Common ACT Math Problem

Question

Of 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

Answer 1

Why not just use numbers?

1/4 of 180 = 45 (A)

1/3 of 180 = 60 (B)

So C must be 180 - 45 - 60 = 75 (done!)

Answer 2

First we know that all of the students in the course earned either an A, B or C. Therefore, (the portion of students who got an A) + (the portion of students who got a B) + (the portion of students who got a C) =1

So let C be the portion of students who got a C

1/4+1/3+C=1

C=1-1/4-1/3

Now find a common denominator:

C=12/12-3/12-4/12=5/12

So 5/12 of the 180 students got a C.

Remember that "of" means to multiply:

5/12 of 180 means 5/12*180=75 students got a C

Answer 3

The quickest way to answer this question is to employ a strategy I always recommend when working with fractions: PROVIDE A COMMON DENOMINATOR. So now we change 1/4 and 1/3 to 3/12 and 4/12 respectively. When added together that means 7/12 got an A or B, leaving 5/12 (of the original 180) a C. At this point I remind students that "of" in math ALWAYS means to multiply, so you would multiply 5/12 by 180 which equals 75.

If you are stuck multiplying 5/12 by 180, the other strategy all my ACT students learn is to CONVERT FRACTIONS TO DECIMALS (easily on your calculator by dividing 5 by 12 which equals .416) And .416 multiplied by 180 = 75!!