After reading $\frac{3}{5}$ of the biology homework on Monday night, Sanjay read $\frac{1}{3}$ of the remaining homework on Tuesday night. What fraction of the original homework would Sanjay have to read on Wednesday night to complete the assignment?

### Concept & Strategy This is a sequential remainder tracking problem. We establish the left-over work iteratively after each night's individual contribution until reaching Wednesday night. ### Step-by-Step Solution * **Given:** * Fraction read on Monday = $\frac{3}{5}$ * **Calculation:** * Remaining homework after Monday: $$ 1 - \frac{3}{5} = \frac{2}{5} $$ * Fraction read on Tuesday = $\frac{1}{3}$ of the remaining homework: $$ \text{Tuesday Read} = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15} $$ * Fraction left for Wednesday night = $\text{Remaining after Monday} - \text{Tuesday Read}$ $$ \text{Wednesday Remaining} = \frac{2}{5} - \frac{2}{15} $$ * Convert to a shared denominator: $$ \text{Wednesday Remaining} = \frac{6}{15} - \frac{2}{15} = \frac{4}{15} $$ ### Exam Strategy & Shortcut **Remainder Factor Multiplication:** Each step leaves a specific fractional balance behind: * If Sanjay reads $\frac{3}{5}$ on Monday, the remainder factor is $\left(1 - \frac{3}{5}\right) = \frac{2}{5}$. * If he reads $\frac{1}{3}$ of that balance on Tuesday, the fraction left for Wednesday is $\left(1 - \frac{1}{3}\right) = \frac{2}{3}$ of the previous remainder. * Total fraction remaining for Wednesday = $\frac{2}{3} \times \frac{2}{5} = \frac{4}{15}$. ### Common Pitfall Mistakenly treating Tuesday's consumption fraction as an absolute subtraction from the absolute start point (e.g., calculating $1 - \frac{3}{5} - \frac{1}{3} = \frac{1}{15}$). Ensure you evaluate expressions dependent on the phrase "of the remaining". ### Final Answer **Therefore, the correct answer is 4/15.**