Additive Identity Property - Examples - Cuemath

Additive Identity Property

The additive identity property is also known as the identity property of addition, which states that adding 0 to any number, results in the number itself. This is due to the fact that when we add 0 to any number, it does not change the number and keeps its identity.

1.	What is the Additive Identity Property?
2.	Additive Identity Property Formula
3.	Additive Identity of Whole Numbers
4.	Additive Identity of Integers
5.	FAQs on Additive Identity Property

What is the Additive Identity Property?

The additive identity property of numbers is one of the important properties of addition. We know that addition is the process of adding two or more numbers together. This property is applied when numbers are added to zero. Zero is known as the identity element in this property. Thus, if we add any number to zero, the obtained result will be the same number. This property can be applied to real numbers, complex numbers, integers, rational numbers, and so on.

For example, if P is any real number, then we can express this fact as follows.

P + 0 = P = 0 + P

Additive Identity Property Formula

The formula of additive identity is written as a + 0 = a. This explains that when any number is added to zero, the sum is the number itself. For example, if we add 5 to 0 we get 5 as the sum. 5 + 0 = 5.

Additive Identity of Whole Numbers

The additive identity of whole numbers is zero. This means when a whole number is added to zero, it results in the number itself. So if 'a' is a whole number that is added to zero then the result will be the whole number. For each and every whole number 'a', a + 0 = 0 + a = a. Zero is the additive identity element in the set of W. Now, let us check this property with a whole number like 54, the result will be the number itself. 54 + 0 = 54.

Additive Identity of Integers

The additive identity of integers states that if any integer is added to zero, it results in the integer itself. We know that integers include whole numbers and negative numbers, for example, 34, 0, -89, and so on are integers. Now let us apply the identity property of addition on integers. For example, if we need to add -65 + 0, we will get -65.

Additive Identity and Multiplicative Identity

The following points show the difference between the additive identity and the multiplicative identity of numbers.

• 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 (p + 0 = p), whereas, 1 is the identity element in the multiplicative identity (p × 1 = p).
• 73 + 0 = 73 is the example of the additive identity property and 73 × 1 = 73 is the example of the multiplicative identity property.

☛ Related Articles

• Properties of Addition
• Commutative Property of Addition
• Associative Property of Addition
• Zero Property of Multiplication
• Multiplicative Identity Property
• Distributive Property
• Commutative Property
• Additive Identity vs Multiplicative Identity