To solve how much of the entire hoagie Evan ate for lunch, we need to follow these steps:
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Determine how much of the hoagie was left after dinner: Evan initially ate three-eighths of a hoagie, which means: \[ 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} \] So, he had five-eighths of the hoagie left after dinner.
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Calculate how much he ate for lunch: On the next day, he ate two-thirds of what was left. We need to find two-thirds of five-eighths: \[ \frac{2}{3} \times \frac{5}{8} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24} \] Simplifying \(\frac{10}{24}\): \[ \frac{10 \div 2}{24 \div 2} = \frac{5}{12} \] Therefore, Evan ate \(\frac{5}{12}\) of the entire hoagie for lunch.
To summarize, Evan ate \(\frac{5}{12}\) of the hoagie for lunch, and the correct process to solve this problem involves multiplying fractions (specifically multiplying \(\frac{2}{3}\) by the remaining portions of the hoagie \(\frac{5}{8}\)).
The final answer corresponds to the choice: \[ \frac{5}{8} \times \frac{2}{3} = \frac{10}{24} = \frac{5}{12} \]