a) \frac{4}{9} + \frac{2}{6} = \frac{4}{9} + \frac{1}{3} = \frac{4}{9} + \frac{3}{9} = \frac{4+3}{9} = \frac{7}{9}
b) \frac{15}{16} - \frac{7}{8} = \frac{15}{16} - \frac{14}{16} = \frac{15-14}{16} = \frac{1}{16}
c) \frac{19}{30} - \frac{7}{15} = \frac{19}{30} - \frac{14}{30} = \frac{19-14}{30} = \frac{5}{30} = \frac{1}{6}
d) 4 \frac{7}{20} + 2 \frac{17}{20} = 4 + 2 + \frac{7}{20} + \frac{17}{20} = 6 + \frac{24}{20} = 6 + \frac{6}{5} = 6 + 1 \frac{1}{5} = 7 \frac{1}{5}
e) \frac{5}{7} \cdot \frac{7}{15} = \frac{5 \cdot 7}{7 \cdot 15} = \frac{35}{105} = \frac{1}{3}
f) (\frac{7}{15} + \frac{2}{5}) \cdot \frac{5}{6} = (\frac{7}{15} + \frac{6}{15}) \cdot \frac{5}{6} = \frac{13}{15} \cdot \frac{5}{6} = \frac{13 \cdot 5}{15 \cdot 6} = \frac{65}{90} = \frac{13}{18}
g) \frac{8}{12} \cdot \frac{4}{5} - \frac{1}{3} \cdot \frac{3}{9} = \frac{2}{3} \cdot \frac{4}{5} - \frac{1}{3} \cdot \frac{1}{3} = \frac{8}{15} - \frac{1}{9} = \frac{24}{45} - \frac{5}{45} = \frac{19}{45}