What is the [reciprocal](https://artofproblemsolving.com/wiki/index.php/Reciprocal) of $\frac{1}{2}+\frac{2}{3}$?
$\mathrm{(A)}\ \frac{6}{7}\qquad\mathrm{(B)}\ \frac{7}{6}\qquad\mathrm{(C)}\ \frac{5}{3}\qquad\mathrm{(D)}\ 3\qquad\mathrm{(E)}\ \frac{7}{2}$
Here's a cheapshot: 
Obviously, $\frac{1}{2}+\frac{2}{3}$ is greater than $1$. Therefore, its reciprocal is less than $1$, and the answer must be $\boxed{\frac{6}{7}}$.