Reciprocal of a Fraction

Remember that a fraction has three parts.


this illustration displays the different parts of a fraction. in a/b, a is the numerator which is the top number while b is the denominator which is the bottom number. the "line segment" that separates the numerator and the denominator is called the fractional bar.
this table identifies the different parts of a fraction namely, the numerator, the denominator, and the fractional bar.

How to Find the Reciprocal of a Fraction

To get the reciprocal of the fraction

this is the standard form of a fraction which is a/b. however, b cannot equal to zero.

simply swap or interchange the roles of the numerator and denominator. You may say that we just turn the original fraction upside down.

this GIF image demonstrates how we swap the roles of the numerator and denominator to get the reciprocal of a given fraction

Examples of Finding the Reciprocal of a Fraction

Example 1: Find the reciprocal of the fraction below.


Let’s turn the fraction [latex]{3 \over 7}[/latex] upside down to get its reciprocal. This gives us


Example 2: Find the reciprocal of the fraction below.


This can be tricky for some. Notice that the numerator is negative. If we turn this fraction upside down, we should naturally get


Since this is a negative fraction, the negative symbol may not always “follow” the number that it is initially attached to.

In other words, the negative symbol can stay in the numerator. And so, after inverting the two numbers, the negative symbol is now attached to 2. This is also a valid answer as the reciprocal of the original fraction.


There is one more way to write the reciprocal of this negative fraction. The negative symbol may not be attached either to the numerator or denominator.

It is also correct to place the negative symbol directly to the left of the fraction bar. This is how it looks!


So in summary, if the fraction is negative its reciprocal can be written three ways.

  • Negative symbol stays with the numerator
  • Negative symbol stays with the denominator
  • Negative symbol stays with the fractional bar

Example 3: Write the reciprocal of the negative fraction below in three different ways.



this table explains three different ways how to express a negative fraction. for example, for negative nine-fourths (-9/4), one way to write it is to attach the negative sign on the numerator. the second is to attach the negative sign in the denominator and thirdly, attaching the negative sign directly on the same level of the fractional bar.

Example 4: Find the reciprocal of the whole number [latex]15[/latex].

Any nonzero whole number can be expressed with a denominator of [latex]1[/latex].


By having a clear denominator, we can easily flip this fraction upside down to get its reciprocal.


Example 5: Find the reciprocal of the integer [latex]- 11[/latex].

First, rewrite this integer with a denominator of [latex]1[/latex] as well.


By having a distinct denominator, we can now find its reciprocal. We have a negative symbol on the numerator, remember that it can be positioned in three different places: numerator, denominator, and by the fraction bar. Here are the possible answers!


You may also be interested in these related math lessons or tutorials:

Adding and Subtracting Fractions with the Same Denominator
Add and Subtract Fractions with Different Denominators
Multiplying Fractions
Dividing Fractions
Simplifying Fractions
Equivalent Fractions