To determine how many patients the doctor can see in 4-1/2 hours, we first convert the time to minutes:
4-1/2 hours = 4.5 hours = 4.5 × 60 minutes = 270 minutes.
Since each patient takes 15 minutes, we can divide the total minutes by the time taken for each patient:
Number of patients = Total minutes / Minutes per patient
Number of patients = 270 minutes / 15 minutes per patient
Number of patients = 18.
Thus, the doctor can see 18 patients in 4-1/2 hours.