1. 7/9 - 5/6 * 4/15.

1. $\frac{7}{9} - \frac{5}{6} \cdot \frac{4}{15} = \frac{7}{9} - \frac{1}{3} \cdot \frac{2}{3} = \frac{7}{9} - \frac{2}{9} = \frac{5}{9}$ 2. $(\frac{2}{3} - \frac{4}{9}) \cdot \frac{3}{8} = (\frac{6}{9} - \frac{4}{9}) \cdot \frac{3}{8} = \frac{2}{9} \cdot \frac{3}{8} = \frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}$ 3. $\frac{2}{7} + \frac{3}{8} : \frac{7}{32} = \frac{2}{7} + \frac{3}{8} \cdot \frac{32}{7} = \frac{2}{7} + \frac{3}{1} \cdot \frac{4}{7} = \frac{2}{7} + \frac{12}{7} = \frac{14}{7} = 2$ 4. $\frac{5}{9} : (\frac{7}{9} + \frac{11}{18}) = \frac{5}{9} : (\frac{14}{18} + \frac{11}{18}) = \frac{5}{9} : \frac{25}{18} = \frac{5}{9} \cdot \frac{18}{25} = \frac{1}{1} \cdot \frac{2}{5} = \frac{2}{5}$ 5. $1 - \frac{4}{7} : \frac{16}{21} = 1 - \frac{4}{7} \cdot \frac{21}{16} = 1 - \frac{1}{1} \cdot \frac{3}{4} = 1 - \frac{3}{4} = \frac{1}{4}$ 6. $\frac{5}{12} \cdot (\frac{1}{5} + \frac{3}{25}) = \frac{5}{12} \cdot (\frac{5}{25} + \frac{3}{25}) = \frac{5}{12} \cdot \frac{8}{25} = \frac{1}{3} \cdot \frac{2}{5} = \frac{2}{15}$ 7. $\frac{9}{14} \cdot (\frac{17}{24} - \frac{5}{12}) = \frac{9}{14} \cdot (\frac{17}{24} - \frac{10}{24}) = \frac{9}{14} \cdot \frac{7}{24} = \frac{3}{2} \cdot \frac{1}{8} = \frac{3}{16}$ 8. $\frac{24}{49} : \frac{6}{7} + \frac{1}{14} = \frac{24}{49} \cdot \frac{7}{6} + \frac{1}{14} = \frac{4}{7} \cdot \frac{1}{1} + \frac{1}{14} = \frac{8}{14} + \frac{1}{14} = \frac{9}{14}$