Classifying a group into two different ways

[Aaron H.]

http://i49.tinypic.com/2wqu986.png


I don't understand this example. It's from an SAT math study guide. I understand that to find the fraction of the group that is both girls and seniors, 2/3 is multiplied times 2/5. Why is A + B equal to 4/9? Same with A + C.

 

[Number Nine]

Why is A + B equal to 4/9?

As the problem tells you, the ratio of seniors to juniors is 4:5. If there are 9 students, then 4/9 are seniors and 5/9 are juniors.

 

[Aaron H.]

Thanks. I had thought of that but I wasn't sure about it. So I guess the idea here is to, when given a fraction for a group, find the fraction that when added would make the sum of the two a whole number. Fractions are decimal numbers, after all. Percentages come to mind as well.