Additive Identity Property Definition and Examples

Additive identity is a fundamental property in mathematics that states that "when we add zero to any number it results in the original number itself." This property is also called the identity property of addition. Additive Property is also called "Additive Property of Zero."

In this article, we will learn about, Additive Identity, its formula, application and examples in detail.

What is Additive Identity?

Additive identity is a fundamental mathematical principle that states that adding zero to any integer yields the same outcome. In simple words, we

For example, if you have 5 apples and add 0 more, you will still have 5. Similarly, if you have Rs. 100 and add Rs. 0, you will still have Rs. 100. So, in any addition operation, adding zero does not affect the original number, demonstrating additive identity.

Additive Identity Property of Zero Definition

Additive identity is a mathematical property that states that adding zero to a number does not affect its value. In other words, zero is a particular number that may be added to any other number without changing the number. For example, adding zero to 5 or 100 results in the same number itself, illustrating additive identity.

Additive Identity in Mathematics

In mathematics, additive identity is a fundamental notion that states that adding or subtracting zero from any integer results in the same value. This theory applies to both addition and subtraction operations, demonstrating the stability of integers when combined with zero.

Additive Identity in Addition

Furthermore, the additive identity principle ensures that adding zero to every integer yields the same result. Zero functions as a neutral element, retaining the original value of the number it is added to.

Example of Additive Identity in Addition

Add: 7 + 0

Result of 7 + 0 = 7

Here the additive identity of addition holds, where 0 is the additive element.

Additive Identity Property Formula

Additive identity formula states that adding 0 to any number does not changes the number and is written as:

• a + 0 = a
• 0 + a = a

For example, adding 8 to zero or zero to 8 ends in 8 as result, i.e. 8 + 0 = 0 + 8 = 8.

Additive Identity of Whole Numbers

Additive identity of whole number states that adding zero to a whole number does not affects the whole number. Now applying additive identity to whole numbers,

• 5 + 0 = 0 + 5 = 5

Additive Identity of Integers

Additive identity for integers tells us that adding zero to any integer gives us the same integer back. Integers include whole numbers and negatives numbers, like 7, 0, and -9. Now applying additive identity to integers,

• -7 + 0 = 0 + (-7) = -7
• 11 + 0 = 0 + 11 = 11

Additive Identity Property

Additive identity property, a fundamental property in mathematics, states that adding zero to any integer results in the number remaining unaltered. We can apply this property to all types of numbers including, real numbers, complex numbers, integers, rational numbers, and so on.

For example, for any real number P we can say that,

P + 0 = P = 0 + P

Additive Identity in Algebra

In algebra, the additive identity is the condition that adding zero to any algebraic statement or variable does not modify its value.

Example of Additive Identity in Algebra

Consider an algebraic expression, such as 2x+3

Add zero to it: (2x + 3) + 0

The expression remains 2x + 3, demonstrating the additive identity in algebra

Additive Identity in Equations

In equations, the additive identity concept is used to preserve balance and solve for unknown variables. We can modify an equation by adding or removing the same value from both sides while keeping the answer constant. This characteristic is crucial for isolating variables and solving equations.

Example of Additive Identity in Equations:

Consider the equation 2x − 5 = 7

Add 5 to both sides: 2x - 5 + 5 = 7 + 5

The equation becomes 2x = 12, demonstrating how the additive identity may be used to solve equations

Additive Identity in Polynomials

Within the domain of polynomials, the additive identity feature remains important. The addition or subtraction of zero polynomials from any polynomial has no effect on its degree or coefficients. This condition is essential for polynomial operations, simplifications, and polynomial equations since it ensures that the original polynomial's properties stay unaltered.

Example of Additive Identity in Polynomials

Consider a polynomial like 3x² + 4x - 2

Add a zero polynomial to it: (3x² + 4x - 2) + 0

The polynomial remains 3x² + 4x - 2, which demonstrates the additive identity in polynomials

Why is Additive Identity Important in Mathematics?

Understanding additive identity is key in math because it forms the basis for addition and subtraction.

• Knowing that adding or subtracting zero from any number doesn't change its value simplifies calculations and problem-solving.
• It's like a foundational rule that keeps math consistent and logical.

Learning additive identity helps students grasp how numbers interact and how arithmetic functions works. This understanding helps in tackling more complex math concepts and improving problem-solving skills.

How is Additive Identity Used in Equations?

Additive identity is important in equations because it helps to keep them balanced and consistent. In equations, when we add or remove the same integer from both sides, we are effectively using the additive identity principle. This approach assures that the equation remains constant, allowing us to isolate variables and solve problems.

For example, if we have the equation 3x + 5 = 10, we may remove 5 from both sides to obtain 3x = 5. Here, the additive identity (subtracting 5) simplifies the problem and makes it easy to solve for the variable x.

Additive Identity and Multiplicative Identity

Additive identity is used in case of addition operation, whereas, the multiplicative identity is used in case of multiplication operation.

• Additive identity states that, A + 0 = 0 + A = A
• Multiplicative identity states that, A × 1 = 1 × A = A

Learn in Detail, Additive Identity Vs Multiplicative Identity

Read More:

• Mathematical Concepts for Beginners
• Basic Arithmetic Operations
• Properties of Whole Numbers

Additive Identity Examples

Example 1: Which of the equations below exhibits the additive identity property?

1. 78 + 5 = 83
2. 90 + 0 = 90

Solution:

• 78 + 5 = 83 does not demonstrate the identity feature of addition.
• 90 + 0 = 90 illustrates the identity feature of addition.

Example 2: If y + 0 = 20, what is the value of y?

Solution:

y + 0 = 20

y = 20 - 0

y = 20

So, 20 + 0 = 20

Example 3: If 14 + n = 14, what is the value of n? Please specify the property that you utilized.

Solution:

14 + n = 14 (given)

n = 14 - 14

n = 0

So, 14 + 0 = 14

Additive identity property is being employed here.

Practice Questions of Additive Identity

Q1: Which of the equations below exhibits the additive identity property?

1. 63 + 0 = 63
2. 52 + 7 = 59

Q2: If x + 0 = 42, what is the value of x?

Q3: Which equation exemplifies the additive identity in subtraction?

1. 90 - 0 = 90
2. 78 - 5 = 73

Q4: To solve for x, use the equation 15 + x = 15. Mention the property utilised.

Q5: Find the value of m if m + 0 = 50. Specify the property used.