# How do you solve 1/a=2/14?

Jan 29, 2017

$a = 7$

#### Explanation:

The right side of the equation can be simplified.

$\Rightarrow \frac{2}{14} = {\cancel{2}}^{1} / {\cancel{14}}^{7} = \frac{1}{7}$

Since the fractions are equal.

$\frac{1}{a} = \frac{1}{7} \Rightarrow a = 7$

Jan 29, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{14} \textcolor{b l u e}{a}$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{14} \textcolor{b l u e}{a} \times \frac{1}{a} = \textcolor{red}{14} \textcolor{b l u e}{a} \times \frac{2}{14}$

$\textcolor{red}{14} \cancel{\textcolor{b l u e}{a}} \times \frac{1}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{a}}}} = \cancel{\textcolor{red}{14}} \textcolor{b l u e}{a} \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{14}}}}$

$14 = 2 a$

Now, divide each side of the equation by $\textcolor{red}{2}$ to solve for $a$ while keeping the equation balanced:

$\frac{14}{\textcolor{red}{2}} = \frac{2 a}{\textcolor{red}{2}}$

$7 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} a}{\cancel{\textcolor{red}{2}}}$

$7 = a$

$a = 7$