Решение задания 2.53

a) $$\frac{4}{9} + \frac{7}{9} - \frac{1}{9} = \frac{4+7-1}{9} = \frac{10}{9} = 1\frac{1}{9}$$

б) $$\frac{6}{7} - (\frac{5}{7} - \frac{1}{7}) = \frac{6}{7} - \frac{4}{7} = \frac{2}{7}$$

в) $$5\frac{6}{39} + 4\frac{7}{78} = 5\frac{12}{78} + 4\frac{7}{78} = 9\frac{19}{78}$$

г) $$7\frac{13}{15} - 3\frac{11}{30} = 7\frac{26}{30} - 3\frac{11}{30} = 4\frac{15}{30} = 4\frac{1}{2}$$

д) $$\frac{7}{8} \cdot \frac{4}{35} \cdot \frac{10}{9} = \frac{7 \cdot 4 \cdot 10}{8 \cdot 35 \cdot 9} = \frac{1 \cdot 1 \cdot 5}{2 \cdot 5 \cdot 9} = \frac{1}{2} \cdot \frac{1}{9} = \frac{1}{18}$$

e) $$(\frac{1}{2} : \frac{3}{4} - \frac{4}{9}) \cdot \frac{5}{3} = (\frac{1}{2} \cdot \frac{4}{3} - \frac{4}{9}) \cdot \frac{5}{3} = (\frac{2}{3} - \frac{4}{9}) \cdot \frac{5}{3} = (\frac{6}{9} - \frac{4}{9}) \cdot \frac{5}{3} = \frac{2}{9} \cdot \frac{5}{3} = \frac{10}{27}$$