# How do you find the product 1/2 times2/8?

Dec 29, 2016

$\frac{1}{8}$

#### Explanation:

First, we can cancel common terms in the numerator and denominator:

$\frac{1}{\textcolor{red}{2}} \times \frac{\textcolor{red}{2}}{8} = \frac{1}{\cancel{\textcolor{red}{2}}} \times \frac{\cancel{\textcolor{red}{2}}}{8} = \frac{1}{1} \times \frac{1}{8}$

$\frac{1}{1} = 1$ therefore we can rewrite the problem as:

$\textcolor{b l u e}{1} \times \frac{1}{8}$

Then, knowing 1 times "anything" is the "anything" or in math terminology $1 \times x = x$:

$1 \times \frac{1}{8} = \frac{1}{8}$

Another way to solve this problem is:

To multiply fractions you multiply the numerators over the denominators multiplied:

$\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}} \times \frac{\textcolor{red}{c}}{\textcolor{b l u e}{d}} = \frac{\textcolor{red}{a \times c}}{\textcolor{b l u e}{b \times d}}$

Applying this rule to our problem gives:

$\frac{\textcolor{red}{1}}{\textcolor{b l u e}{2}} \times \frac{\textcolor{red}{2}}{\textcolor{b l u e}{8}} = \frac{\textcolor{red}{1 \times 2}}{\textcolor{b l u e}{2 \times 8}} = \frac{\textcolor{red}{2}}{\textcolor{b l u e}{2 \times 8}} = \frac{\cancel{\textcolor{red}{2}} 1}{\textcolor{b l u e}{\cancel{2} 1 \times 8}} = \frac{1}{8}$