A high school senior said she knows all the seniors, half the juniors, 1/3 of the sophomores, and 1/4 of the freshmen. If each class has the same numbers of students, then she knows what fraction of the school?

This classic puzzle demonstrates how to find the average of several different fractions. The key is to remember that since each of the four classes has the same number of students, we can treat each class as an equal one-quarter of the school's total population. The student’s knowledge isn't uniform across the school, so we need to calculate the overall proportion based on the individual parts.

To solve this, we first add the fractions representing the students she knows from each class: 1 (for all seniors), 1/2 (for juniors), 1/3 (for sophomores), and 1/4 (for freshmen). To add these, we find a common denominator, which is 12. The sum becomes 12/12 + 6/12 + 4/12 + 3/12, which equals 25/12.

This sum of 25/12 isn't the final answer, however. That number represents the total proportion if all the students were combined into one giant group. Since this knowledge is spread across four distinct and equally sized classes, we must divide that sum by 4 to find the average fraction she knows of the entire school. Dividing 25/12 by 4 gives us the correct final proportion of 25/48.