David's motorcycle uses \( 2 / 5 \) of a gallon of gasoline to travel 8 miles. At this rate, how many miles can it travel on 5 gallons of gasoline?

To determine how many miles David's motorcycle can travel on 5 gallons of gasoline, we first need to find the distance it can travel per gallon. Given that the motorcycle uses \( \frac{2}{5} \) of a gallon to travel 8 miles, we can calculate the distance it travels per gallon by setting up a proportion. 1. **Calculate the distance per gallon:** \[ \text{Distance per gallon} = \frac{\text{Distance traveled}}{\text{Gallons used}} = \frac{8 \text{ miles}}{\frac{2}{5} \text{ gallons}} \] To divide by a fraction, we multiply by its reciprocal: \[ \text{Distance per gallon} = 8 \text{ miles} \times \frac{5}{2} = 8 \times 2.5 = 20 \text{ miles} \] Thus, the motorcycle can travel 20 miles on 1 gallon of gasoline. 2. **Calculate the distance for 5 gallons:** \[ \text{Distance for 5 gallons} = 20 \text{ miles/gallon} \times 5 \text{ gallons} = 100 \text{ miles} \] Therefore, David's motorcycle can travel **100 miles** on 5 gallons of gasoline.