What Is the Reciprocal of a Fraction?
The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. It represents the multiplicative inverse of the given fraction.
A reciprocal of any non-zero number is simply written as 1 divided by that number.
The reciprocal of a fraction is a value which, when multiplied with the given fraction, results in 1.

Examples of Reciprocal of Fractions:
- The reciprocal of
is or simply 2. - The reciprocal of
is .
Recommended Games
Reciprocal of a Fraction Definition
The reciprocal of a fraction is a multiplicative inverse of the original fraction. It is a new fraction that is obtained by interchanging the numerator and the denominator of the original fraction.
Recommended Worksheets
How to Find the Reciprocal of a Fraction
Finding reciprocal of fractions is simple. We only need to interchange or swap the numerator and denominator in order to determine the reciprocal of a fraction.
In general, reciprocal of a fraction
For example, the reciprocal of
Note: You can also find the reciprocal of a fraction by dividing 1 by the fraction.
Reciprocal of 0
The reciprocal of 0 is not defined. There is no value or number which, when multiplied with 0, results in 1. Thus, 10 is undefined.
Reciprocal of a Fraction Visualization
We know that the reciprocal of
How many halves make 1 whole?
Two halves make 1 whole.
Two

Similarly, the reciprocal of
How many quarters
Four

Reciprocal of a Mixed Fraction
To find the reciprocal of a mixed fraction, we first need to convert it to an improper fraction. An improper fraction has a numerator that is greater than or equal to the denominator. After getting the improper fraction, we can take its reciprocal by interchanging the numerator and denominator.
Example: Consider a mixed fraction
To convert it to an improper fraction, we multiply the whole number (4) by the denominator (7) and add the numerator (5). This value is the numerator. Denominator stays the same.
Therefore, the improper fraction for the mixed fraction
Now, the reciprocal of
Thus, the reciprocal of
Reciprocal of a Negative Fraction
If a fraction has a negative sign, its reciprocal also has a negative sign. In this case, simply take the reciprocal of the positive fraction and assign the negative sign to it.
The reciprocal of a negative fraction
Example: The reciprocal of
Reciprocal of a Fraction with Exponents
The form of fractions with exponents is
An expression
Now, swap the numerator and denominator to find the reciprocal.
Therefore, the reciprocal of apbp is
Example: Find the reciprocal of
We can write
Hence, the reciprocal of
Facts about the Reciprocal of a Fraction
- The reciprocal of a fraction is also known as its multiplicative inverse. When we multiply a fraction by its reciprocal, the result is always 1.
- The reciprocal of a proper fraction is always an improper fraction.
- The reciprocal of an improper fraction is always a proper fraction.
- The reciprocal of a unit fraction is always a whole number. For example, the reciprocal of
is 10. - The reciprocal of a whole number (non-zero) is a fraction with the numerator 1 and the original whole number as the denominator. For example, the reciprocal of 10 is
. - The reciprocal of 0 is undefined.
- The reciprocal of 1 is 1.
- The reciprocal of a reciprocal is the original fraction itself.
Conclusion
In this article, we learned about the reciprocal of a fraction, its definition, examples of reciprocal fractions, the reciprocal of mixed fractions, the reciprocal of fractions with exponents, the methods of finding reciprocal of fractions, and interesting facts. Let’s move ahead and solve a few examples and practice problems based on all these concepts.
Solved Examples on Reciprocal of a Fraction
- Find the reciprocal of
.
Solution:
The reciprocal of a fraction is obtained by interchanging its numerator and denominator.
Hence, the reciprocal of
- What is the reciprocal of the sum of
and ?
Solution:
Sum of the given fraction
Hence, the reciprocal of sum
- If a is the reciprocal of
, then find the value of .
Solution:
- Find the reciprocal of
.
Solution:
To find the reciprocal of a mixed number, we first need to convert it to an improper fraction.
Reciprocal of
Hence, the reciprocal of
- Find the reciprocal of
?
Solution:
We can write the given mixed fraction as an improper fraction.
Reciprocal of
- John can mow a lawn in 5 hours. What is the reciprocal of the fraction representing John’s hourly mowing rate?
Solution:
John can mow a lawn in 5 hours.
John’s hourly mowing rate is
Hence, the reciprocal of
Therefore, John’s reciprocal hourly mowing rate is 5 lawns per hour.
- Find the reciprocal of
?
Solution:
Reciprocal of
Practice Problems on the Reciprocal of a Fraction
Reciprocal of a Fraction - Definition, Steps, Examples, FAQs
What is the reciprocal of 0?
Reciprocal of
What is the reciprocal of the fraction ?
The reciprocal of
What is the reciprocal of the fraction ?
To find the reciprocal of a fraction, we flip the fraction by interchanging the numerator and the denominator.
So, the reciprocal of
What is the reciprocal of the mixed number ?
To find the reciprocal of a mixed number, we first need to convert it to an improper fraction.
The reciprocal of
What is the reciprocal of the fraction ?
To find the reciprocal of a fraction, we flip it over.
So, the reciprocal of
Frequently Asked Questions about the Reciprocal of a Fraction
What is a reciprocal of a fraction?
The reciprocal of a fraction is simply the fraction obtained by interchanging the numerator and the denominator. The numerator becomes the denominator, and the denominator becomes the numerator.
What is the reciprocal of a mixed fraction?
To find the reciprocal of a mixed fraction, we first need to convert it to an improper fraction. The reciprocal of the improper fraction thus obtained represents the reciprocal of the mixed fraction.
What is the relationship between a fraction and its reciprocal?
The product of a fraction and its reciprocal is always 1. For example, if we multiply
What is the reciprocal of a decimal?
The reciprocal of a decimal can be found by converting the decimal to a fraction and then taking its reciprocal.
For example, to find the reciprocal of 0.25, first convert decimal to fraction.
Hence, the reciprocal of 0.25 is
What is the reciprocal of zero?
The reciprocal of 0 is undefined because any number multiplied by zero is always zero, which means there is no number that can be multiplied by zero to give a product of 1.
What is the difference between a fraction and its reciprocal?
The difference between a fraction and its reciprocal is that the numerator and denominator are swapped. For example, the reciprocal of
What is the reciprocal of a negative fraction?
Find the reciprocal of the fraction ignoring the sign, attach the negative sign to theresulting fraction to find the reciprocal of the negative fraction.