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
\(4\frac{1}{2}\) = 9/2Now, 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
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