A beach has dedicated \( \frac{1}{4} \) of its area to sunbathing spaces, Of that section, \( \frac{2}{5} \) is reserved for umbrella rentals. What fraction of the entire beach is reserved for umbrella rentals?

To find the fraction of the entire beach that is reserved for umbrella rentals, we can follow these steps: 1. **Identify the area dedicated to sunbathing spaces**: The beach has dedicated \( \frac{1}{4} \) of its area to sunbathing spaces. 2. **Identify the fraction of the sunbathing area reserved for umbrella rentals**: Of the sunbathing area, \( \frac{2}{5} \) is reserved for umbrella rentals. 3. **Calculate the area reserved for umbrella rentals**: To find the fraction of the entire beach that is reserved for umbrella rentals, we multiply the fraction of the beach dedicated to sunbathing spaces by the fraction of that area reserved for umbrella rentals. Let's denote: - \( A \) as the total area of the beach. - The area dedicated to sunbathing spaces is \( \frac{1}{4}A \). - The area reserved for umbrella rentals is \( \frac{2}{5} \) of the sunbathing area. Now, we can calculate the area reserved for umbrella rentals: \[ \text{Area for umbrella rentals} = \left(\frac{1}{4}A\right) \times \left(\frac{2}{5}\right) \] Calculating this gives: \[ \text{Area for umbrella rentals} = \frac{1}{4} \times \frac{2}{5} A = \frac{2}{20} A = \frac{1}{10} A \] Thus, the fraction of the entire beach that is reserved for umbrella rentals is \( \frac{1}{10} \). Therefore, the final answer is: \[ \frac{1}{10} \]