Вычислите: $\frac{5}{6} - \frac{3}{22}$

1. Вычислите: 1) $$\frac{5}{6} - \frac{3}{22} = \frac{5 \cdot 11}{6 \cdot 11} - \frac{3 \cdot 3}{22 \cdot 3} = \frac{55}{66} - \frac{9}{66} = \frac{55 - 9}{66} = \frac{46}{66} = \frac{23}{33}$$ 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) $$\left(\frac{1}{6} + \frac{5}{18}\right) - \left(\frac{1}{18} + \frac{1}{24}\right) = \left(\frac{3}{18} + \frac{5}{18}\right) - \left(\frac{4}{72} + \frac{3}{72}\right) = \frac{8}{18} - \frac{7}{72} = \frac{4}{9} - \frac{7}{72} = \frac{4 \cdot 8}{9 \cdot 8} - \frac{7}{72} = \frac{32}{72} - \frac{7}{72} = \frac{25}{72}$$ 6) $$4 - 2\frac{4}{7} = 4 - \frac{18}{7} = \frac{28}{7} - \frac{18}{7} = \frac{10}{7} = 1\frac{3}{7}$$ 7) $$2,5 + 1\frac{2}{3} - 3\frac{1}{6} = \frac{5}{2} + \frac{5}{3} - \frac{19}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{5 \cdot 2}{3 \cdot 2} - \frac{19}{6} = \frac{15}{6} + \frac{10}{6} - \frac{19}{6} = \frac{15 + 10 - 19}{6} = \frac{6}{6} = 1$$ 8) $$0,36 - \frac{9}{75} + \frac{2}{15} = \frac{36}{100} - \frac{9}{75} + \frac{2}{15} = \frac{9}{25} - \frac{9}{75} + \frac{2}{15} = \frac{9 \cdot 3}{25 \cdot 3} - \frac{9}{75} + \frac{2 \cdot 5}{15 \cdot 5} = \frac{27}{75} - \frac{9}{75} + \frac{10}{75} = \frac{27 - 9 + 10}{75} = \frac{28}{75}$$ 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) $$3\frac{2}{9} + 4\frac{1}{6} - 1\frac{8}{27} = \frac{29}{9} + \frac{25}{6} - \frac{35}{27} = \frac{29 \cdot 6}{9 \cdot 6} + \frac{25 \cdot 9}{6 \cdot 9} - \frac{35 \cdot 2}{27 \cdot 2} = \frac{174}{54} + \frac{225}{54} - \frac{70}{54} = \frac{174 + 225 - 70}{54} = \frac{329}{54} = 6\frac{5}{54}$$ 11) $$11 - 6\frac{2}{3} - 3\frac{5}{7} = 11 - \frac{20}{3} - \frac{26}{7} = \frac{11 \cdot 21}{1 \cdot 21} - \frac{20 \cdot 7}{3 \cdot 7} - \frac{26 \cdot 3}{7 \cdot 3} = \frac{231}{21} - \frac{140}{21} - \frac{78}{21} = \frac{231 - 140 - 78}{21} = \frac{13}{21}$$ 12) $$\frac{27}{75} + 0,32 - \frac{7}{15} = \frac{9}{25} + \frac{32}{100} - \frac{7}{15} = \frac{9}{25} + \frac{8}{25} - \frac{7}{15} = \frac{17}{25} - \frac{7}{15} = \frac{17 \cdot 3}{25 \cdot 3} - \frac{7 \cdot 5}{15 \cdot 5} = \frac{51}{75} - \frac{35}{75} = \frac{16}{75}$$ 13) $$\left(\frac{1}{3} - \frac{1}{4}\right) - \left(\frac{1}{5} - \frac{1}{6}\right) = \left(\frac{4}{12} - \frac{3}{12}\right) - \left(\frac{6}{30} - \frac{5}{30}\right) = \frac{1}{12} - \frac{1}{30} = \frac{5}{60} - \frac{2}{60} = \frac{3}{60} = \frac{1}{20}$$