# Reciprocal

Reciprocal of a number is defined as 1 divided by the number.The reciprocal definition is also stated as follows :

• It is also called as multiplicative inverse
• The reciprocal of a fractional number is found interchanging the numerator and denominator
• All the numbers have reciprocal except 0
• The reciprocal of the product of a number is 1

Generally, it is given by

The reciprocal of a number ,

$x=\frac{1}{x}$

Examples: The reciprocals of 3, 8 are 1/3 and 1 /8

You can be able to find the reciprocal of a number, fractions and decimal numbers. The reciprocal notation of a number is also expressed by the number raised to the power of negative one.

For example, the reciprocal of a number 3 is 1/3 and it is also denoted as 3-1.

In reciprocal math, when you take the reciprocal twice, you will get the same number what you started with.

Consider an example, the reciprocal of 4 is 1/4 . When you take the reciprocal again it becomes 4/1 or 4. Here you get the same number where you started with.

## Reciprocal of a Number

The reciprocal of a number is defined as one over that number.

Example :

Find the reciprocal of 5

Solution :

To find : Reciprocal of 5

The reciprocal of a number ,

$x=\frac{1}{x}$

Therefore, $5=\frac{1}{5}$

## Reciprocal of a Fraction

The reciprocal of a fraction can be found by interchanging the numerator and the denominator values.

Example : Find the reciprocal of 5 / 8

Solution :

To find : Reciprocal of 5/8

The reciprocal of 5/8 is 8/5 . (or)

The reciprocal of a number ,

$x=\frac{1}{x}$
$\frac{5}{8}=\frac{\frac{1}{5}}{\frac{1}{8}}$

Therefore, the reciprocal of a fraction 5/8 is 8/5.

In order to find the reciprocal of a mixed fraction, convert it into improper fractions and do the reciprocal operation.

Consider a mixed fraction, $4\frac{1}{2}$.

First step is to convert a mixed fraction into an improper fraction.

$4\frac{1}{2}$= 1+1+1+1+1/2

= (2/2) + (2/2) + (2/2) + (2/2) + (1/2 )

= (2+2+2+2+1)/2

=9/2

$4\frac{1}{2}$ = 9/2

Now, you get the fraction and do the same operation for finding the reciprocal by flipping the numerator and the denominator.

Therefore, the reciprocal of 9/2 is 2/9

## Reciprocal of a Decimal

The reciprocal of a decimal is same as the reciprocal of a number defined by one over the number.

Example: Find the reciprocal of a decimal 0.75

Solution:

To find : Reciprocal of 0.75

The reciprocal of a number ,

$x=\frac{1}{x}$

Therefore, $0.75=\frac{1}{0.75}$

Alternate method to find the reciprocal of a decimal is given below.

Consider the same example, 0.75.

First , you have to check whether the given decimal number is possible for converting into fractional number. Here 0.75 is written as 3/4

Now, find the reciprocal of 3/4 which gives 4/3

When you verify both the solutions, it results the same.

That is, 1/0.75 = 1.33 and

4/3 = 1.33

For more information on finding reciprocals and other maths concepts, visit BYJU’S and also get various maths related videos to understand the concept in an easy and engaging way.

 Related Links Types of Fractions Decimals Integers Number System

#### Practise This Question

A person bought 312kg of apples, 223kg of grapes and 113kg of oranges. He wants to divide them among 4 people. Find the amount of fruits(in kg) that each person will receive.