Reciprocal Calculator

The reciprocal calculator swiftly finds the reciprocal of different types of numbers, integers, simple fractions, and mixed fractions. Through this tool, you can easily get the multiplicative inverse of any number or fraction along with the step-by-step calculation.

How To Find The Reciprocal?

The procedure of finding the reciprocal of an integer/decimal, simple, and mixed fractions is as follows:

Reciprocal of Integer/Decimal Numbers:

First of all, divide it by 1 to make a numerator: After that perform swapping of numerator and denominator as below:

The reciprocal of 24.75 is:

\(\dfrac{24.75}{1} ? \dfrac{1}{24.75}\)

\(\dfrac{1}{24.75}\ is\ a\ reciprocal\ of\dfrac{1}{24.75}\)

Change the decimal to fraction:

\(\dfrac{1\times100}{24.75\times 100}=\dfrac{100}{2475}=\dfrac{4}{99}\)

Reciprocal of Simple Fractions:

Swap the numerator and denominator:

\(\dfrac{20}{24} ? \dfrac{24}{20}=\ 1.2\)

\(\dfrac{24}{20}=\ is\ a\ reciprocal\ of\ \dfrac{20}{24}\)

Reciprocal of Mixed Fraction:

Solve the proper fraction and then flip it into its reciprocal as below:

\(\ 3\dfrac{4}{5}=\dfrac{19}{5} ? \dfrac{5}{19}=\ 1.2\)

To precisely compute the reciprocals of the decimals/numbers, fractions, and mixed fractions, use the reciprocal calculator. It simplifies the process of finding the multiplicative inverse. 

Example:

Lets suppose you have the following mixed fraction, find the reciprocal: 

\(\ The\ mixed\ fraction=\ 3\dfrac{5}{7}\)

Solution:

Change the mixed fraction to a simple fraction by multiplying the “7” by “3” and adding “5”:

We get 

\(\ Mixed\ fraction=\ 3\dfrac{5}{7}=\dfrac{21+5}{7}=\dfrac{26}{7}\)

Now we have the improper fraction. Converting the numerator to the denominator and vice versa:

\(\dfrac{26}{7},\ we\ get\ \dfrac{7}{26}\)

By multiplying:

\(\dfrac{26}{7}\times\dfrac{7}{26}=\ 1\)

You can perform the manual calculations as we have done above, or for convenience, you can use the reciprocal fraction calculator. 

FAQs:

What Is Meant by The Negative of A Reciprocal?

A negative reciprocal has a negative sign before the number. The negative reciprocal is specially designed for negative numbers and fractions.

\(\ Examples:\dfrac{-7}{1}.\dfrac{-4}{3}, \ -5\dfrac{3}{2}\ etc\)

What Is The Reciprocal of 1?

A reciprocal of the unIty or “1” is one Itself. For this, find the inverse of “1” as: \(\dfrac{1}{1}(i.e.\dfrac{1}{1} =\ 1)\ and \ (1\times 1 =\ 1)\)

What Is The Reciprocal Rule of The Division?

The simple rule of the division is "Multiply the dividend by the reciprocal of the divisor", simply you need to invert the divisor and multiply It by the dividend. 

References: From the source of Wikipedia: Multiplicative inverse, Examples and counterexamples From the source of expii.com: Explanation, Turn that Frown Upside Down