Ruth can make a maximum of 5 yards of fabric.
Given she bought 8 3/4 yards and 1 1/2 is needed, we can set up an equation:
1.5x ≈ 8.75
8.75 / 1.5 gives us 5.8333 repeating. Because it is irrational to make 5.8 sweaters, we should round down to the necessary approximation. Rounded down, 5.8 is 5. Therefore, Ruth can make a maximum of 5 sweaters.