To add these fractions together, we need to find a common denominator. In this case, the common denominator is 44.

Converting all fractions to have a denominator of 44:

-43/88 = -19/44
-1/2 = -22/44
3/4 = 33/44
21/44 = 21/44
8/11 = 32/44

Now add all fractions together:

-19/44 + (-22/44) + 33/44 + 21/44 + 32/44
= (-19 - 22 + 33 + 21 + 32) / 44
= (45) / 44

Therefore, the sum of -43/88, -1/2, 3/4, 21/44, and 8/11 is 45/44.