2.169 Вычислите: a) $$\frac{23}{24} - (\frac{1}{6} + \frac{1}{4})$$; б) $$\frac{4}{35} + (\frac{3}{5} - \frac{4}{7})$$; в) $$\frac{11}{15} - (\frac{2}{3} - \frac{3}{20})$$; г) $$\frac{5}{18} + (\frac{2}{9} + \frac{1}{27})$$. 2.170 Найдите значение выражения: a) $$\frac{7}{40} + \frac{11}{60}$$; б) $$\frac{27}{56} - \frac{5}{42}$$; в) $$\frac{11}{72} - \frac{7}{54}$$; г) $$\frac{16}{45} + \frac{17}{60}$$. 2.171 Выполните действия: a) $$\frac{19}{24} - \frac{25}{32} + (\frac{2}{48} + \frac{1}{96})$$; б) $$(\frac{11}{12} - \frac{3}{15}) + (\frac{7}{20} - \frac{1}{30}) - \frac{2}{3}$$. 2.172 Решите уравнение: a) $$t - \frac{11}{18} = \frac{11}{12} - \frac{5}{9}$$; в) $$(z + \frac{5}{12}) - \frac{9}{20} = \frac{11}{15}$$; б) $$\frac{4}{5} - (\frac{9}{10} - z) = \frac{1}{5}$$; г) $$\frac{4}{5} - (x + \frac{1}{60}) = \frac{2}{3}$$.

Решения: 2. 169 a) $$ \frac{23}{24} - (\frac{1}{6} + \frac{1}{4}) = \frac{23}{24} - (\frac{2}{12} + \frac{3}{12}) = \frac{23}{24} - \frac{5}{12} = \frac{23}{24} - \frac{10}{24} = \frac{13}{24}. $$ б) $$ \frac{4}{35} + (\frac{3}{5} - \frac{4}{7}) = \frac{4}{35} + (\frac{21}{35} - \frac{20}{35}) = \frac{4}{35} + \frac{1}{35} = \frac{5}{35} = \frac{1}{7}. $$ в) $$ \frac{11}{15} - (\frac{2}{3} - \frac{3}{20}) = \frac{11}{15} - (\frac{40}{60} - \frac{9}{60}) = \frac{11}{15} - \frac{31}{60} = \frac{44}{60} - \frac{31}{60} = \frac{13}{60}. $$ г) $$ \frac{5}{18} + (\frac{2}{9} + \frac{1}{27}) = \frac{5}{18} + (\frac{6}{27} + \frac{1}{27}) = \frac{5}{18} + \frac{7}{27} = \frac{15}{54} + \frac{14}{54} = \frac{29}{54}. $$ 2. 170 a) $$ \frac{7}{40} + \frac{11}{60} = \frac{21}{120} + \frac{22}{120} = \frac{43}{120}. $$ б) $$ \frac{27}{56} - \frac{5}{42} = \frac{81}{168} - \frac{20}{168} = \frac{61}{168}. $$ в) $$ \frac{11}{72} - \frac{7}{54} = \frac{33}{216} - \frac{28}{216} = \frac{5}{216}. $$ г) $$ \frac{16}{45} + \frac{17}{60} = \frac{64}{180} + \frac{51}{180} = \frac{115}{180} = \frac{23}{36}. $$ 2. 171 a) $$ \frac{19}{24} - \frac{25}{32} + (\frac{2}{48} + \frac{1}{96}) = \frac{19}{24} - \frac{25}{32} + (\frac{4}{96} + \frac{1}{96}) = \frac{19}{24} - \frac{25}{32} + \frac{5}{96} = \frac{76}{96} - \frac{75}{96} + \frac{5}{96} = \frac{6}{96} = \frac{1}{16}. $$ б) $$ (\frac{11}{12} - \frac{3}{15}) + (\frac{7}{20} - \frac{1}{30}) - \frac{2}{3} = (\frac{55}{60} - \frac{12}{60}) + (\frac{21}{60} - \frac{2}{60}) - \frac{2}{3} = \frac{43}{60} + \frac{19}{60} - \frac{2}{3} = \frac{62}{60} - \frac{40}{60} = \frac{22}{60} = \frac{11}{30}. $$ 2. 172 a) $$ t - \frac{11}{18} = \frac{11}{12} - \frac{5}{9}; $$ $$ t = \frac{11}{12} - \frac{5}{9} + \frac{11}{18} = \frac{33}{36} - \frac{20}{36} + \frac{22}{36} = \frac{35}{36}. $$ в) $$ (z + \frac{5}{12}) - \frac{9}{20} = \frac{11}{15}; $$ $$ z = \frac{11}{15} + \frac{9}{20} - \frac{5}{12} = \frac{44}{60} + \frac{27}{60} - \frac{25}{60} = \frac{46}{60} = \frac{23}{30}. $$ б) $$ \frac{4}{5} - (\frac{9}{10} - z) = \frac{1}{5}; $$ $$ \frac{4}{5} - \frac{9}{10} + z = \frac{1}{5}; $$ $$ z = \frac{1}{5} - \frac{4}{5} + \frac{9}{10} = -\frac{3}{5} + \frac{9}{10} = -\frac{6}{10} + \frac{9}{10} = \frac{3}{10}. $$ г) $$ \frac{4}{5} - (x + \frac{1}{60}) = \frac{2}{3}; $$ $$ \frac{4}{5} - x - \frac{1}{60} = \frac{2}{3}; $$ $$ x = \frac{4}{5} - \frac{1}{60} - \frac{2}{3} = \frac{48}{60} - \frac{1}{60} - \frac{40}{60} = \frac{7}{60}. $$