We want to solve the following equation finding the value of k:
[tex]\frac{3}{2}=\frac{9}{10}k[/tex]Since both sides are equal we can multiply each side by 10:
[tex]\begin{gathered} 10\cdot\frac{3}{2}=10\cdot\frac{9}{10}k \\ 10\cdot\frac{3}{2}=1\cdot9k \\ 10\cdot\frac{3}{2}=9k \\ 5\cdot3=9k \\ 15=9k \end{gathered}[/tex]dividing both sides by 9:
[tex]\begin{gathered} \frac{15}{9}=\frac{9k}{9} \\ \frac{15}{9}=1\cdot k \\ \frac{15}{9}=k \\ \end{gathered}[/tex]Simplifying the answer dividing both sides by 3:
[tex]\frac{15}{9}=\frac{5}{3}[/tex]