To find the area of Cara's bathroom floor that is not covered by the rug, you need to subtract the area of the rug from the total area of the floor.
The total area of the floor is 3 2/3 square yards, which can also be expressed as 11/3 square yards.
The area of the rug is 1 1/4 square yards, which can also be expressed as 5/4 square yards.
To find the area not covered by the rug, subtract the area of the rug from the total area of the floor:
(11/3) - (5/4) = 44/12 - 15/12 = 29/12
Therefore, the area of Cara's floor that is not covered by the rug is 29/12 square yards.