3 and 1/4 would become 13/4 since 3 times the denominator, 4, is 12, and that plus the current numerator, 1, is 13, becoming the new numerator.
Converting 1/2 into 4ths is 2/4, and 13-2 (the numerators of the numbers) is 11. That means that 3 and 1/4 minus 1/2 is 11/4, or 2 3/4.