2019 Cayley Problem 10

Matilda and Ellie divide a white wall in their bedroom in half, each taking half of the wall. Matilda paints half of her section red. Ellie paints one third of her section red. The fraction of the entire wall that is painted red is

\textbf{(A)}\ \frac{5}{12}\quad \textbf{(B)}\ \frac{2}{5}\quad \textbf{(C)}\ \frac{2}{3}\quad \textbf{(D)}\ \frac{1}{6}\quad \textbf{(E)}\ \frac{1}{2}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.