Suppose $\frac ab = \frac35$,$\frac bc=\frac{6}{15}$, and $\frac cd = \frac{1}{6}$. What is the value of $\frac ad$? Express your answer in simplest form.
\(\frac{a}{b} = \frac{3}{5}, \frac{b}{c} = \frac{6}{15},\space and\quad \frac{c}{d} = \frac{1}{6}. \ \textcolor{red}{What \ is \ the \ value \ of \frac{a}{d}}?\)
