Выполним вычисления:
1. \[ \frac{4}{7} + \frac{2}{5} = \frac{20}{35} + \frac{14}{35} = \frac{34}{35}. \]
2. \[ \frac{7}{12} - \frac{5}{9} = \frac{21}{36} - \frac{20}{36} = \frac{1}{36}. \]
3. \[ 2 \frac{3}{4} + 3 \frac{2}{5} = \frac{11}{4} + \frac{17}{5} = \frac{55}{20} + \frac{68}{20} = \frac{123}{20} = 6 \frac{3}{20}. \]
4. \[ 3 \frac{4}{9} - 2 \frac{1}{6} = \frac{31}{9} - \frac{13}{6} = \frac{62}{18} - \frac{39}{18} = \frac{23}{18} = 1 \frac{5}{18}. \]