Solve for: (10)/(y)=(11)/(8)

Expression: $\frac{ 10 }{ y }=\frac{ 11 }{ 8 }$

Determine the defined range

$\begin{array} { l }\frac{ 10 }{ y }=\frac{ 11 }{ 8 },& y≠0\end{array}$

Simplify the equation using cross-multiplication

$80=11y$

Swap the sides of the equation

$11y=80$

Divide both sides of the equation by $11$

$\begin{array} { l }y=\frac{ 80 }{ 11 },& y≠0\end{array}$

Check if the solution is in the defined range

$\begin{align*}&y=\frac{ 80 }{ 11 } \\&\begin{array} { l }y=7 \frac{ 3 }{ 11 },& y=7.\overset{ \cdot }{ 2 } \overset{ \cdot }{ 7 } \end{array}\end{align*}$