**Reciprocal of a Fraction** – The reciprocal of a fraction is nothing interchanging or switching the numerator and denominator. That means numerator becomes denominator and denominator becomes the numerator. In the case of a mixed fraction, you have to convert the mixed fraction to the improper fraction and then switch the numerator and denominator (top number to the bottom number). Learn how to find the reciprocal of a fraction with the help of the below examples.

**Example:** Suppose the fraction is a/b then the reciprocal of the fraction is b/a. Here b becomes numerator and a becomes denominator.

**Do Refer:**

- Reducing the Equivalent Fractions
- Simplification of Fractions
- Conversion of Fractions into Fractions having Same Denominator

### How to find the Reciprocal of a Fraction?

Go through the simple process listed below to determine the reciprocal of a fraction. They are as follows

- Initially, determine the numerator and denominator of a given fraction.
- Fractions Reciprocal can be obtained by swapping or interchanging the numerator and denominators.
- In the case of Mixed Fraction, you first need to change to improper fractions and then interchange the numerator and denominator of the improper fraction.

### Reciprocal of a Fraction Examples

**Example 1.**

What is the opposite reciprocal of \(\frac{5}{6}\)?

**Solution:**

The opposite reciprocal of the fraction is nothing but changing the sign of the number. A positive number becomes a negative number.

So, the opposite reciprocal of the fraction \(\frac{5}{6}\) is –\(\frac{6}{5}\)

**Example 2.**

Find the reciprocal of the fraction \(\frac{2}{1}\)

**Solution:**

Given the fraction \(\frac{2}{1}\)

The reciprocal of a fraction is nothing interchanging or switching the numerator and denominator.

Thus the reciprocal of the fraction \(\frac{2}{1}\) is \(\frac{1}{2}\)

**Example 3.**

Find the reciprocal of the fraction \(\frac{17}{58}\)

**Solution:**

Given the fraction \(\frac{17}{58}\)

The reciprocal of a fraction is nothing interchanging or switching the numerator and denominator.

Thus the reciprocal of the fraction \(\frac{17}{58}\) is \(\frac{58}{17}\)

**Example 4.**

Find the reciprocal of the fraction \(\frac{16}{64}\)

**Solution:**

Given the fraction \(\frac{16}{64}\)

The reciprocal of a fraction is nothing interchanging or switching the numerator and denominator.

Thus the reciprocal of the fraction \(\frac{16}{64}\) is \(\frac{64}{16}\) or \(\frac{4}{1}\)

**Example 5.**

Find the reciprocal of the fraction \(\frac{2}{3}\)

**Solution:**

Given the fraction \(\frac{2}{3}\)

The reciprocal of a fraction is nothing interchanging or switching the numerator and denominator.

Thus the reciprocal of the fraction \(\frac{2}{3}\) is \(\frac{3}{2}\)

**Example 6.**

Find the negative reciprocal of the fraction \(\frac{7}{129}\)

**Solution:**

Given the fraction \(\frac{7}{129}\)

The opposite reciprocal of the fraction is nothing but changing the sign of the number. A positive number becomes a negative number.

Therefore the negative reciprocal of the fraction \(\frac{7}{129}\) is –\(\frac{129}{7}\)

**Example 7.**

Find the negative reciprocal of the fraction \(\frac{3}{5}\)

**Solution:**

Given the fraction \(\frac{3}{5}\)

The opposite reciprocal of the fraction is nothing but changing the sign of the number. A positive number becomes a negative number.

Therefore the negative reciprocal of the fraction \(\frac{3}{5}\) is –\(\frac{5}{3}\)

**Example 8.**

Write the reciprocal of the fraction \(\frac{3}{9}\)

**Solution:**

Given the fraction \(\frac{3}{9}\)

The reciprocal of a fraction is nothing interchanging or switching the numerator and denominator.

Therefore the reciprocal of the fraction \(\frac{3}{9}\) is \(\frac{9}{3}\) or \(\frac{3}{1}\) or 3.

### FAQs on Reciprocal of a Fraction

**1. What is a reciprocal of the fraction?**

The reciprocal of a fraction will be obtained by interchanging the numerator and denominator.

**2. Is 1 the reciprocal of 1?**

Yes, 1 is the reciprocal of 1 itself. Since 1 can be written as \(\frac{1}{1}\)

**3. What is the reciprocal of \(\frac{1}{3}\) as a fraction?**

The reciprocal of the given fraction is \(\frac{3}{1}\) which means 3.