Yuna hikes a trail that is \( \frac{3}{5} \) miles long. She hikes \( \frac{5}{8} \) of the trail before she rests. How many more niles does Yuna hike to reach the end of the trail?

Yuna needs to hike a certain distance to complete the trail after her initial hike. Let's break down the problem step by step. 1. **Total Length of the Trail:** \[ \frac{3}{5} \text{ miles} \] 2. **Distance Yuna Hiked Before Resting:** She hiked \( \frac{5}{8} \) of the trail: \[ \frac{5}{8} \times \frac{3}{5} = \frac{15}{40} = \frac{3}{8} \text{ miles} \] 3. **Remaining Distance to Complete the Trail:** Subtract the distance she has already hiked from the total trail length: \[ \frac{3}{5} - \frac{3}{8} \] To subtract these fractions, find a common denominator. The least common multiple of 5 and 8 is 40: \[ \frac{3}{5} = \frac{24}{40} \quad \text{and} \quad \frac{3}{8} = \frac{15}{40} \] Now, subtract: \[ \frac{24}{40} - \frac{15}{40} = \frac{9}{40} \text{ miles} \] **Answer:** Yuna needs to hike an additional \( \frac{9}{40} \) miles to reach the end of the trail.