Division of Fractions Calculator

Published on: March 17, 2024
Final Answer: Free Full Steps: Free

This Division of Fractions Calculator helps you divide one fraction by another and shows the working clearly at every step. Dividing by a fraction is the same as multiplying by that fraction turned upside down. So keep the first fraction as it is, swap the top and bottom of the second one, and change the divide sign into a times sign. Then multiply as normal and check whether the answer can be written with smaller numbers. Following the same pattern every time is what makes dividing fractions easy to picture, check, and repeat on your own with any two fractions.

Step-by-step method

  1. Set up the problem.
  2. Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.
  3. Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.
  4. Do a simplifying of fractions at the end if you can.
See Example 1 Hide Example 1

Problem

\(\frac{3}{4} \div \frac{1}{2}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.
  3. Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.
  4. Do a simplifying of fractions at the end if you can.

Step 1

Step 1 - Set up the problem.

In this problem: We are dividing \(\frac{3}{4}\) by \(\frac{1}{2}\).

\(\frac{3}{4} \div \frac{1}{2}\)

Step 2

Step 2 - Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.

In this problem: Swapping the top and bottom of \(\frac{1}{2}\) gives \(\frac{2}{1}\), because the top \(1\) moves down and the bottom \(2\) moves up.

\(\frac{3}{4} \div \frac{1}{2} \;\rightarrow\; \frac{3}{4} \times \frac{2}{1}\)

Step 3

Step 3 - Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.

In this problem: Now we change ÷ into × and multiply: \(3 \times 2 = 6\) and \(4 \times 1 = 4\).

\(\frac{3}{4} \times \frac{2}{1} = \frac{6}{4}\)

Step 4

Step 4 - Do a simplifying of fractions at the end if you can.

In this problem: The biggest number that divides both \(6\) and \(4\) is \(2\). Dividing each by it gives \(6 \div 2 = 3\) and \(4 \div 2 = 2\).

\(\frac{6}{4} = \frac{3}{2}\)

Final Answer

\(\frac{3}{4} \div \frac{1}{2} = \frac{3}{2}\)
See Example 2 Hide Example 2

Problem

\(\frac{2}{3} \div \frac{4}{9}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.
  3. Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.
  4. Do a simplifying of fractions at the end if you can.

Step 1

Step 1 - Set up the problem.

In this problem: We are dividing \(\frac{2}{3}\) by \(\frac{4}{9}\).

\(\frac{2}{3} \div \frac{4}{9}\)

Step 2

Step 2 - Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.

In this problem: Swapping the top and bottom of \(\frac{4}{9}\) gives \(\frac{9}{4}\), because the top \(4\) moves down and the bottom \(9\) moves up.

\(\frac{2}{3} \div \frac{4}{9} \;\rightarrow\; \frac{2}{3} \times \frac{9}{4}\)

Step 3

Step 3 - Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.

In this problem: Now we change ÷ into × and multiply: \(2 \times 9 = 18\) and \(3 \times 4 = 12\).

\(\frac{2}{3} \times \frac{9}{4} = \frac{18}{12}\)

Step 4

Step 4 - Do a simplifying of fractions at the end if you can.

In this problem: The biggest number that divides both \(18\) and \(12\) is \(6\). Dividing each by it gives \(18 \div 6 = 3\) and \(12 \div 6 = 2\).

\(\frac{18}{12} = \frac{3}{2}\)

Final Answer

\(\frac{2}{3} \div \frac{4}{9} = \frac{3}{2}\)