# Identity Property of Multiplication

## What is identity property of multiplication?

According to the property, if we multiply any given number with 1, we will get the same number.

The property can be expressed as:

Where A can be any possible real number.

### Why the property is named as “Identity”?

Because after multiplying the number A with 1, we get back the same number A.

The identity of number A is protected after the multiplication, that’s why the property is called identity property.

### Identity Property Explanation using Number line

Let A = 5

Using identity property:
⟹ A x 1
⟹ 5 x 1
⟹ 5

### Example of Identity Property

Example 01
Let A = 9

Calculate A x 1
⟹ A x 1
⟹ 9 x 1
⟹ 9

Hence, 9 x 1 = 9

Example 02
Let A = 1/3

Calculate A x 1
⟹ A x 1
⟹ 1/3 x 1
⟹ 1/3

Hence, 1/3 x 1 = 1/3

Example 03
Let A = -11

Calculate A x 1
⟹ A x 1
⟹ -11 x 1
⟹ -11

Note:
In all the above examples, the value of number remains the same after multiplication with 1.

### Frequently asked questions on Identity Property?

#### How is identity different from inverse property of multiplication?

Identity Property says that if you multiply any number with 1, you will get the same number.

Inverse Property says that multiplication of any number with its reciprocal results in number 1.

#### Difference between Identity Property and Zero property of multiplication

Identity Property
Multiplication of any number with 1 results in same number

Zero Property
Multiplication of any number with 0 results in 0

#### How is Commutative Property different from Identity Property of Multiplication?

Commutative Property:
While multiplying two or more numbers, changing the location of number will not affect the final result.

Identity Property is all about multiplication of number with 1.

#### If we multiply number with 2, will it still be identity property?

No!!!

When we multiply any number with 2, we get completely different number.

For example:
Let A = 5

Calculate A x 2
⟹ A x 2
⟹ 5 x 2
⟹ 10

Here 10 is completely different number.
The identity of number 5 is changed after multiplication, hence this operation cannot be called Identity Property.

#### Will the identity property works for division?

Yes!!

If we divide any number with 1, we will get the same number.

#### What is identity property of addition?

According to the property, if we add any number with zero we will get the same number.

## Questions on Identity Property of Multiplication

(01) Identity property works on following math operation
(b) Multiplication
(c) Subtraction
(d) Division
(e) All of the above

Option (e) is correct.
The identity property is available for all the above math operation.

(02) Fill in the blanks with suitable number
5 x _______ = 5

(a) 5
(b) 2
(c) 1
(d) -1

Option (c) is correct

Explanation:
This math expression is an example of Identity Operation.
5 x 1 = 5

(03) Below expression is representation of identity property, True or False?
5 x (1/5) = 1

(a) True
(b) False

Option (b) is correct

Explanation:
The expression represents inverse property of multiplication.

Inverse property is given by:
A x 1/A = 1

(04) Fill in the blanks
________ x 1 = 1/7

(a) 7
(b) -7
(c) 1/7
(d) 1/7

Option (c) is correct

Explanation
Using identity property of multiplication:
1/7 x 1 = 1/7

(05) Dave x 1 = ___________

(a) 1 + Dave
(b) 1/Dave
(c) Dave Ramsey
(d) Dave