How to Divide Fractions (Step-by-Step)

Understanding How to Divide Fractions

Dividing fractions may seem confusing at first, but once you learn the main rule, the process becomes very simple.

The key idea is this: when dividing fractions, we change the division problem into a multiplication problem. To do this, we flip the fraction to the right of the division symbol (this is called finding the reciprocal).

After flipping the fraction, we simply multiply the fractions as usual.

For example:

\large \frac{1}{4}\div\frac{3}{5}=\frac{1}{4}\times\frac{5}{3}

Let’s walk through the steps.

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Steps to Divide Fractions

1. 1. Change any mixed numbers to improper fractions.
      If the problem contains mixed numbers, convert them before dividing.
   2. Flip the fraction to the right of the division symbol.
      This is also called finding the reciprocal.
   3. Change the division problem to multiplication.
   4. Multiply the fractions.
   5. Simplify the final answer if possible.

Example: How to Divide Fractions

Let’s solve:

\large \frac{5}{6}\div\frac{2}{9}

Step 1: Check the fractions.

Both fractions are already proper fractions.

Step 2: Flip the fraction to the right of the division symbol.

\large \frac{2}{9}\rightarrow\frac{9}{2}

Step 3: Change the problem to multiplication.

\large \frac{5}{6}\div\frac{2}{9}=\frac{5}{6}\times\frac{9}{2}

Step 4: Multiply the fractions.

\large \frac{5\times9}{6\times2}=\frac{45}{12}

Step 5: Simplify the final answer.

\large \frac{45}{12}=\frac{15}{4}

If you want, you can write the answer as a mixed number:

\large \frac{15}{4}=3\frac{3}{4}

Final answer:

\large \frac{15}{4}

or

\large 3\frac{3}{4}

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Watch How to Divide Fractions

Check out this video to watch John explain how to divide fractions step-by-step:

Practice Problems

Try these on your own:

1. \large \frac{1}{2}\div\frac{1}{3}

2. \large \frac{3}{5}\div\frac{1}{2}

3. \large \frac{3}{4}\div\frac{2}{5}

Answers

1. \large \frac{1}{2}\div\frac{1}{3}=\frac{3}{2}

2. \large \frac{3}{5}\div\frac{1}{2}=\frac{6}{5}

3. \large \frac{3}{4}\div\frac{2}{5}=\frac{15}{8} or \large 1\frac{7}{8}

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Common Mistakes

• Forgetting to flip the second fraction before multiplying.
• Flipping the wrong fraction instead of the one to the right of the division symbol.
• Trying to divide the numerators and denominators instead of changing the problem to multiplication.
• Forgetting to simplify the final answer when possible.

Need More Help with Fractions?

If you want more help with fractions, check out John’s full courses. They include complete lessons, worksheets, quizzes, and step-by-step solution videos to help students truly master fractions.

👉 Explore the Pre-Algebra Course
👉 Explore the Foundations Math Course