Additive Identity Vs Multiplicative Identity

Additive Identity Vs Multiplicative Identity: In the world of Numbers which we deal with on daily basis, many of the properties of real numbers are used in operations such as addition, subtraction, multiplication, division, etc. One such property involves a specific operation on numbers resulting in obtaining the same number!! This property of numbers is called IDENTITY property. This article looks at this identity property and its characteristics.

What is Additive Identity?

Additive identity of numbers, as the name suggests, is a property of numbers which is applied when carrying out addition operations. The property states that when a number is added to zero it will give the same number. “Zero” is called the identity element, (also known as additive identity) If we add any number with zero, the resulting number will be the same number. This is true for any real numbers, complex numbers and even for imaginary numbers.

Suppose, ‘a’ is any real number, then

a + 0 = a =  0 + a

For example, 120 + 0 =  120, illustrates identity property of addition, where 0 is the additive identity.

What is Multiplicative Identity?

Multiplicative identity of numbers, as the name suggests, is a property of numbers which is applied when carrying out multiplication operations Multiplicative identity property says that whenever a number is multiplied by the number \(1\) (one) it will give that number as product. “\(1\)” is the multiplicative identity of a number. It is true if the number being multiplied is \(1\) itself. The multiplicative identity property is represented as:

a × 1 = a = 1 × a  (a is any real number)

Some examples:

−1 + 0 = −1 (−1 here is the number on which the operation is carried out and “0” is additive identity.  

0 + 259 = 259 

−1 × 1 = −1 (−1 here is the number on which the operation is carried out and “1” is a multiplicative identity)  

Note: (−1) × (−1) = 1     (proves that −1 is not a multiplicative identity)

Solved Example

Example:

Which of the following illustrates the multiplicative identity and additive identity?

  1. 45 + 1 = 46 
  2. 50 × 2 = 100 
  3. 14 × 1 = 14 
  4. −54 + 0 =  −54

Solution:

According to the identity property of multiplication, the product of any number multiplied by 1 is the number itself.  

Here, only 14 × 1 = 14 satisfies the property.  

Therefore, 14 × 1= 14 illustrates the Multiplicative identity.  

According to the identity property of addition, the sum of any number added to 0 is the number itself.  

Here, only −54 + 0 = −54 satisfied the property.  

Therefore, −54 + 0 = −54 illustrates the additive identity.

To solve more problems on the topic, download BYJU’S – The Learning App from Google Play Store and watch interactive videos.

Frequently Asked Questions – FAQs

What is additive identity?

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.

Which is the multiplicative identity, 0 or 1?

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

Is -1 also a multiplicative identity?

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

What is the multiplicative identity of 5?

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

What is the additive identity of x?

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

Test your knowledge on Additive identity and Multiplicative identity

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