what is -113/24 + 3 8/9

$$\\\frac{-113}{24} + 3\frac{ 8}{9}\\\\
-\frac{113}{24}+3\frac{ 8}{9}\\\\
-4\frac{17}{24}+ 3\frac{ 8}{9}\\\\
-4\frac{17*3}{24*3}+ 3\frac{ 8*8}{9*8}\\\\
-4\frac{51}{72}+ 3\frac{ 64}{72}\\\\
-(4\frac{51}{72}- 3\frac{ 64}{72})\\\\
-(4\frac{51}{72}- 3-\frac{ 64}{72})\\\\
-(4- 3\frac{51}{72}-\frac{ 64}{72})\\\\
-(1\frac{51}{72}-\frac{ 64}{72})\\\\
-(\frac{72+51}{72}-\frac{ 64}{72})\\\\
-(\frac{72+51-64}{72})\\\\$$

 

$$\\-(\frac{59}{72})\\\\
-\frac{59}{72}\\\\$$

 

check

$${\mathtt{\,-\,}}{\frac{{\mathtt{113}}}{{\mathtt{24}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{8}}}{{\mathtt{9}}}} = {\mathtt{\,-\,}}{\frac{{\mathtt{59}}}{{\mathtt{72}}}} = -{\mathtt{0.819\: \!444\: \!444\: \!444\: \!444\: \!4}}$$

.