What fraction should be added to the fraction $\frac{1}{9}$ so that the obtained fraction is the same as a result obtained on subtracting $\frac{1}{6}$ from $\frac{1}{2}$?

First, subtracting $\frac{1}{6}$ from $\frac{1}{2}$ = $\frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6}=\frac{2}{6}=\frac{1}{3}$.

∴ The result obtained by subtracting $\frac{1}{6}$ from $\frac{1}{2}$ is $\frac{1}{3}$.

Now, we have to find a fraction that should be added to $\frac{1}{9}$ so the obtained fraction is  $\frac{1}{3}$ can be found by subtracting $\frac{1}{9}$ from $\frac{1}{3}$. 

This can be done as:

$\frac{1}{3}-\frac{1}{9}=\frac{3}{9}-\frac{1}{9}=\frac{2}{9}$

Thus, the required fraction is $\frac{2}{9}$.