BOT 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

38÷23=916
3 eighths divided by 2 thirds is equal to 9 over 16

38+23=2524=1124
3 eighths plus 2 thirds is equal to 25 over 24 is equal to 1 and 1 over 24

38×23=6÷624÷6=14
3 eighths times 2 thirds is equal to the fraction with numerator 6 divided by 6 and denominator 24 divided by 6 is equal to 1 fourth

58×23=10÷224÷2=512
5 eighths times 2 thirds is equal to the fraction with numerator 10 divided by 2 and denominator 24 divided by 2 is equal to 5 over 12

58÷23=1516

3 answers

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

  1. Determine how much of the hoagie was left after dinner: Evan initially ate three-eighths of a hoagie, which means: \[ 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} \] So, he had five-eighths of the hoagie left after dinner.

  2. Calculate how much he ate for lunch: On the next day, he ate two-thirds of what was left. We need to find two-thirds of five-eighths: \[ \frac{2}{3} \times \frac{5}{8} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24} \] Simplifying \(\frac{10}{24}\): \[ \frac{10 \div 2}{24 \div 2} = \frac{5}{12} \] Therefore, Evan ate \(\frac{5}{12}\) of the entire hoagie for lunch.

To summarize, Evan ate \(\frac{5}{12}\) of the hoagie for lunch, and the correct process to solve this problem involves multiplying fractions (specifically multiplying \(\frac{2}{3}\) by the remaining portions of the hoagie \(\frac{5}{8}\)).

The final answer corresponds to the choice: \[ \frac{5}{8} \times \frac{2}{3} = \frac{10}{24} = \frac{5}{12} \]

a b c or d

The correct response that matches the process used to solve the problem is:

d) \( \frac{5}{8} \times \frac{2}{3} = \frac{10}{24} \div 2 = \frac{5}{12} \)

This indicates the step of multiplying \(\frac{5}{8}\) (the remaining hoagie) by \(\frac{2}{3}\) (the portion he ate for lunch), which leads to the final answer of \(\frac{5}{12}\) of the entire hoagie.