[tex] \frac{1}{6}: \frac{5}{4}= \frac{4*6+1}{6}: \frac{5}{4} = \frac{24+1}{6}: \frac{5}{4} = \frac{25}{6}: \frac{5}{4} = \frac{25}{6}* \frac{4}{5} = \frac{5}{3} * \frac{2}{1} = \frac{5*6}{3} = \frac{30}{3} = 10[/tex]
[tex] \frac{8}{9} : 5 \frac{1}{3} = \frac{8}{9} : \frac{5*3+1}{3} = \frac{8}{9} : \frac{15+1}{3} = \frac{8}{9} : \frac{16}{3} = \frac{8}{9} * \frac{3}{16} = \frac{1}{3} * \frac{1}{2} = \frac{2*3}{6} = \frac{6}{6} = 1[/tex]
