jmc

We might recognize the top as $\frac{2}{3}$, and the bottom as $\frac{4}{3}$, thereby giving you a value of $\frac{1}{2}$. If not, call the numerator $x$. Multiplying by 10, and subtracting $x$, you get 9x = 6, and thus, $x=\frac{2}{3}$. We then notice that the denominator is $1+\frac{x}{2}$, thereby giving us a value of $\boxed{\frac{1}{2}}$ for the entire fraction.