 # Identity Property – 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 ‘identity.’ The identity property is true for all arithmetic operations.

The identity property of addition is that when a number n is 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 = 3          (Positive Integers)

-3 + 0 = -3       (Negative Integers)

4/5 + 0 = 4/5    (Fractions)

0.5 + 0 = 0.5    (Decimals)

x + 0 = x          (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 is multiplied by one, the result is the number itself i.e.

n × 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 × 1 = 3          (Positive Integers)

-3 × 1 = -3       (Negative Integers)

4/5 × 1 = 4/5    (Fractions)

0.5 × 1 = 0.5    (Decimals)

x × 1 = x          (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.

### Practice Problems

1. Find the missing numbers in the expressions given below.

a. __ × -9 = -9

b. -2 × __ = -2

c. ___ × 1 = 0.981

d. (7/3 + 2/3) × 1 = ___

e. ___ × 1 = 99/100

f. (85 – 23 + 32) × 1 = ___

1. Jane can place 12 eggs per crate. How many eggs must be there in 1 crate?

1. There are 8 rooms in a house. Each room has 1 bed. How many beds are there in total?

1. Sam works in a coffee shop and earns $20 per hour. How much he earns on a particular day when he works for 1 hour only? Answer:$20