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Multiplying Fractions
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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.

Multiplying Fractions

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: $$\displaystyle \frac{2}{5}\cdot\frac{3}{4}=\frac{2\cdot3}{5\cdot2\cdot2}=\frac{2}{2}\cdot\frac{3}{5\cdot2}=1\cdot\frac{3}{10}=\frac{3}{10}$$

### Practice Problems

Multiply the following fractions:
1. $$\displaystyle \frac{1}{4}\cdot \frac{1}{3}=$$ (
Solution
Solution: $$\displaystyle \frac{1}{4}\cdot \frac{1}{3}=\frac{1}{12}$$
Details: When we multiply two fractions together we multiply straight across. We have the following:
$$\displaystyle \frac{1}{4}\times\frac{1}{3}$$

Which is equal to the following:
$$\displaystyle \frac{1\times1}{4\times3}$$

Which equals as shown:
$$\dfrac{1}{12}$$
)
2. $$\displaystyle \frac{1}{4}\cdot \frac{5}{8}=$$ (
Solution
Solution: $$\displaystyle \frac{1}{4}\times \frac{5}{8}=\frac{5}{32}$$
Details: When we multiply two fractions together we multiply straight across. We have the following:
$$\displaystyle \frac{1}{4}\times\frac{5}{8}$$

Which is equal to the following:
$$\displaystyle \frac{1\times5}{4\times8}$$

Which equals as shown:
$$\dfrac{5}{32}$$
)
3. $$\displaystyle \frac{3}{7}\cdot \frac{2}{5}=$$ (
Solution
Solution:
$$\displaystyle \frac{3}{7}\cdot \frac{2}{5}=\frac{6}{35}$$
)
4. $$\displaystyle \frac{3}{4}\cdot \frac{2}{9}=$$ (
Video Solution
Solution: $$\displaystyle \frac{3}{4}\cdot \frac{2}{9}=\frac{1}{6}$$
Details:

(Video Source | Transcript)
)
5. $$\displaystyle \frac{3}{4}\cdot 10=$$ (
Solution
Solution:
$$\displaystyle \frac{3}{4}\cdot10=\frac{3}{4}\cdot\frac{10}{1}=\frac{30}{4}=\frac{15}{2}$$
)
6. $$\displaystyle 6\cdot \frac{2}{3}=$$ (
Video Solution
Solution: $$\displaystyle 6 \cdot \frac{2}{3}=4$$
Details:

(Video Source | Transcript)
)

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