imani is planning her citys juneteenth festival. there will be 3 1/2 hours of peformances on the main stage. each performers time slot lasts 3/4 hour. how many time slots can imani plan to have?
plez help!!!
3 1/2 = 7/2
(7/2) / (3/4) = (7/2) x (4/3) = 14/3 = 4.6
4 time slots
To determine how many time slots Imani can plan for the Juneteenth festival, we need to divide the total duration of performances by the length of each time slot.
First, let's convert the given half-hour into a fraction. Half an hour is equivalent to 1/2 hour.
To calculate the number of time slots, divide the total duration of performances by the length of each time slot:
Total duration of performances: 3 1/2 hours
Length of each time slot: 3/4 hour
To simplify the calculation, let's convert the mixed number into an improper fraction:
3 1/2 = (3 * 2 + 1) / 2 = 7 / 2
Now, divide the total duration by the length of each time slot:
(7 / 2) / (3 / 4) = (7 / 2) * (4 / 3) = (7 * 4) / (2 * 3) = 28 / 6
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 2:
(28 / 2) / (6 / 2) = 14 / 3
Therefore, Imani can plan to have 14 time slots for the Juneteenth festival.