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# Multiplicative Inverse of Rational Numbers

Let's discuss about the multiplicative inverse of Rational Numbers. Simply the multiplicative inverse is the reciprocal of a fraction like multiplicative inverse of 'm/n' is 'n/m'. The reciprocal or multiplicative inverse for a number z is denoted by 1/z or z-1. In rational numbers, zero does not have a reciprocal because no rational numbers or Real Numbers multiplied by 0 produces 1. The multiplicative inverse or reciprocal function, the function f(z) that maps z to 1/z, is the simplest examples of a function which is self-inverse. Some example of multiplicative inverse are, the inverse or reciprocal of 7 is 1/7 and the reciprocal or inverse of 0.25 is 4.

## Find the Multiplicative inverse of given rational number 4/5?

Step 1: First of all we will write the given rational number in the form 'p/q',

p/q=4/5,

Step 2: For multiplicative Inverse we have to write the reciprocal of the given rational number. The reciprocal can be written as:

=>  p/q = q/p = 5/4,

Step 3:  Now, we will multiply both the Rational Numbers, on doing so we get,
Multiplicative Inverse = p/q x q/p,
= 4/5 x 5/4,
= 20/20 =1.

## Find the Multiplicative Inverse of -3/4?

Step 1: Write the given rational number in p/q form, on doing so, we get:

p/q=-3/4,

Step 2: For multiplicative inverse we write the reciprocal rational number,

p/q = q/p = 4/-3,

Step 3:  Now, we multiply both the terms,

Multiplicative Inverse = p/q x q/p,
= -3/4 x 4/-3,
=1.

## Find the Multiplicative Inverse of given Rational Number (|-2|/3)?

Step 1: First of all we will write the given rational number in the form 'p/q',

=> p/q=|-2|/3 = 2/3,

Step 2:  For multiplicative Inverse we have to write the reciprocal of the given rational number. The reciprocal can be written as:
=>  p/q = q/p = 3/|-2|= 3/2,

Step 3:  Now, we will multiply both the Rational Numbers,we get
Multiplicative Inverse = p/q x q/p,
= 2/3 x 3/2,
= 1.

## Find the Multiplicative Inverse of given rational number(|-5|)?

Step 1: First of all we will write the given rational number in the form 'p/q',

=> p/q=|-5|/1 =5/1,

Step 2: For multiplicative Inverse we have to write the reciprocal of the given rational number. The reciprocal can be written as:

=>  p/q = q/p = 1/|-5|=1/5,

Step 3 : Now, we will multiply both the Rational Numbers and we get,
Multiplicative Inverse = p/q x q/p,
= 5/1 x 1/5,
=1.