# How do you solve 5/12g+2/3=1/8?

Jun 20, 2017

$g = - \frac{13}{10} = - 1 \frac{3}{10}$

#### Explanation:

Given: $\frac{5}{12} g + \frac{2}{3} = \frac{1}{8}$

One of the easiest ways is to get rid of the fractions by multiplying everything by the common denominator $24$:

$24 \left(\frac{5}{12} g + \frac{2}{3} = \frac{1}{8}\right)$

Divide first, then multiply, it's easier:

$\frac{24}{12} \cdot 5 g + \frac{24}{3} \cdot 2 = \frac{24}{8} \cdot 1$

$2 \cdot 5 g + 8 \cdot 2 = 3 \cdot 1$

$10 g + 16 = 3$

Subtract $16$ from both sides:
$10 g = 3 - 16$

$10 g = - 13$

Divide by 10:

$\frac{10}{10} g = - \frac{13}{10}$

$g = - \frac{13}{10} = - 1 \frac{3}{10}$

CHECK:

$\frac{5}{12} \cdot - \frac{13}{10} + \frac{2}{3} = \frac{1}{8}$

$- \frac{65}{120} + \frac{2}{3} = \frac{1}{8}$

$- \frac{13}{24} + \frac{2}{3} = \frac{1}{8}$

$- \frac{13}{24} + \frac{2}{3} \cdot \frac{8}{8} = \frac{1}{8} \cdot \frac{3}{3}$

$- \frac{13}{24} + \frac{16}{24} = \frac{3}{24}$ TRUE