Fractions:

Multiplying Fractions

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 just 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: $3=\frac{3}{1}$

Reduce when needed.

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

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

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:

$\frac{1}{4}\cdot \frac{1}{3}=$
$\frac{1}{4}\cdot \frac{5}{8}=$
$\frac{3}{7}\cdot \frac{2}{5}=$
$\frac{3}{4}\cdot \frac{2}{9}=$
$\frac{3}{4}\cdot 10=$
$6\cdot \frac{2}{3}=$

Solutions

$\frac{1}{4}\cdot \frac{1}{3}=\frac{1}{12}$ (Written Solution)

$The problem ¼ times ⅓ is listed. ¼ is shown in green and ⅓ in blue. To the right of the problem there’s an equal sign and the problem is rewritten is as 1 times 1 on top of a fraction line, and 4 times 3 written below the line in the denominator of the fraction. To the right of this is another equal sign and 1 twelfth is written in red.$

When we multiply two fractions together we multiply straight across. We have:

$\frac{1}{4}\times\frac{1}{3}$

Which is equal to:

$\frac{1\times1}{4\times3}$

Which equals:

$\frac{1}{12}$
$\frac{1}{4}\times \frac{5}{8}=\frac{5}{32}$ (Written Solution)

$The problem ¼ times 5/8 is listed. ¼ is shown in green and ⅝ in blue. To the right of the problem, there’s an equal sign. Right of that, the problem is rewritten as 1 times 5 on the top of a fraction line in the numerator. Below that line, in the denominator, is written 4 times 8. To the right of this is another equal sign and 5 thirty seconds is written in red.$

When we multiply two fractions together we multiply straight across. We have:

$\frac{1}{4}\times\frac{5}{8}$

Which is equal to:

$\frac{1\times5}{4\times8}$

Which equals:

$\frac{5}{32}$
$\frac{3}{7}\cdot \frac{2}{5}=\frac{6}{35}$
$\frac{3}{4}\cdot \frac{2}{9}=\frac{1}{6}$ (Solution Video | Transcript)
$\frac{3}{4}\cdot10=\frac{3}{4}\cdot\frac{10}{1}=\frac{30}{4}=\frac{15}{2}$
$6 \cdot \frac{2}{3}=4$ (Solution Video | Transcript)