Now that we’ve learned how to add and subtract fractions, we will learn how to multiply fractions. Multiplying fractions is a lot simpler than adding or subtracting fractions because we don’t need to find a common denominator. Instead, we multiply across numerators and denominators. The following video will explain why this works and show a few examples.

Video Source (05:48 mins) | Transcript

When multiplying fractions, we simply multiply the numerators together and the denominators together. Remember, any whole number can be represented as a fraction by putting it over 1.

Example: \(\displaystyle 3=\frac{3}{1}\)

Reduce when needed.

Example when reducing is not needed: \(\displaystyle \frac{2}{5}\cdot\frac{2}{3}=\frac{2\cdot2}{5\cdot3}=\frac{4}{15}\)

Example when reducing is needed: \(\displaystyle \frac{2}{5}\cdot\frac{3}{4}=\frac{2\cdot3}{5\cdot2\cdot2}=\frac{2}{2}\cdot\frac{3}{5\cdot2}=1\cdot\frac{3}{10}=\frac{3}{10}\)

## Additional Resources

- Khan Academy: Introduction to Multiplying 2 Fractions (05:05 mins, Transcript)
- Khan Academy: Multiplying 2 Fractions: Fraction Model (04:56 mins, Transcript)
- Khan Academy: Fractions - Number Line (04:45 mins, Transcript)
- Khan Academy: Multiplying 2 Fractions: 5/6 x 2/3 (02:25 mins, Transcript)

### Practice Problems

**Multiply the following fractions:**

- \(\displaystyle \frac{1}{4}\cdot \frac{1}{3}=\) (Solution
- \(\displaystyle \frac{1}{4}\cdot \frac{5}{8}=\) (Solution
- \(\displaystyle \frac{3}{7}\cdot \frac{2}{5}=\) (Solution
- \(\displaystyle \frac{3}{4}\cdot \frac{2}{9}=\) (Video Solution
- \(\displaystyle \frac{3}{4}\cdot 10=\) (Solution
- \(\displaystyle 6\cdot \frac{2}{3}=\) (Video Solution

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