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Problem of the Week 2

Directions: Billy Bob thinks that $\frac{2}{3}+\frac{1}{5}=\frac{3}{8}$. Of course, being the well-rounded person that you are, you know otherwise. Using the figure below and a well-written paragraph, explain to Billy Bob why $$\frac{2}{3}+\frac{1}{5}=\frac{13}{15}.$$ $$ \begin{array}{|c|c|c|c|c|} \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \end{array} + \begin{array}{|c|c|c|c|c|} \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \end{array} = \begin{array}{|c|c|c|c|c|} \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, & \,\,\,\, \\ \hline \end{array} $$