Identity Property - Definition, Additive, Multiplicative, Examples

Identity Property

Identity property is applied to a group of numbers in the form of sets. The identity of these numbers remains the same as 1 and 0 even when the numbers are added, subtracted, multiplied, and divided. Among the arithmetic operations, addition and multiplication are used more often. Let us learn more about the identity property, types, and solve a few examples.

1.	Identity Property Definition
2.	Additive Identity Property
3.	Multiplicative Identity Property
4.	Additive Vs Multiplicative
5.	FAQs on Identity Property

Identity Property Definition

Identity property is defined as the property where if any arithmetic operations are used to combine an identity with a number (n), the end result will be n. Any number can be considered as an identity when added, subtracted, multiplied, or divided with another number such as n, allows n to remain the same. This identity or end result will always be a 0 or 1 depending on the arithmetic operation used. In the case of addition and subtraction, the result is 0 i.e. when 0 is added or subtracted from n, then the value of n remains the same. Whereas in multiplication and division, the identity is 1 i.e. when 1 is multiplied or divided with n, the value of n remains the same. Look at the image below to understand the concept better.

Identity is Always 0 and 1

As we already learned that the identity will always be 0 and 1 depending on the arithmetic operation used. The reason for this is as follows:

• In mathematics, addition is considered as the process of adding any one number to another number. According to the identity property, when a number is added to 0, the result will be the same. For example, 25 + 0 = 25.
• Subtraction is the process of taking away one number from the given whole number. Hence, when 0 is subtracted from a number, the result is the same. For example, 16 - 0 = 16.
• Multiplication is the process of repeated addition i.e. the number is repeatedly added by the number of times stated by the other number. For example, 6 × 5, 6 is repeatedly being added 5 times. According to the identity property of multiplication, when a number is multiplied by the number 1, the product will be the number itself, 6 × 1 = 6.
• Division is the process of separating a number into parts. According to the identity property, when a number is divided by 1, the result will be the number itself. For example, 4 ÷ 1 = 4.

Additive Identity Property

The additive identity property states that when a number is added to 0 then the result obtained will be the same as the number. Here, 0 is known as the identity element. This property is applicable for real numbers, complex numbers, integers, rational numbers, whole numbers, and so on. For example, 23 + 0 = 23.

Therefore, the additive identity formula is a + 0 = a (a is any real number)

Multiplicative Identity Property

The multiplicative identity property states that when a number is multiplied by 1, the product will be the number itself. Here, 1 is considered as the identity element. This property can be applied to real numbers, complex numbers, and so on. The multiplicative property is applicable for any non-zero rational number p/q and in the case of integers. For example, 87 × 87 = 87, where 87 is the number on which we applied the multiplicative identity.

Note: The multiplicative identity is not applied when any number is multiplied by -1 because the result will not be the same number. For example, 29 × -1 = -29.

The multiplicative identity formula is expressed as a × 1 = a (a is any real number)

Additive Vs Multiplicative

The below table shows the difference between additive identity and multiplicative identity.

Additive Identity Property	Multiplicative Identity Property
Used in addition	Used in multiplication
The additive identity element is 0	The multiplicative identity element is 1
Formula: a + 0 = a	Formula: a × 1 = a

☛ Related Articles

Listed below are a few articles related to identity property.

• Zero Property of Multiplication
• Associative Property of Addition
• Additive Identity vs Multiplicative Identity
• Associative Property of Multiplication