The equation in which $\begin{array}{l}1\\ \overline{3}\end{array}$ is a solution is

Option ( A) : $\frac{2}{3}+c=\frac{2}{3}\Rightarrow c=0$

Option ( B) :  $15x=3\Rightarrow x=\frac{1}{5}$

Option ( C):  $\frac{-1}{6}+w=\frac{-1}{6}\Rightarrow w=\frac{-1}{6}+\frac{1}{6}=0$

Option ( D ) :  $\frac{z}{3}=\frac{+1}{9}\Rightarrow z=\frac{1}{9}\times 3\Rightarrow z=\frac{1}{3}$