Final answer:
The fraction of patients left on the floor on Friday is 9/16.
Step-by-step explanation:
To find the fraction of patients that will be left on the floor on Friday, let's break down the information given. Initially, 1/4 of the patients will have surgery on Monday and go home on Wednesday. This means 3/4 of the patients will remain. Then, another 1/4 of the remaining patients will go home on Thursday. This means 3/4 * 1/4 = 3/16 of the patients will go home on Thursday. Therefore, the fraction of patients left on the floor on Friday is 3/4 - 3/16 = 9/16.