# How do you solve (p-2)/5=p/8?

Apr 17, 2017

$p = \frac{16}{3}$

#### Explanation:

$\text{if "a/b=c/d" than } a \cdot d = b \cdot c$

$\frac{p - 2}{5} = \frac{p}{8}$

$8 \cdot \left(p - 2\right) = 5 \cdot p$

$8 \cdot p - 8 \cdot 2 = 5 p$

$8 p - 16 = 5 p$

$\text{add -5p to both sides of equation }$

$8 p - 5 p - 16 = \cancel{5 p} - \cancel{5 p}$

$3 p - 16 = 0$

$\text{add +16 to both sides of equation.}$

$3 p - \cancel{16} + \cancel{1} 6 = 16$

$3 p = 16$

$\text{divide both sides of equation by 3}$

$\frac{\cancel{3} p}{\cancel{3}} = \frac{16}{3}$

$p = \frac{16}{3}$

Apr 17, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by the lowest common denominator of the two fractions which is $\textcolor{red}{40}$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{40} \times \frac{p - 2}{5} = \textcolor{red}{40} \times \frac{p}{8}$

$\cancel{\textcolor{red}{40}} 8 \times \frac{p - 2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} = \cancel{\textcolor{red}{40}} 5 \times \frac{p}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}}$

$8 \left(p - 2\right) = 5 p$

Next, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{8} \left(p - 2\right) = 5 p$

$\left(\textcolor{red}{8} \times p\right) - \left(\textcolor{red}{8} \times 2\right) = 5 p$

$8 p - 16 = 5 p$

Then, add $\textcolor{red}{16}$ and subtract $\textcolor{b l u e}{5 p}$ from each side of the equation to isolate the $p$ term while keeping the equation balanced:

$- \textcolor{b l u e}{5 p} + 8 p - 16 + \textcolor{red}{16} = - \textcolor{b l u e}{5 p} + 5 p + \textcolor{red}{16}$

$\left(- \textcolor{b l u e}{5} + 8\right) p - 0 = 0 + 16$

$3 p = 16$

Now, divide each side of the equation by $\textcolor{red}{3}$ to solve for $p$ while keeping the equation balanced:

$\frac{3 p}{\textcolor{red}{3}} = \frac{16}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} p}{\cancel{\textcolor{red}{3}}} = \frac{16}{3}$

$p = \frac{16}{3}$

Apr 17, 2017

$p = \frac{16}{3}$

#### Explanation:

Cross multiply

$\frac{\textcolor{g r e e n}{p - 2}}{\textcolor{red}{5}} = \frac{\textcolor{red}{p}}{\textcolor{g r e e n}{8}}$

$\textcolor{b l u e}{8} \left(p - 2\right) = 5 p$

Distribute the $8$ into $p - 2$

$\textcolor{b l u e}{8} p - 2 \left(\textcolor{b l u e}{8}\right) = 5 p$

$8 p - 16 = 5 p$

Subtract $5 p$ from both sides

$8 p \textcolor{b l u e}{- 5 p} - 16 = \cancel{5 p \textcolor{b l u e}{- 5 p}}$

$3 p - 16 = 0$

Add $16$ to both sides

$3 p \cancel{- 16 \textcolor{b l u e}{+ 16}} = 0 \textcolor{b l u e}{+ 16}$

$3 p = 16$

Divide both sides by 3

$\frac{\cancel{3} p}{\cancel{\textcolor{b l u e}{3}}} = \frac{16}{\textcolor{b l u e}{3}}$

$p = \frac{16}{3}$

This is the final answer (it cannot be simplified furthermore)