Final answer:
Diego practices guitar 13 times per week by dividing the total weekly practice time of 9 3/4 hours by the length of each session, 3/4 hour.
Step-by-step explanation:
The question asks how many times per week Diego practices guitar given that he practices a total of 9 3/4 hours each week and each session is 3/4 hour long. To find the number of practice sessions, we divide the total weekly practice time by the length of each practice session.
First, convert the mixed number 9 3/4 hours to an improper fraction, which is (9×4 + 3)/4 = 39/4 hours.
Then, divide 39/4 hours by 3/4 hours per session to get the number of sessions:
39/4 ÷ 3/4 = (39/4) × (4/3) = 39/3 = 13.
So, Diego practices 13 times per week.