At boarding school, students spend $$\frac{1}{4}$$ of their time eating and sleeping, $$\frac{3}{5}$$ of their time in class, and $$\frac{1}{12}$$studying. The rest of the time is considered free time, which the student can spend doing activities of their own choosing. What fraction is considered free time?

$$\frac{1}{15}$$

Explanation

First you need to find a common denominator for these fractions. The common denominated for 4, 5, and 12 is 60. The fractions convert accordingly to: $$\frac{15}{60}$$, $$\frac{36}{60}$$, $$\frac{5}{60}$$
$$\frac{15}{60}+ \frac{36}{60} + \frac{5}{60} = \frac{56}{60}$$
Compute for the time left by subtracting $$\frac{56}{60}$$ from the fraction representing the whole day $$\frac{60}{60}$$:
$$\frac{60}{60} - \frac{56}{60} = \frac{4}{60} = \frac{1}{15}$$ (Reduced to the lowest terms)