[tex]\begin{gathered} 3\frac{8}{9}+8\frac{1}{2}=\frac{3\cdot9+8}{9}+\frac{2\cdot8+1}{2} \\ =\frac{27+8}{9}+\frac{16+1}{2} \\ =\frac{35}{9}+\frac{17}{2} \\ \\ =\frac{35\cdot2+17\cdot9}{9\cdot2} \\ =\frac{70+153}{18} \\ =\frac{223}{18} \\ =12\frac{7}{8} \end{gathered}[/tex]
