# How do you solve 6/5=2/(5n)?

Feb 15, 2017

$\frac{6}{5} = \frac{2}{\text{5n}} : n = \frac{1}{3}$ (Decimal = 0.33333333333333333333............)

#### Explanation:

$\frac{6}{5} \cdot \frac{x}{x} = \frac{2}{\text{5n}}$
Solve for $x$
$x = \frac{2}{6} = 0.33333333333333333 \ldots \ldots , \frac{1}{3}$

$\frac{6}{5} \cdot \frac{0.3333333}{0.33333333} = \frac{2}{\text{5n}}$

$5 \cdot 0.333333333333333333 \ldots \ldots \ldots \ldots \ldots \ldots \ldots = 5 n$

This means n = 0.3333333333333333333333......, $\frac{1}{3}$

Feb 15, 2017

$n = \frac{1}{3}$

#### Explanation:

Multiply both sides of the equation by the $\textcolor{b l u e}{\text{lowest common multiple}}$ (LCM) of the denominators 5 and 5n

the LCM of 5 and 5n is 5n

${\cancel{5}}^{1} n \times \frac{6}{\cancel{5}} ^ 1 = \cancel{5 n} \times \frac{2}{\cancel{5 n}}$

$\Rightarrow 6 n = 2$

To solve for n, divide both sides by 6

$\frac{\cancel{6} n}{\cancel{6}} = \frac{2}{6}$

$\Rightarrow n = \frac{2}{6} = \frac{1}{3}$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the right side and if it equals the left side then it is the solution.

$\text{right side } = \frac{2}{5 \times \frac{1}{3}} = \frac{2}{\frac{5}{3}} = = \frac{2}{1} \times \frac{3}{5} = \frac{6}{5}$

$\Rightarrow n = \frac{1}{3} \text{ is the solution}$