Using the commutative and associative properties of multiplication to simplify multiplication of two rational numbers
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. 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.
To find out how many total students participated in the track-and-field day, we need to calculate the fraction of seventh graders and eighth graders who participated, and then add them together.
First, let's find out how many seventh graders participated. To do this, we multiply the total number of students by the fraction of seventh graders (5/8), and then multiply that by the fraction of seventh graders who participated (4/5):
(584) x (5/8) x (4/5) = (292) x (4/5) = 233.6
So, approximately 233.6 seventh graders participated.
Next, let's find out how many eighth graders participated. To do this, we multiply the total number of students by the fraction of eighth graders (3/8), and then multiply that by the fraction of eighth graders who participated (7/8):
(584) x (3/8) x (7/8) = (219.75) x (7/8) = 191.43
So, approximately 191.43 eighth graders participated.
Finally, to find out the total number of students who participated, we add the approximate number of participating seventh graders and eighth graders together:
Approximate total number of participating students = 233.6 + 191.43 = 425.03
Therefore, approximately 425 students participated in the track-and-field day.