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?

\( \frac{1}{15}\)


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 \(\frac{56}{60}\) 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)

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