Multiplicative Identity

In mathematics, the multiplicative Identity defines so as to the multiplication of whichever number and one (=1) is the number itself. Therefore, the multiplicative identity satisfying the following definition, such as

a x 1 = 1 x a = 1.

or

a x `(1)/(a)` = `(1)/(a)` x a

Definition of Multiplicative Identity

Multiplicative Identity states that the product of any number and one (=1) is the number itself.

More about Multiplicative Identity

Multiplicative identity is also called the identity property of one or the identity property of multiplication.

Examples of Multiplicative Identity

59 ? 1 = 59 (As the number is multiplied by 1, the result is the number itself.)

a ? 1 = a

Solved Example on Multiplicative Identity

Which number sentence illustrates the identity property of multiplication?
Choices:

A. 54 + 1 = 54

B. 54 ? 1 = 55

C. 54 ? 1 = 54

D. 54 ? 1 = 0

Correct Answer: C

Solution:

Step 1: According to identity property of multiplication, the product of any number and 1 is the number itself.
Step 2: Here, only '54 ? 1 = 54' satisfies the property.
Step 3: So, the number sentence '54 ? 1 = 54' illustrates the identity property of multiplication.

Related Terms for Multiplicative Identity

Number

One

Product

Property

A number e designed for which definition is (a).(e)=(e).(a)=a for each factor a of a set. Here, the sets are N (natural numbers), Z (integers), Q (Rational numbers), R (real numbers), C (complex numbers) the multiplicative identity is 1.

Multiplicative identity is as well labeled the identity property of one (=1) or the multiplications of identity property.

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Multiplicative Identity Examples:

Example 1:

Check the following expression satisfy multiplicative identity property?

49 ? 1 = 49

Solution:

Given : 49 x 1 = 49.

Here, when the number 49 is multiplied by multiplication identity 1, then the product is the number itself.

i.e., a ? 1 = a

Hence, the above expression satisfied the multiplicative identity property.

Some more Examples on Multiplicative Identity:

Example 2

Check whether the following expressions are satisfying the multiplicative identity?

A. 44 + 1 = 44

B. 33 ? 1 = 33

C. 66 ? 1 = 54

D. 45 ? 1 = 0

Solution:

(A) 44 + 1 = 44

Here, 44 + 1 = 45.

Therefore, the addition of 44 and 1 is produced the number is 45.

Hence, the above expression is not satisfied the multiplicative identity property.

(B) 33 x 1 = 33

Here, 33 x 1 = 33.

Therefore, the multiplication of 33 and the multiplicative identity 1is produce that number itself.

Hence the above expression satisfied the multiplicative identity property.

(C) 66 x 1 = 54

Here, 66 x 1 = 66, but the given product of result is not same.

Hence, the above expression not satisfies the multiplicative identity definition.

(D) 45 x 1 = 0

Here, 45 x 1 = 0.

That is, the multiplication of 45 as well as multiplicative identity 1 is produce the result is 0.

Hence, the above expression not satisfied the multiplicative identity definition.

Example 3:

Verify the following expression satisfy the multiplicative identity definition?

78 x `(1)/(78)` = 1

Solution:

Given: 78 x `(1)/(78)` = 1

Here, 78 x `(1)/(78)` = 78 x 1 = 78.

Therefore, the multiplication of 78 and it's reciprocal number produce the multiplicative identity 1.

Hence, the above expression is satisfied the multiplicative identity definition.

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