Question 6770
You have the right idea but the second ratio of your proportion is inverted.

Remember to keep like-items in the tops and like-items in the bottoms of the ratios.

 Teachers/students = 4/52  You had this correctly shown.
Let x = # of students, so you want to see the number of teachers on top and the number of students (x) on the bottom.

27/x

The proportion looks like:
  4/52 = 27/x  Solve for x by cross-multiplying.
4x = (52)(27) Divide both sides by 4.
x = 1404/4
x = 351 This is the  number of students.

Check:

4/52 = 27/351 Reduce the fractions.
1/13 = 1/13