**What is Inverse Property of Multiplication?**

The property says that **when we multiply a number with its reciprocal we get number 1**.

Th property is expressed as:

Where A can be any possible real number.

**If the number is fraction** then the inverse property is expressed as:

In the above expression A/B is the given fraction and B/A is its reciprocal.

When we multiply the fraction with its reciprocal we get number 1.

**Note**: Remember that the property will not work when either of A or B is equal to zero

**What is the reciprocal of number?**

When you **rotate the digit upside down you get reciprocal** of the number.

In reciprocal, numerator becomes denominator and denominator becomes numerator.

**Note**: The reciprocal is also called **multiplicative inverse**.

Let us find reciprocal of number for our understanding.

\mathtt{( a) \ 3\ \Longrightarrow \ \frac{1}{3}}\\\ \\ \mathtt{( b) \ \frac{2}{5} \ \Longrightarrow \ \frac{5}{2}}\\\ \\ \mathtt{( c) \ \frac{-7}{9} \ \Longrightarrow \ \frac{-9}{7}}\\\ \\ \mathtt{( d) \ 1\ \Longrightarrow \ \frac{1}{1}}\\\ \\ \mathtt{( e) \ \ 0\ \Longrightarrow \ not\ defined}\\\ \\ \mathtt{( f) \ \frac{1}{0} \Longrightarrow \ not\ defined}\\\ \\

Note:

(i) There is** no reciprocal for number 0 **because when we inverse the digits, the number 0 gets into the denominator whose value is not defined in mathematics.

(ii) Similarly there is **no reciprocal for number (1/0)**

**Why the property is called Inverse property?**

Because we multiply the number with its multiplicative inverse to get the number 1.

**Inverse Property of Multiplication Example**

For your understanding we have provided some examples of inverse property

**Example 01**

Let A = 7

Then 1/A = 1/7

Calculating A x 1/A

\Longrightarrow \ 7\ \times \ \frac{1}{7}\\\ \\ \Longrightarrow \ \frac{7}{7}\\\ \\ \Longrightarrow \ 1

**Example 02**

Let A = 1/11

Then 1/A = 11

Calculating A x 1/A

\Longrightarrow \ \frac{1}{11} \ \times \ 11\\\ \\ \Longrightarrow \ \frac{11}{11}\\\ \\ \Longrightarrow \ 1

**Example 03**

Let A = -13

Then 1/A = -1/13

Calculating A x 1/A

\mathtt{\Longrightarrow \ -13\ \times \ \frac{-1}{13}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-13}{-13}}\\\ \\ \mathtt{\Longrightarrow \ 1}

**Example 04**

Let A = 8/9

Then inverse of A = 9/8

Calculating A x 1/A

\mathtt{\Longrightarrow \ \frac{8}{9} \times \ \frac{9}{8}}\\\ \\ \mathtt{\Longrightarrow \ \frac{8\times 9}{9\times 8}}\\\ \\ \Longrightarrow \ \frac{72}{72}\\\ \\ \mathtt{\Longrightarrow \ 1}

**Frequently asked Question – Inverse Property of Multiplication**

**How Is inverse property different from Identity Property**?

In i**dentity property**, we multiply the given number with 1 to get the same number.

Where A can be any real number.

In **inverse property**, we multiply number with its reciprocal to get number 1

**Can you name other important properties of multiplication?**

Important properties of multiplication are given below:

(a) Commutative Property

(b) Associative Property

(c) Distributive Property

(d) Identity Property

(e) Inverse property

(f) Multiplication property of equality

**Solved Problems – Inverse Property of Multiplication**

**(01) What is the reciprocal of -1/2**

(a) -1

(b) 1/2

(c) -2

(d) 2

**Option (c) is correct**

In reciprocal, we turn the number upside-down, i.e. numerator becomes denominator and denominator becomes numerator.

**(02) if 3 x 1/y = 1**

Find the value of y

(a) 1

(b) 1/3

(c) -3

(d) 3

**Option (d) is correct**

**Explanation:**

The expression is of inverse property of multiplication.

It can be written as:

3 x 1/3 = 1

On comparing, we get value of y = 3

**(03) what is the reciprocal of number 1/0**

(a) Not defined

(b) 0

(c) -1

(d) 1

**Option (a) is correct**

**Explanation:**

Any number with denominator 0 is not defined. So its reciprocal is also not defined.

**(04) Find the value of below expression**(11/98) x (98/11) = ?

(a) 2

(b) 11

(c) 9

(d) 1

**Option (d) is correct****Explanation:**

The expression shows property of multiplicative inverse

Solving the given expression:

\mathtt{\Longrightarrow \ \frac{11}{98} \times \ \frac{98}{11}}\\\ \\ \mathtt{\Longrightarrow \ \frac{11\times 98}{98\times 11}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1078}{1078}}\\\ \\ \mathtt{\Longrightarrow \ 1}

**(05) Find the reciprocal of number (6/17)**

(a) -6/17

(b) 17/6

(c) -17/6

(d) 6/19

**Option (b) is correct****Explanation:**

Reciprocal can be found by inverting number upside down