Вычислите выражения

1. Вычислите: 1) $$ \frac{5}{6} - \frac{3}{22} = \frac{5 \cdot 11}{6 \cdot 11} - \frac{3 \cdot 3}{22 \cdot 3} = \frac{55}{66} - \frac{9}{66} = \frac{46}{66} = \frac{23}{33} $$ 2) $$ 0,75 - \left( \frac{3}{16} + \frac{1}{24} \right) = \frac{3}{4} - \left( \frac{3 \cdot 3}{16 \cdot 3} + \frac{1 \cdot 2}{24 \cdot 2} \right) = \frac{3}{4} - \left( \frac{9}{48} + \frac{2}{48} \right) = \frac{3}{4} - \frac{11}{48} = \frac{3 \cdot 12}{4 \cdot 12} - \frac{11}{48} = \frac{36}{48} - \frac{11}{48} = \frac{25}{48} $$ 3) $$ \frac{9}{16} + \left( 0,25 - \frac{5}{24} \right) = \frac{9}{16} + \left( \frac{1}{4} - \frac{5}{24} \right) = \frac{9}{16} + \left( \frac{1 \cdot 6}{4 \cdot 6} - \frac{5}{24} \right) = \frac{9}{16} + \left( \frac{6}{24} - \frac{5}{24} \right) = \frac{9}{16} + \frac{1}{24} = \frac{9 \cdot 3}{16 \cdot 3} + \frac{1 \cdot 2}{24 \cdot 2} = \frac{27}{48} + \frac{2}{48} = \frac{29}{48} $$ 4) $$ 0,88 - \frac{2}{15} = \frac{88}{100} - \frac{2}{15} = \frac{22}{25} - \frac{2}{15} = \frac{22 \cdot 3}{25 \cdot 3} - \frac{2 \cdot 5}{15 \cdot 5} = \frac{66}{75} - \frac{10}{75} = \frac{56}{75} $$ 5) $$ \left( \frac{1}{6} + \frac{5}{18} \right) - \left( \frac{1}{18} + \frac{1}{24} \right) = \left( \frac{3}{18} + \frac{5}{18} \right) - \left( \frac{4}{72} + \frac{3}{72} \right) = \frac{8}{18} - \frac{7}{72} = \frac{4}{9} - \frac{7}{72} = \frac{32}{72} - \frac{7}{72} = \frac{25}{72} $$ 6) $$ 4 - 2\frac{4}{7} = 3\frac{7}{7} - 2\frac{4}{7} = 1\frac{3}{7} $$ 7) $$ 2,5 + 1\frac{2}{3} - 3\frac{1}{6} = 2\frac{1}{2} + 1\frac{2}{3} - 3\frac{1}{6} = \frac{5}{2} + \frac{5}{3} - \frac{19}{6} = \frac{15}{6} + \frac{10}{6} - \frac{19}{6} = \frac{15+10-19}{6} = \frac{6}{6} = 1 $$ 8) $$ 0,36 - \frac{9}{75} + \frac{2}{15} = \frac{36}{100} - \frac{3 \cdot 3}{25 \cdot 3} + \frac{2}{15} = \frac{9}{25} - \frac{3}{25} + \frac{2}{15} = \frac{6}{25} + \frac{2}{15} = \frac{6 \cdot 3}{25 \cdot 3} + \frac{2 \cdot 5}{15 \cdot 5} = \frac{18}{75} + \frac{10}{75} = \frac{28}{75} $$ 9) $$ \left( \frac{1}{2} - \frac{1}{3} \right) - \left( \frac{1}{4} - \frac{1}{5} \right) = \left( \frac{3}{6} - \frac{2}{6} \right) - \left( \frac{5}{20} - \frac{4}{20} \right) = \frac{1}{6} - \frac{1}{20} = \frac{10}{60} - \frac{3}{60} = \frac{7}{60} $$ 10) $$ 3\frac{2}{9} + 4\frac{1}{6} - 1\frac{8}{27} = \frac{29}{9} + \frac{25}{6} - \frac{35}{27} = \frac{29 \cdot 6}{54} + \frac{25 \cdot 9}{54} - \frac{35 \cdot 2}{54} = \frac{174}{54} + \frac{225}{54} - \frac{70}{54} = \frac{174+225-70}{54} = \frac{329}{54} = 6\frac{5}{54} $$ 11) $$ 11 - 6\frac{2}{3} - 3\frac{5}{7} = 10\frac{21}{21} - 6\frac{14}{21} - 3\frac{15}{21} = 4\frac{7}{21} - 3\frac{15}{21} = 3\frac{28}{21} - 3\frac{15}{21} = \frac{13}{21} $$ 12) $$ \frac{27}{75} + 0,32 - \frac{7}{15} = \frac{9}{25} + \frac{32}{100} - \frac{7}{15} = \frac{9}{25} + \frac{8}{25} - \frac{7}{15} = \frac{17}{25} - \frac{7}{15} = \frac{17 \cdot 3}{75} - \frac{7 \cdot 5}{75} = \frac{51}{75} - \frac{35}{75} = \frac{16}{75} $$ 13) $$ \left( \frac{1}{3} - \frac{1}{4} \right) - \left( \frac{1}{5} - \frac{1}{6} \right) = \left( \frac{4}{12} - \frac{3}{12} \right) - \left( \frac{6}{30} - \frac{5}{30} \right) = \frac{1}{12} - \frac{1}{30} = \frac{5}{60} - \frac{2}{60} = \frac{3}{60} = \frac{1}{20} $$ 14) $$ 5\frac{7}{12} - 2\frac{4}{9} + 1\frac{5}{18} = 5\frac{21}{36} - 2\frac{16}{36} + 1\frac{10}{36} = 3\frac{5}{36} + 1\frac{10}{36} = 4\frac{15}{36} = 4\frac{5}{12} $$ 15) $$ 10 - 3\frac{4}{5} - 5\frac{2}{3} = 9\frac{5}{5} - 3\frac{4}{5} - 5\frac{2}{3} = 6\frac{1}{5} - 5\frac{2}{3} = 6\frac{3}{15} - 5\frac{10}{15} = 5\frac{18}{15} - 5\frac{10}{15} = \frac{8}{15} $$ 16) $$ \frac{3}{4} \cdot \frac{8}{9} = \frac{3 \cdot 8}{4 \cdot 9} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3} $$ 17) $$ 1\frac{7}{8} \cdot 0,4 = \frac{15}{8} \cdot \frac{4}{10} = \frac{15}{8} \cdot \frac{2}{5} = \frac{3 \cdot 1}{4 \cdot 1} = \frac{3}{4} $$ 18) $$ 1\frac{1}{3} \cdot \frac{3}{7} + \frac{4}{7} \cdot 1\frac{1}{3} = 1\frac{1}{3} \cdot \left( \frac{3}{7} + \frac{4}{7} \right) = 1\frac{1}{3} \cdot \frac{7}{7} = 1\frac{1}{3} \cdot 1 = 1\frac{1}{3} $$ 19) $$ \frac{5}{7} \cdot \frac{21}{25} = \frac{5 \cdot 21}{7 \cdot 25} = \frac{1 \cdot 3}{1 \cdot 5} = \frac{3}{5} $$ 20) $$ 2\frac{1}{12} \cdot 0,8 = \frac{25}{12} \cdot \frac{8}{10} = \frac{25}{12} \cdot \frac{4}{5} = \frac{5 \cdot 1}{3 \cdot 1} = \frac{5}{3} = 1\frac{2}{3} $$ 21) $$ 2\frac{1}{4} \cdot \frac{7}{9} + \frac{2}{9} \cdot 2\frac{1}{4} = 2\frac{1}{4} \cdot \left( \frac{7}{9} + \frac{2}{9} \right) = 2\frac{1}{4} \cdot \frac{9}{9} = 2\frac{1}{4} \cdot 1 = 2\frac{1}{4} $$