How to Multiply Fractions

Understanding How to Multiply Fractions

Multiplying fractions is actually much easier than many students think. Unlike adding or subtracting fractions, you do not need to find the LCD (Lowest Common Denominator). Instead, multiplying fractions follows a simple rule: multiply the numerators and multiply the denominators.

Once you understand this basic idea, multiplying fractions becomes quick and straightforward.

For example:

\large \frac{2}{3}\times\frac{4}{7}=\frac{8}{21}

Now let’s take a look at the step-by-step process for multiplying fractions.

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Steps to Multiply Fractions

1. 1. Change any mixed numbers to improper fractions.
      If the problem contains mixed numbers, convert them before multiplying.
   2. Multiply the numerators.
      Multiply the top numbers.
   3. Multiply the denominators.
      Multiply the bottom numbers.
   4. Simplify the final fraction if possible

Example: How to Multiply Fractions

Let’s solve:
\large \frac{4}{9}\times\frac{3}{8}

Step 1: Check the fractions.

Both fractions are already proper fractions, so no changes are needed.

Step 2: Multiply the numerators.

\large 4\times3=12

Step 3: Multiply the denominators.

\large 9\times8=72

So:

\large \frac{4}{9}\times\frac{3}{8}=\frac{12}{72}

Step 4: Simplify the final answer.

\large \frac{12}{72}=\frac{1}{6}

Final Answer:

\large \frac{1}{6}

 

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Watch How to Multiply Fractions

Check out this video to watch John show the process of multiplying fractions step-by-step:

Practice Problems

Try these on your own:

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

2. \large \frac{4}{7}\times\frac{1}{2}

3. \large \frac{5}{6}\times\frac{4}{3}

Answers

1. \large \frac{2}{3}\times\frac{3}{5}=\frac{6}{15}=\frac{2}{5}

2. \large \frac{4}{7}\times\frac{1}{2}=\frac{4}{14}=\frac{2}{7}

3. \large \frac{5}{6}\times\frac{4}{3}=\frac{20}{18}=\frac{10}{9} or \large 1\frac{1}{9}

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Common Mistakes

• Trying to find the LCD before multiplying fractions.
• Forgetting to multiply both the numerators and the denominators.
• Not simplifying the final fraction 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