To solve the problem, we need to first find out how much of the hoagie was left after Evan ate three-eighths of it, and then determine how much he ate for lunch, which is two-thirds of the remaining portion.
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Calculate the remaining portion of the hoagie after dinner: Total hoagie = 1 (i.e., the whole hoagie) Portion eaten for dinner = \( \frac{3}{8} \) Remaining portion = \( 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} \)
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Calculate how much was eaten for lunch: Portion eaten for lunch = \( \frac{2}{3} \) of the remaining portion \( \text{Lunch eaten} = \frac{2}{3} \times \frac{5}{8} \)
To calculate that: \[ \frac{2}{3} \times \frac{5}{8} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24} \] Simplifying \( \frac{10}{24} \) gives: \[ \frac{10 \div 2}{24 \div 2} = \frac{5}{12} \]
Thus, the answer to how much of the entire hoagie Evan ate for lunch is \( \frac{5}{12} \).
The correct process to solve this problem is option: 5/8×2/3=10÷2/24÷2=5/12.
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