1) $\frac{5}{6} : \frac{8}{9} = \frac{5}{6} * \frac{9}{8} = \frac{5}{2} * \frac{3}{8} = \frac{15}{16}$;
2) $\frac{8}{9} : \frac{5}{6} = \frac{8}{9} * \frac{6}{5} = \frac{8}{3} * \frac{2}{5} = \frac{16}{15} = 1\frac{1}{15}$;
3) $\frac{5}{6} : \frac{11}{12} = \frac{5}{6} * \frac{12}{11} = \frac{5}{1} * \frac{2}{11} = \frac{10}{11}$;
4) $\frac{11}{12} : \frac{5}{6} = \frac{11}{12} * \frac{6}{5} = \frac{11}{2} * \frac{3}{5} = \frac{33}{10} = 3\frac{3}{10}$;
5) $\frac{8}{9} : \frac{11}{12} = \frac{8}{9} * \frac{12}{11} = \frac{8}{3} * \frac{4}{11} = \frac{32}{33}$;
6) $\frac{11}{12} : \frac{8}{9} = \frac{11}{12} * \frac{9}{8} = \frac{11}{4} * \frac{3}{8} = \frac{33}{32} = 1\frac{1}{32}$.