## How to Multiply and Divide Fractions

#### How do I multiply fractions with different denominators?

The same way you multiply them if they had the same denominator! Check out our guide below for more details.

#### Common Questions

The same way you multiply them if they had the same denominator! Check out our guide below for more details.

Multiplying and dividing fractions might seem confusing, but they're actually much easier than adding and subtracting fractions.

The key thing to remember is that if we have the same number in the numerator and denominator, they cancel out:

$\frac{5 \times 2}{5 \times 3} = \frac{\textcolor{#00bbff}{\cancel{\textcolor{#a0a0a0}{5}}}\times 2}{\textcolor{#00bbff}{\cancel{\textcolor{#a0a0a0}{5}}}\times 3} = \frac{2}{3}$

Check out our example below or try out our calculator.

$3\frac{2}{5} \div \frac{20}{6}$
1. Flip the second fraction (if dividing): The funny thing about division is that it's actually just multiplying. We just need to first flip the second fraction:$3\frac{2}{5} \div \frac{20}{6} = 3\frac{2}{5} \times \frac{6}{20}$
2. Simplify the fractions: Now, we'll simplify our fractions to make multiplying easier.

Simplify Fraction 1: Our first fraction is a mixed number, so we'll convert it to an improper fraction. If you're not sure how, check out this guide.\begin{aligned} 3\frac{2}{5} &= (3 + \frac{2}{5}) \\[1em]&= \frac{15}{5} + \frac{2}{5} \\[1em]&= \frac{17}{5}\end{aligned}
Simplify Fraction 2: Our second fraction doesn't have whole numbers, but we can reduce it a little by dividing the top and bottom by the same number.$\frac{20}{6} = \frac{20 \div 2}{6 \div 2} = \frac{10}{3}$
3. Merge the fractions: Now, using our two simplified fractions, we multiply by merging our two fractions:
4. $\frac{17}{5} \times \frac{10}{3} = \frac{17 \times 10}{5 \times 3}$
5. Cancelling: Now, our favorite part - cancelling numbers. Basically, we're going to see if there is anything we can divide both a number in the top and a number in the bottom by. In this case, we can divide both 10 and 5 by 5:\begin{aligned} \frac{17 \times 10}{5 \times 3} &= \frac{17 \times \textcolor{#00bbff}{\cancel{\textcolor{#a0a0a0}{10}}} \> \textcolor{#00bbff}{2}}{\textcolor{#00bbff}{1 \> \cancel{\textcolor{#a0a0a0}{5}}}\times 3}\\[1em] &= \frac{17 \times 2}{1 \times 3}\end{aligned}
6. Multiply / Simplify: Now, we just multiply the tops and the bottoms, and we're done!$\frac{17 \times 2}{1 \times 3} = \textcolor{#00bbff}{\frac{34}{3}}$

## Multiplying and Dividing Fractions Calculator

Try it out - enter in two fractions to multiply or divide.