Yes, a fraction can be negative! -1/2 -3/4
But depending on how you write the equations the '-' sign might be for negative or subtraction.
12*(-3/4) or 12(-3/4) is twelve times negative three-quarters
12-3/4 is twelve minus three-quarters
Also in your question here it is not clear what your question is.
In the last line (4/4) is indeed equal to 1.
But in the first two lines what are you asking?
Is it what those two lines are equal to? If so...
2*(5/2) - 3*(1/4) = (10/2) - (3/4) = (20/4) - (3/4) = 17/4 = 4 1/4
(9/2) - (5/4)(9- 5/4) = (9/2) - (5/4)(36/4 - 5/4)
= (9/2) - (5/4)(31/4) = (18/4) - (155/4) = -137/4 = -34 1/4