Multiplying Fractions — Process & Examples

How to Multiply Fractions

Any two fractions can be multiplied together with three steps!

1. Multiply the numerators. This product will be the new numerator.
2. Multiply the denominators. This product will be the new denominator.
3. Simplify your answer if needed. That is, write the answer in simplest form.

Multiplying fractions is actually much easier than adding fractions. To add fractions, you have to find common denominators before you can add them together at all.

Multiplication has no such requirement. We can multiply any fraction together immediately, without any preparation. It takes just a couple of simple steps. Let's use the example of: $$\frac{3}{5} \times \frac{2}{3}$$ to help us through this progress. The most important thing to remember is to simply keep the numerators (numbers on the top of the fraction) separate from the denominators (numbers on the bottom of the fraction). We don't multiply them together at all, and we can treat them as completely separate.

Multiply numerators with numerators and denominators with denominators

Let's use our example, and do each of the numerator and denominator separately.

Let's start with the numerators: $$\frac{\color{#29A603}{3}}{5} \times \frac{\color{#29A603}{2}}{3}$$ The numerators above are highlighted in $\color{#29A603}{\text{green}}$. Pulling them out, we can multiply them on their own: $$3 \times 2 = 6$$ We keep the result of that for the solution, which we now have half of: $\frac{6}{?}$.

Let's continue with the denominators: $$\frac{3}{\color{#29A603}{5}} \times \frac{2}{\color{#29A603}{3}}$$ The denominators above are highlighted in $\color{#29A603}{\text{green}}$. Pulling them out, we can multiply them on their own: $$5 \times 3 = 15$$ We then put that result in the solution: $$\frac{6}{15}$$

Simplify, if possible

But wait, we're not done yet! The last step, as with most fraction problems, is to simplify the result, if possible. The above result, $\frac{6}{15}$, can be reduced to lowest terms. We factor the numerator and denominator. It turns out the greatest common factor (GCF) is $3$, then reduce: $$\frac{6}{15} = \frac{(2)(3)}{(3)(5)} = \frac{2}{5}$$ Our final answer is $\frac{2}{5}$.

(Video) Multiplying Fractions

by Math Antics

Math Antics has a great video explaining how to multiply fractions.

$\large{\text{Summary}}$

Multiplying fractions is the easiest fraction operation. You simply multiply all the top numbers together and then multiply all the bottom numbers together. $$\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}$$ Here's an example with numbers: $$\frac{1}{3}\times\frac{2}{5}=\frac{1\times 2}{3\times 5}=\frac{2}{15}$$ See! Super simple. You can even do this with more than two fractions. $$\frac{1}{3}\times\frac{2}{5}\times\frac{3}{2}=\frac{1\times 2\times 3}{3\times 5\times 2}=\frac{6}{30}$$

Multiplication is commutative. That means can multiply the fractions in any order.