Half of the class scored 90 in the test. One third of the class scored 87. One-sixth of the class scored 89. What is the average grade of the entire class?
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First, let us confirm that all the class’ scores were covered by making sure that the sum of all probabilities is 1.
Thus,
.
Thus, the scores of the entire class are represented.
The LCD of the denominators is
, so let the total number of students in the class be 
, then 
students scored 90, 
students scored 87, and 
students scored 89.
Thus, the average grade of the entire class is given by
.