Real numbers are a systematic set of numbers that have unique properties. The standard properties are commutative, associative, distributive, and identity. An identity property is a property that puts on a set of numbers in the form of a group. You can only apply it to a specific number.

It is called identity property since when related to a number. And the number keeps its ‘identity.’ Therefore, you must know the identity property is true for all arithmetic operations.

**Addition: Identity Property**

The identity property of addition is when a number n is included in zero, the result is the number itself i.e.

n + 0 = n.

Zero is called an additive identity; you can add it to any real number without changing its value. Here are minority instances 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 symbols).

This property is also true for subtraction since subtracting 0 from any number equates to the number itself. For that reason, 0 is additionally referred to as a subtractive identity.

**Multiplication: Identity Property**

The identity property of multiplication is when a number n is multiplied by one, the outcome is the number itself i.e.

n × 1 = n

One is called the multiplicative identity, and also without changing its value, it can be multiplied with every real number. Here are a couple of instances of identity property of multiplication.

Three × 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 applies to departments also because dividing any number by one equates to the number itself. Therefore, one is also called divisive identity.

**Identity is Constantly 0 as well as 1**

We have discovered that the identity will invariably be 0 and 1 depending upon the arithmetic operation used. The reason for this is as follows:

In maths, addition is thought about as adding any number to an additional number. According to the identity property, the result will coincide when a number is included in 0. For instance, 25 + 0 = 25.

Subtraction is the procedure of removing one number from the provided whole number. Therefore, the result is the same when 0 is subtracted from a number. As an example, 16 – 0 = 16.

Read Also:Set Notation Explained with Examples

Reproduction is the system of repeated addition, i.e. the number is again added by the number of times presented by the various other numbers. For instance, six × 5, 6 is continuously added five times. According to the identity property of reproduction, when multiplication is done with the number, the product will undoubtedly be the number itself, six × 1 = 6.

The division is the process of separating a number right into the segment. According to the concept of identity property, when a number is divided by 1, the outcome will undoubtedly be the number itself. For instance, four ÷ 1 = 4.

**Example**

**State true or false.**

- a) The additive identity property is additionally known as the zero property of addition.
- b) According to the multiplicative identity property, multiplying 0 by any number results in the number itself.

**Solution:**

- a) True, the additive identity property is referred to as the zero property of addition.
- b) False. According to the multiplicative identity property, multiplying one by any number leads to the number itself.