be applied to any individual number only.

It is named identity property because when applied to a number, the number keeps its â€˜identity.’ The identity property is true for all arithmetic operations.

## Identity Property of Addition

The identity property of addition is that when a number *n i*s added to zero, the result is the number itself i.e.

n + 0 = n

Zero is called an additive identity and it can be added to any real number without changing its value. Here are the few examples of identity property of addition,

3 + 0 = 3Â Â Â Â Â Â Â Â Â (Positive Integers)

-3 + 0 = -3Â Â Â Â Â Â (Negative Integers)

4/5 + 0 = 4/5Â Â Â (Fractions)

0.5 + 0 = 0.5Â Â Â (Decimals)

x + 0 = xÂ Â Â Â Â Â Â Â Â (Algebraic notation)

This property holds true for subtraction as well because subtracting 0 from any number equals the number itself. Therefore, 0 is also called a subtractive identity.

## Identity Property of Multiplication

The identity property of multiplication is that when a number *n i*s multiplied by one, the result is the number itself i.e.

n Ã— 1 = n

One is called the multiplicative identity, and it can be multiplied with any real number without changing its value. Here are a few examples of identity property of multiplication,

3 Ã— 1 = 3Â Â Â Â Â Â Â Â Â (Positive Integers)

-3 Ã— 1 = -3Â Â Â Â Â Â (Negative Integers)

4/5 Ã— 1 = 4/5Â Â Â (Fractions)

0.5 Ã— 1 = 0.5Â Â Â (Decimals)

x Ã— 1 = xÂ Â Â Â Â Â Â Â Â (Algebraic notation)

This property holds true for division as well because dividing any number by 1 equals the number itself. Therefore, 1 is also called divisive identity.