Additive Identity Property

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. 

• While calculating a bank account balance with no deposits or withdrawals, this property is used.

• This property helps in reading temperatures when there is no increase or decrease.

• Dietitians can assess if a patient’s weight remains the same, when there is no loss or gain.

• When a parked vehicle has zero motion, the total distance covered remains 0 km.

• The total marks acquired by a student in a particular subject will remain unchanged if no extra marks are added.