Last updated on July 23rd, 2025
The additive identity property states that adding 0 to any number does not change its value. It is useful while solving equations as it can simplify expressions. This article explains the additive identity property in detail.
The additive identity property is a significant property of addition that states that adding zero to a given number does not change its value. It is also known as the identity property of addition. Since zero is the additive identity, adding any number to zero retains its original value. The numbers to be added can be real numbers, complex numbers, rational numbers, integers, etc.
For example: b + 0 = b and 0 + b = b (where b is any real number).
The additive identity property can be mathematically expressed as a + 0 = a or 0 + a = a. This denotes that when zero is added to any number, the result is the number itself. For example: 6 + 0 = 0 + 6 = 6
Additive Identity of Whole Numbers
The additive identity property also applies to whole numbers; adding zero to a whole number does not change its value.
For example: 4 + 0 = 0 + 4 = 4
Additive Identity of Integers
According to the additive identity of integers, adding a zero to any integer will not change the value of the integer. The rule applies to both positive and negative integers. For example,
- 3 + 0 = 0 + (- 3) = - 3
10 + 0 = 0 + 10 = 10
Additive identity property can be applied to all kinds of numbers. Here, we will look at how it can be used in math equations:
Additive Identity in Algebra
The additive identity property can be applied to any algebraic expression as adding a zero to such an expression will not affect its value.
For example, let’s try adding 0 to the algebraic expression, (6y + 3)
(6y + 3) + 0 = 6y + 3
This proves that the additive identity property works in algebra.
Additive Identity in Equations
The additive identity (0) plays a key role in solving equations as it helps maintain the balance of the equation. In an equation, whenever we add or subtract a number from one side, the same must be done on the other side to maintain balance. This is done to solve for unknown variables. This can be better understood with an example.
4x – 6 = 6
Adding 6 to both sides eliminates the constant term on the left side, where x is the unknown variable. So let’s add 6 on both sides.
4x – 6 + 6 = 6 + 6
4x = 12
x = 12/4 = 3
This is how additive identity property can be used to solve equations.
Additive Identity in Polynomials
When we add or subtract the zero polynomial, which has all coefficients equal to zero, from any polynomial, it does not change the polynomial’s degree or its coefficients. This idea can be used while simplifying polynomials, performing polynomial operations, and solving equations. For example, adding the zero polynomial (0) to 5x2 + 2x – 3 does not change or affect the polynomial. Here, the polynomial 5x2 + 2x – 3 remains the same.
In real life, additive identity properties are used for financial transactions, tracking calories, or in data management. As zero is a neutral number, it is easier for calculation.
Mostly, the students confuse additive with multiplicative property. Here, few common mistakes are listed along with the solution to avoid them.
Verify the additive identity property for the number 8.
8 + 0 = 8
We use the additive identity property:
8 + 0 = 8
Adding 0 to 8 does not change its value, confirming the additive identity property.
Anna has $3000 in her savings account. If she doesn’t add any money, how much does she have?
3000 + 0 = 3000
Using the property, we add the identity (0) to the given number:
3000 + 0 = 3000
Since adding $0 does not change the amount, Anna still has $3000.
Rhea scores 65 marks on an exam. If no additional marks are added, what is the final score?
65 + 0 = 65
Using the property, we add 0 to the given number:
65 + 0 = 65
Since adding 0 marks does not change the marks obtained, the property holds true.
The current temperature is 16oC. If the temperature does not increase or decrease, what will it be?
16 + 0 = 16
Using the property, we add 0 to the given number:
16 + 0 = 16
Since adding 0 does not change the temperature, the property holds true.
Check the additive identity property of -26.
-26 + 0 = -26
Using the property, we add 0 to the given number:
-26 + 0 = -26
Since adding 0 to -26 does not change the number, the property holds true.
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.
: She loves to read number jokes and games.