Reciprocal of a Fraction Notes

Published on: September 29, 2026

This Reciprocal of a Fraction Calculator helps you flip a fraction upside down and shows the working clearly at every step. The numerator moves down and the denominator moves up, and the flipped fraction is called the reciprocal. It is the move that turns a division into a multiplication, which is why it shows up whenever you do a division of fractions. Following the same pattern every time is what makes reciprocals easy to picture, check, and repeat on your own with any fraction.

Step-by-step method

  1. Set up the problem.
  2. Swap the numerator and denominator over.
See Example 1 Hide Example 1

Problem

\(\frac{5}{2}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Swap the numerator and denominator over.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the reciprocal of \(\frac{5}{2}\).

\(\frac{5}{2}\)

Step 2

Step 2 - Swap the numerator and denominator over.

In this problem: The numerator \(5\) moves down and the denominator \(2\) moves up, so \(\frac{5}{2}\) becomes \(\frac{2}{5}\).

\(\frac{5}{2} \;\rightarrow\; \frac{2}{5}\)

Final Answer

\(\frac{5}{2} \;\rightarrow\; \frac{2}{5}\)
See Example 2 Hide Example 2

Problem

\(\frac{3}{4}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Swap the numerator and denominator over.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the reciprocal of \(\frac{3}{4}\).

\(\frac{3}{4}\)

Step 2

Step 2 - Swap the numerator and denominator over.

In this problem: The numerator \(3\) moves down and the denominator \(4\) moves up, so \(\frac{3}{4}\) becomes \(\frac{4}{3}\).

\(\frac{3}{4} \;\rightarrow\; \frac{4}{3}\)

Final Answer

\(\frac{3}{4} \;\rightarrow\; \frac{4}{3}\)
See Example 3 Hide Example 3

Problem

\(\frac{2}{9}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Swap the numerator and denominator over.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the reciprocal of \(\frac{2}{9}\).

\(\frac{2}{9}\)

Step 2

Step 2 - Swap the numerator and denominator over.

In this problem: The numerator \(2\) moves down and the denominator \(9\) moves up, so \(\frac{2}{9}\) becomes \(\frac{9}{2}\).

\(\frac{2}{9} \;\rightarrow\; \frac{9}{2}\)

Final Answer

\(\frac{2}{9} \;\rightarrow\; \frac{9}{2}\)
See Example 4 Hide Example 4

Problem

\(\frac{11}{4}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Swap the numerator and denominator over.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the reciprocal of \(\frac{11}{4}\).

\(\frac{11}{4}\)

Step 2

Step 2 - Swap the numerator and denominator over.

In this problem: The numerator \(11\) moves down and the denominator \(4\) moves up, so \(\frac{11}{4}\) becomes \(\frac{4}{11}\).

\(\frac{11}{4} \;\rightarrow\; \frac{4}{11}\)

Final Answer

\(\frac{11}{4} \;\rightarrow\; \frac{4}{11}\)