#### Answer

$\frac{9}{10}$ of the students

#### Work Step by Step

Given, The San Juan School District operates an after school program for students. This year $\frac{2}{5}$ of the students played after school sports, $\frac{1}{6}$ participated in arts and crafts, and $\frac{1}{3}$ spent their time in tutoring and study hall.
To find the total students participated in these activities .We need to add all the activities.
$\frac{2}{5}$ + $\frac{1}{6}$ + $\frac{1}{3}$
The least common multiple of 5, 6 and 3 is 30. Rewrite both fractions as fractions with a least common denominator of 30.
Rewrite as like fraction
$\frac{2}{5}$ + $\frac{1}{6}$ + $\frac{1}{3}$ = $\frac{12}{30}$ + $\frac{5}{30}$ + $\frac{10}{30}$
Add the numerator = $\frac{12 + 5 + 10}{30}$ = $\frac{27}{30}$
$\frac{27}{30}$ is not in lowest term. So divide the numerator and denominator by the common factor 3.
$\frac{27}{30}$ = $\frac{9}{10}$