To solve this problem, we will first establish how much of the hoagie Evan consumed on the first day and then determine how much was left for lunch the next day. Finally, we will calculate how much he ate for lunch.
Steps to Solve the Problem:
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Calculate how much of the hoagie Evan ate for dinner:
- Total hoagie = 1 (whole)
- Amount eaten for dinner = \(\frac{3}{8}\)
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Calculate how much of the hoagie is left after dinner: \[ \text{Left after dinner} = 1 - \frac{3}{8} \] To subtract, convert 1 into eighths: \[ 1 = \frac{8}{8} \] So: \[ \text{Left after dinner} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} \]
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Determine how much Evan ate for lunch on the next day:
- Amount eaten for lunch = \(\frac{2}{3}\) of what was left
- We calculate \(\frac{2}{3}\) of \(\frac{5}{8}\): \[ \text{Amount eaten for lunch} = \frac{2}{3} \times \frac{5}{8} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24} \] Simplifying \(\frac{10}{24}\): \[ \frac{10 \div 2}{24 \div 2} = \frac{5}{12} \]
Conclusion:
Evan ate \(\frac{5}{12}\) of the entire hoagie for lunch.
Process to Solve the Problem:
- Subtract fractions to find what was left.
- Multiply fractions to find the portion eaten for lunch.
- Simplify the resulting fraction if necessary.
This process involves basic arithmetic operations on fractions, which is key to solving this type of problem.
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