Question

Question
Evan ate three-eighths of a hoagie for dinner. On the next day, he ate two-thirds of what was left for lunch. How much of the entire hoagie did Evan eat for lunch? Which process will you use to solve this problem?(1 point)
Responses

Answer 1

To solve the problem of how much of the entire hoagie Evan ate for lunch, we can follow these steps:

1. **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.

2. **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 \( \frac{5}{12} \).

3. **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.