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
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
Answers
GPT-4o mini
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.
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.