Question

The event coordinator asks you to determine how many students participated in the track-and-field day. The total number of students in seventh and eighth grade combined is 584; 5/8 of them are seventh graders and 3/8 of them are eighth graders. 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 your answer.

Answer 1

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.