\( 2 \frac{1}{4} \) pounds of trail mix into bags that each weigh \( \frac{3}{8} \) pound. They bring \( \frac{2}{3} \) of the bags of trail mix on a hiking trip. Can you determine how many bags of trail mix are left by completing just one step? Explain.

To determine how many bags of trail mix are left after bringing \( \frac{2}{3} \) of the bags on a hiking trip, we first need to find out how many bags of trail mix can be made from \( 2 \frac{1}{4} \) pounds of trail mix, with each bag weighing \( \frac{3}{8} \) pound. 1. **Convert \( 2 \frac{1}{4} \) pounds to an improper fraction:** \[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ pounds} \] 2. **Determine the number of bags:** To find the number of bags, we divide the total weight of the trail mix by the weight of each bag: \[ \text{Number of bags} = \frac{\frac{9}{4}}{\frac{3}{8}} = \frac{9}{4} \times \frac{8}{3} = \frac{9 \times 8}{4 \times 3} = \frac{72}{12} = 6 \text{ bags} \] 3. **Calculate how many bags are taken on the trip:** They take \( \frac{2}{3} \) of the bags: \[ \text{Bags taken} = \frac{2}{3} \times 6 = 4 \text{ bags} \] 4. **Determine how many bags are left:** The total number of bags is 6, and if 4 bags are taken, the number of bags left is: \[ \text{Bags left} = 6 - 4 = 2 \text{ bags} \] Thus, by completing just one step (finding the total number of bags), we can conclude that there are **2 bags of trail mix left** after the hiking trip.