Question is in the description.

Question

An event coordinator asks you to determine how man students participated in a track-and-field day. The total number of students in seventh and eighth grade combined are 584. 5/8 of them are seventh graders and 3/8 of them are eighth graders. Using commutative and associative properties of multiplication, if 4/5 of the seventh graders participated in track-and-field day and 7/8 of the eighth graders participated, about how many total students participated? Describe the process you used to find the answer.

 

Answer 1

I would rather just explain how to find the answer. So, here goes.

 

584 is the total number of students in the school.

 

5/8 are in seventh grade and 3/8 are in eighth grade.

 

4/5 of the seventh graders participated in the track meet, so there were (4/5 · 5/8) · 584 students in the seventh grade participating in the track meet.

 

7/8 of the eighth graders participated, so there were (7/8 · 3/8) · 584 students in the eighth grade participating in the track meet.

 

So, all together, there were 

 

(4/5 · 5/8) · 584 + (7/8 · 3/8) · 584 students from the school in the track meet.

 

Let's simplify as you asked:

 

(4/5 · 5/8) · 584 + (7/8 · 3/8) · 584 = [(4/5 · 5/8) + (7/8 · 3/8)] · 584   (distributive property - factoring)

 

      = [20/40 + 21/64] · 584   (multiply fractions)

 

      = (1/2 + 21/64) 584    (reduce the first fraction to lowest terms)

 

      = (32/64 + 21/64) 584    (getting a common denominator)

 

      = (53/64) 584    (combine/add the two fractions)

 

      = 483.625   (multiply together)

 

All together, there were: 483.625 students in the meet.

I would answer 484, just to be safe. This really is not a good problem, but I tried my best. Some of us old-timers recall problems like this in the 1960s and 1970s, and they gave some of us headaches (as well as the teachers). I am sorry you have to suffer with this sort of question, but please feel free to post a reply or question if you have one.