At boarding school, students spend \(\frac{1}{4}\) of their time eating and sleeping, \(\frac{3}{5}\)of their time in class, and \(\frac{1}{4}\) 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?



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: \(\frac{15}{60}\), \(\frac{36}{60}\), \(\frac{5}{60}\).
Now add these three fractions:
\(\frac{15}{60}+ \frac{36}{60} + \frac{5}{60} = \frac{56}{60}\).
Compute for the time left by subtracting 56/60 from the fraction representing the whole day 60/60:
\(\frac{60}{60} - \frac{56}{60} = \frac{4}{60} = \frac{1}{15}\) (Reduced to the lowest terms)

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