To determine how much of the entire hoagie Evan ate for lunch, we need to first find out how much hoagie was left after his dinner, and then determine how much he ate for lunch based on that.
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Amount eaten for dinner: Evan ate three-eighths (\(\frac{3}{8}\)) of the hoagie. Therefore, the remaining amount is: \[ 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} \]
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Amount eaten for lunch: The next day, Evan ate two-thirds (\(\frac{2}{3}\)) of what was left. We calculate that as follows: \[ \text{Amount eaten for lunch} = \frac{2}{3} \times \frac{5}{8} \] To multiply these fractions, we multiply the numerators and the denominators: \[ = \frac{2 \times 5}{3 \times 8} = \frac{10}{24} \] Simplifying \(\frac{10}{24}\): \[ = \frac{5}{12} \]
So, Evan ate \(\frac{5}{12}\) of the entire hoagie for lunch.
The correct process to solve this problem is:
- First, subtract the fraction of the hoagie eaten (three-eighths) from the total (which is 1, or the whole hoagie) to find what remains.
- Then, multiply the remaining fraction (five-eighths) by two-thirds to find how much was eaten for lunch.
The response that corresponds to this process is:
58×23=10÷224÷2=512
Because it corresponds to finding \(\frac{2}{3}\) of the \(\frac{5}{8}\) remaining hoagie.