# How do you solve 5/2w - 1/3 = 5/6w - 1/8?

Jun 23, 2018

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

#### Explanation:

The easiest way is to convert all the factions so they have the same denominator.

$L C M \left(2 , 3 , 6 , 8\right) = 24$

So we will use $24$ as our common denominator.

$\textcolor{w h i t e}{\text{XXX}} \frac{5}{2} = \frac{5 \times 12}{2 \times 12} = \frac{60}{24}$

$\textcolor{w h i t e}{\text{XXX}} \frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}$

$\textcolor{w h i t e}{\text{XXX}} \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}$

$\textcolor{w h i t e}{\text{XXX}} \frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$

So we can re-write the given equation: $\frac{5}{2} w - \frac{1}{3} = \frac{5}{6} w - \frac{1}{8}$ as
$\frac{60}{24} w - \frac{8}{24} = \frac{20}{24} w - \frac{3}{24}$

After multiplying both sides by $24$:
$60 w - 8 = 20 w - 3$

Simplifying
$40 w = 5$

$w = \frac{5}{40} = \frac{1}{8}$