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You'll Be Surprised to Know About the Identity Property of Addition

Omkar Phatak Apr 23, 2019
What is the identity property of addition? If you are looking for a clear answer to that question, keep reading ahead. Here, we elucidate the property and illustrate it through examples.
Starting with your first math course, one of the first things that you will learn is how to add, subtract, multiply, and divide numbers. These are the four basic mathematical operations that you need to understand properly.
They are elements of what is called basic arithmetic or mathematics. There are many properties related to each of these mathematical operations, which need to be understood by you.

Adding Numbers

The addition operation between two numbers, denoted by the '+' sign, is summing two small numbers together to get a bigger number. Suppose you have 5 dollars in your pocket and your father gives you 10 dollars more. How may dollars are left with you?
To know the answer, you must 'sum up' or 'add' the two amounts. So you will have (5 + 10 = 15) dollars now. One way of visualizing addition of numbers is by looking at the number line as a series of steps in a staircase.
Each step in the staircase is labeled with numbers starting from 1, 2, 3, 4, ... up to the maximum number possible, in ascending order. When you add, you ascend steps and when you subtract, you descend steps downwards.
So if you are standing on step number 5, and you need to add 10, you ascend ten steps on the staircase, to reach 15. To make this number line and staircase analogy more precise, know that the staircase is never ending on both sides. There are positive and negative integers extending on both sides of it.


This property deals with the consequence of 'zero' to any positive or negative number. It states that, 'On adding zero to any number or any algebraic variable, the resultant sum is the same number again.' In the form of an equation, it can be stated as:

X + 0 = X
where X is any variable or a number. It is called the identity property, as when zero is added to a number, the resultant sum is the same as the number's identity. Here, zero is known as the 'identity element'. Let me illustrate the concept further, through examples.

Illustrative Examples

Here are some examples which demonstrate the property succinctly.
  • 1 + 0 = 1
  • -1 + 0 = -1
  • XY + 0 = XY
  • 0 + 0 = 0
  • X/Y + 0 = X/Y
  • 0 + 88 = 88
  • 99.99 + 0 = 99.99
This property of identity, in addition arises due to the peculiar nature of zero as a number, which denotes 'nothing.' In terms of our staircase analogy, adding zero is like taking neither a step up or step down on the staircase. It is just jumping on the same step, which leaves you right where you are.
It is one of the most important properties when it comes to defining addition of numbers, though it looks trivial at face value. To put it in simplest of words, the property states that when you add 'nothing' to any number, all that you get is the same number back again. Remember this explanation and understanding the identity property is simple enough.