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 identity 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
