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Additive Identity Vs Multiplicative Identity - Understanding The Difference

Last Updated on Jul 31, 2023
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Additive Identity and Multiplicative Identity are fundamental concepts in mathematics. If you add an additive identity to any number, you get the same number back. Similarly, if you multiply any number by a multiplicative identity, you also get the original number back. These properties hold true for all real numbers . This article will explore the differences between these two identities and how they function.

For all numbers, including whole numbers, natural numbers, and integers, the additive identity is zero (0) and the multiplicative identity is one (1).

Table of Contents:

Defining Additive Identity

When it comes to addition, the additive identity plays a crucial role. This property states that when you add zero to any number, you end up with the same number. This holds true for all types of numbers, be it real, complex, or even imaginary.

Let's say 'b' is any real number, then:

b + 0 = b = 0 + b

For instance, if we add 0 to 200, we get 200, which shows the identity property of addition, with 0 acting as the additive identity.

Defining Multiplicative Identity

The multiplicative identity is a property that comes into play when you're multiplying numbers. According to this property, any number multiplied by 1 gives the same number. So, '1' is the multiplicative identity. This is true even if the number being multiplied is 1 itself.

Let's denote it as follows:

b x 1 = b = 1 x b (where b is any real number)

Comparing Additive and Multiplicative Identity
Additive Identity Multiplicative Identity
The additive identity for any real number is 0. For any real number, the multiplicative identity is 1.
It can be represented as b + 0 = b, where b is any real number. It can be denoted as b x 1 = b, where b is any real number.
It is used in addition operations. It is used in multiplication operations.
Example: 9 + 0 = 9 Example: 9 x 1 = 9

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Practical Examples

Example 1: Show that 200 is an additive identity.

Solution: If we add 0 to 200, we get 200. So, 0 is the additive identity of 200.

Example 2: Show that 1000 is a multiplicative identity.

Solution: If we multiply 1000 by 1, we get 1000. So, 1 is the multiplicative identity of 1000.

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Frequently Asked Questions

Additive identity is the value when added to a number, results in the original number. When we add 0 to any real number, we get the same real number. For example, 5 + 0 = 5. Therefore, 0 is the additive identity of any real number.

The multiplicative identity of a real number is 1. When we multiply 1 by any real number then we get the same number. Examples are 3 x 1 = 3, -9 x 1 = -9, ½ x 1 = ½.

-1 is not a multiplicative identity, because if we multiply -1 by any real number, the sign of that number gets changed. Examples are 4 x -1 = -4, -4 x -1 = 4.

Multiplicative identity of 5 is 1 only, since 5 x 1 = 5.

Additive identity of x is 0, since x+0 = x.
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