2¾-5½ is the same as 2+¾-(5+½)=2-5+¾-½=-3+3/4-2/4=-3+¼=-2¾, because 1/2 is the same as 2/4 and we have a common denominator 4.
Another way, since 5½ is bigger than 2¾, we know the answer is going to be negative, so work out 5½-2¾, which is positive:
5-2+½-¾=3+2/4-3/4=3-¼=2+1-¼=2+¾=2¾. Now make it negative: -2¾.
Another way: convert to vulgar fractions:
2¾=(4×2+3)/4=11/4; 5½=(2×5+1)/2=11/2.
11/2=22/4 (so we have a common denominator),
2¾-5½=11/4-22/4=(11-22)/4=-11/4=-2¾ (4 goes into 11 twice, remainder 3).