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157 LearnersLast updated on October 10, 2025
Identity Property
In identity property, a number remains unchanged when combined with 1 or 0. This property is not applicable to subtraction, and division. However, addition and multiplication are the most commonly used arithmetic operations.
What is the Identity Property?
The identity property is a key concept in mathematics that applies to operations like addition and multiplication. It says that when a number (n) is combined with a specific identity element using an arithmetic operation, the result remains the same.
The special numbers (0 and 1) are called identity elements because they keep the value of a number intact. The number stays the same after the operation as well.
The identity property shows how the numbers behave in arithmetic operations in different groups of numbers.
There are two kinds of identity properties:
Additive Identity: 0 is the identity for addition because, adding 0 to a number, keeps the number the same.
n + 0 = n
Multiplicative Identity: 1 is the identity for multiplication because multiplying a number by 1 keeps it the same.
n × 1 = n
Conditions for Identity Property
For the identity property to hold in a mathematical operation, the following conditions must be met:
- There must be a unique number, called the identity element that, when used in an operation with any number n, leaves n unchanged.
- The additive identity is 0, meaning a + 0 = 0 + a = a. This must be applied to all numbers in the given set.
- The multiplication identity is 1, meaning a × 1 = 1 × a = a. This must be true for all numbers in the set.
- The mathematical operation should be properly defined within the number set (e.g., real numbers, integers) for the identity element to work correctly.
- The identity element must be unique for each operation. There is only one additive identity (0) and one multiplicative identity (1) in standard number systems.
- Exponentiation does not have identity property. For example, ae = ea = a is only valid if both a and e are equal to 1, which means exponentiation does not satisfy the identity property for all real numbers.
Additive Identity Vs Multiplicative Identity
Let’s understand the two identity property differences in a simple table format.
| Property |
Additive Identity |
Multiplicative Identity |
| Definition |
A number that, when added to another number, does not change its value. |
A number that, when multiplied by another number, does not change its value. |
| Operation | Addition | Multiplication |
|
Identity Element |
0 |
1 |
|
Example (Positive) |
6+0=6 |
8×1=8 |
|
Example (Negative) |
(−4)+0=−4 |
(−5)×1=−5 |
Real-life Applications of Identity Property
The identity property isn’t just a math rule. It applies to real-life situations, too.
Whether dealing with money, shopping, or counting, this property helps us understand how numbers stay the same when adding zero or multiplying by one. Here are some everyday examples.
- Money Transactions (Additive Identity ): If you have $20 in your wallet. If you don’t add any money ($0), the total amount of money doesn't change. You still have $20. This follows the rule $20 + $0 = $20.
- Multiplying by One in Shopping (Multiplicative Identity): Let's say you are at a shop, and you buy a pack of gum for $2, the total price is $2 × 1 = $2. The number stays the same because multiplying by 1 doesn’t change the value. So, whether it's gum or fruits, if you buy only one item, the total cost is the price of that one item.
Solved Examples for Identity Property
Problem 1
What is 15 + 0?
15
Explanation
The identity property of addition states that adding 0 to any number does not change its value.
Problem 2
What is 1 24?
24
Explanation
The identity property of multiplication states that multiplying any number by 1 keeps the number the same.
Problem 3
Lily has $50 in her bank. She does not deposit any money. How much does she have now?
$50
Explanation
Since Lily started with $50 in her bank and didn't deposit any money ($0), as per the identity property, balance remains unchanged.
Problem 4
Solve for x in the equation: x + 0 = 56.
x = 56.
Explanation
Since adding 0 to any number does not change it. Means x must be 56. This follows the identity property of addition.
Problem 5
A box contains 1 set of 93 pencils. How many pencils are in the box?
There are 93 pencils in the box.
Explanation
The box contains 93 pencils because 1 set of 93 is the same of 1 × 93. This follows the identity property of multiplication.
FAQs Related to Identity Property
1.Why is the identity property important in math?
2.What is the identity property, in simple terms?
3.Does the identity property work for subtraction and division?
4.Why is 0 called the additive identity?
5.Why is 1 called the multiplicative identity?
6.How can families in United States create number-rich environments to improve Identity Property skills?
7.What are some fun ways kids in United States can practice Identity Property with numbers?
8.What role do numbers and Identity Property play in helping children in United States develop problem-solving skills?
9.How can children in United States use numbers in everyday life to understand Identity Property?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
