Problem 478

Each of the vertical strips accounts for $\frac{1}{2}$ of the total area of the rectangle. The left strip is divided into three equal pieces, so $\frac{2}{3}$ of the left strip is shaded, accounting for $\frac{2}{3} imes \frac{1}{2}=\frac{1}{3}$ of the large rectangle. The right strip is divided into four equal pieces, so $\frac{2}{4}=\frac{1}{2}$ of the right strip is shaded, accounting for $\frac{1}{2} imes \frac{1}{2}=\frac{1}{4}$ of the large rectangle. Therefore, the total fraction of the rectangle that is shaded is $\frac{1}{3}+\frac{1}{4}=\frac{4}{12}+\frac{3}{12}=\frac{7}{12}$.