First, we need to convert the mixed numbers into fractions, as follows:
[tex]\begin{gathered} -7\frac{2}{3}=-\frac{7\cdot3+2}{3}=-\frac{23}{3} \\ -5\frac{1}{2}=-\frac{5\cdot2+1}{2}=-\frac{11}{2} \\ 8\frac{3}{4}=\frac{8\cdot4+3}{4}=\frac{35}{4} \end{gathered}[/tex]
Now, we can compute the addition as follows:
[tex]\begin{gathered} -7\frac{2}{3}+(-5\frac{1}{2})+8\frac{3}{4}= \\ -\frac{23}{3}-\frac{11}{2}+\frac{35}{4}=\frac{-23\cdot4-11\cdot6+35\cdot3}{12}=\frac{-92-66+105}{12}=\frac{-53}{12} \end{gathered}[/tex]
