# Reciprocal of a Fraction

Remember that a fraction has three parts.

## How to Find the Reciprocal of a Fraction

To get the reciprocal of the fraction

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

### Examples of Finding the Reciprocal of a Fraction

Example 1: Find the reciprocal of the fraction below.

Let’s turn the fraction ${3 \over 7}$ 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.

Solution:

Example 4: Find the reciprocal of the whole number $15$.

Any nonzero whole number can be expressed with a denominator of $1$.

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 $- 11$.

First, rewrite this integer with a denominator of $1$ 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!

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