Solve frac{V_{s}}{V_{p}}=frac{N_{s}}{N_{p}}

$$\frac { V _ { s } } { V _ { p } } = \frac { N _ { s } } { N _ { p } }$$

Solve for N_p

$$\left\{\begin{matrix}N_{p}=\frac{N_{s}V_{p}}{V_{s}}\text{, }&N_{s}\neq 0\text{ and }V_{p}\neq 0\text{ and }V_{s}\neq 0\\N_{p}\neq 0\text{, }&V_{s}=0\text{ and }N_{s}=0\text{ and }V_{p}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable N_{p} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by N_{p}V_{p}, the least common multiple of V_{p},N_{p}.

$$N_{p}V_{s}=V_{p}N_{s}$$

The equation is in standard form.

$$V_{s}N_{p}=N_{s}V_{p}$$

Divide both sides by V_{s}.

$$\frac{V_{s}N_{p}}{V_{s}}=\frac{N_{s}V_{p}}{V_{s}}$$

Dividing by V_{s} undoes the multiplication by V_{s}.

$$N_{p}=\frac{N_{s}V_{p}}{V_{s}}$$

Variable N_{p} cannot be equal to 0.

$$N_{p}=\frac{N_{s}V_{p}}{V_{s}}\text{, }N_{p}\neq 0$$

Solve for N_s

$$N_{s}=\frac{N_{p}V_{s}}{V_{p}}$$

$$V_{p}\neq 0\text{ and }N_{p}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by N_{p}V_{p}, the least common multiple of V_{p},N_{p}.

$$N_{p}V_{s}=V_{p}N_{s}$$

Swap sides so that all variable terms are on the left hand side.

$$V_{p}N_{s}=N_{p}V_{s}$$

Divide both sides by V_{p}.

$$\frac{V_{p}N_{s}}{V_{p}}=\frac{N_{p}V_{s}}{V_{p}}$$

Dividing by V_{p} undoes the multiplication by V_{p}.

$$N_{s}=\frac{N_{p}V_{s}}{V_{p}}$$