To solve the problem of how much of the entire hoagie Evan ate for lunch, we can follow these steps:
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Determine how much of the hoagie is left after dinner:
- Evan ate \( \frac{3}{8} \) of the hoagie for dinner.
- To find out how much is left, we subtract the amount he ate from the whole hoagie: \[ 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} \]
- So, \( \frac{5}{8} \) of the hoagie is left.
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Calculate how much he ate for lunch:
- Evan ate \( \frac{2}{3} \) of what was left for lunch.
- To find out how much this is, we multiply \( \frac{2}{3} \) by the amount of hoagie left: \[ \frac{2}{3} \times \frac{5}{8} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24} \]
- We can simplify \( \frac{10}{24} \) to \( \frac{5}{12} \).
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Result:
- Evan ate \( \frac{5}{12} \) of the entire hoagie for lunch.
Process: The mathematical processes used in this solution are subtraction to find the remaining amount of the hoagie and multiplication to determine the amount consumed during lunch.