# How do you solve \frac { 8} { 3} = \frac { m - 5} { m - 10}?

Aug 1, 2017

$m = 13$

#### Explanation:

$\frac{8}{3} = \frac{m - 5}{m - 10}$

Multiply both sides by $3 \left(m - 10\right)$.

$3 \left(m - 10\right) \times \frac{8}{3} = 3 \left(m - 10\right) \times \frac{m - 5}{m - 10}$

$\cancel{3} \left(m - 10\right) \times \frac{8}{\cancel{3}} = 3 \cancel{\left(m - 10\right)} \times \frac{m - 5}{\cancel{m - 10}}$

$\left(m - 10\right) \times 8 = 3 \times \left(m - 5\right)$

Open the brackets and simplify.

$8 m - 80 = 3 m - 15$

Subtract $3 m$ from each side.

$8 m - 3 m - 80 = 3 m - 3 m - 15$

$5 m - 80 = - 15$

Add $80$ to each side.

$5 m + 80 - 80 = 80 - 15$

$5 m = 65$

Divide both sides by $5$.

$\frac{5 m}{5} = \frac{65}{5}$

$\frac{\cancel{5} m}{\cancel{5}} = \frac{13 \cancel{65}}{1 \cancel{5}}$

$m = 13$

Aug 1, 2017

$m = 13$

Refer to the explanation for the process.

#### Explanation:

Solve:

$\frac{8}{3} = \frac{m - 5}{m - 10}$

Cross multiply. Multiply the denominators by the numerators of the opposite fractions.

$\frac{8 \left(m - 10\right)}{3 \left(m - 5\right)}$

Expand.

$8 m - 80 = 3 m - 15$

Subtract $3 m$ from both sides.

$8 m - 80 - 3 m = 3 m - 3 m - 15$

Cancel $3 m$ on the right side.

$8 m - 80 - 3 m = \textcolor{red}{\cancel{\textcolor{b l a c k}{3 m}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{3 m}}} - 15$

Simplify.

$5 m - 80 = - 15$

Add $80$ to both sides.

$5 m - 80 + 80 = - 15 + 80$

Cancel $80$ on the left side.

$5 m - \textcolor{red}{\cancel{\textcolor{b l a c k}{80}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{80}}} = - 15 + 80$

Simplify.

$5 m = 65$

Divide both sides by $5$.

$\frac{5 m}{5} = \frac{65}{5}$

Cancel $5$ on the left side.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{{5}^{1}}}} m}{\textcolor{red}{\cancel{\textcolor{b l a c k}{{5}^{1}}}}} = \frac{65}{5}$

Simplify.

$m = 13$