To solve this problem, we need to figure out how much of the hoagie Evan had left after eating three-eighths of it and then determine how much he ate when he consumed two-thirds of what was left for lunch.
Step 1: Determine what is left after dinner
Evan ate three-eighths of the hoagie, which is denoted as:
\[
\text{Amount eaten for dinner} = \frac{3}{8}
\]
Thus, the amount left after dinner is:
\[
\text{Amount left} = 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}
\]
Step 2: Determine what he ate for lunch
Evan then ate two-thirds of what was left, which can be calculated as:
\[
\text{Amount eaten for lunch} = \frac{2}{3} \times \frac{5}{8}
\]
To perform this multiplication, multiply the numerators and the denominators:
\[
\text{Amount eaten for lunch} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24}
\]
Step 3: Simplify the fraction
Now, simplify \( \frac{10}{24} \):
\[
\frac{10}{24} = \frac{5}{12}
\]
Thus, Evan ate \( \frac{5}{12} \) of the entire hoagie for lunch.
Process Used
The process used to solve this problem is:
- Multiplication of fractions to find how much of the remaining hoagie Evan consumed.
Final Answers
So, when looking at the responses you provided, we can conclude:
- How much of the entire hoagie did Evan eat for lunch? \( \frac{5}{12} \)
- Which process will you use to solve this problem? The specific answer choice should reflect that he multiplied three-eighths of the remaining hoagie left:
The closest correct operation is:
- 58 × 23 = 10 ÷ 22 = 5/12, meaning you multiply \( \frac{5}{8} \) by \( \frac{2}{3} \).
If that choice is not listed, just take note of the multiplication of the remaining hoagie portion and the fraction eaten for lunch.
2 answers