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.

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.

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)

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)

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

☛ 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

What is Identity Property?

Identity property states that when any number is combined with an identity either 0 or 1, the end result will be the number itself. The property is applicable while using the four main arithmetic operations - addition, multiplication, subtraction, and division.

What is the Additive Identity Property in Math?

The additive identity property states that when a number is added to zero, it results in the number itself. For example, if 8 is added to 0, the sum is the number itself. 8 + 0 = 8. Here, zero is known as the identity element which keeps the identity of the number.

What does the Multiplicative Identity Property Mean in Math?

According to the multiplicative identity property, if a number is multiplied by 1, it results in the number itself. For example, if 12 is multiplied by 1, the product is the number itself (12 × 1 = 12). Here, one is known as the identity element which keeps the identity of the number.

What is the Difference Between Additive Identity and Multiplicative Identity?

The following points show the differences between Additive Identity and Multiplicative Identity.

• The additive identity of numbers is used for the addition operation, whereas, the multiplicative identity is used for a multiplication operation.
• 0 is the identity element in the additive identity (a + 0 = a), whereas, 1 is the identity element in the multiplicative identity (a × 1 = a).
• 25 + 0 = 25 is the example of the additive identity property and 25 × 1 = 25 is the example of the multiplicative identity property.

What is the Identity Element in Additive Identity and Multiplicative Identity?

• 0 is the identity element in additive identity.
• 1 is the identity element in the multiplicative identity.