Вычислите примеры

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. $$0,75 - \left(\frac{3}{16} + \frac{1}{24}\right)$$ 1) $$\frac{3}{16} + \frac{1}{24} = \frac{3 \cdot 3}{16 \cdot 3} + \frac{1 \cdot 2}{24 \cdot 2} = \frac{9}{48} + \frac{2}{48} = \frac{11}{48}$$ 2) $$0,75 - \frac{11}{48} = \frac{3}{4} - \frac{11}{48} = \frac{3 \cdot 12}{4 \cdot 12} - \frac{11}{48} = \frac{36}{48} - \frac{11}{48} = \frac{25}{48}$$ 3. $$\frac{9}{16} + \left(0,25 - \frac{5}{24}\right)$$ 1) $$0,25 - \frac{5}{24} = \frac{1}{4} - \frac{5}{24} = \frac{1 \cdot 6}{4 \cdot 6} - \frac{5}{24} = \frac{6}{24} - \frac{5}{24} = \frac{1}{24}$$ 2) $$\frac{9}{16} + \frac{1}{24} = \frac{9 \cdot 3}{16 \cdot 3} + \frac{1 \cdot 2}{24 \cdot 2} = \frac{27}{48} + \frac{2}{48} = \frac{29}{48}$$ 4. $$0,88 - \frac{2}{15}$$ $$0,88 - \frac{2}{15} = \frac{88}{100} - \frac{2}{15} = \frac{22}{25} - \frac{2}{15} = \frac{22 \cdot 3}{25 \cdot 3} - \frac{2 \cdot 5}{15 \cdot 5} = \frac{66}{75} - \frac{10}{75} = \frac{56}{75}$$ 5. $$\left(\frac{1}{6} + \frac{5}{18}\right) - \left(\frac{1}{18} + \frac{1}{24}\right)$$ 1) $$\frac{1}{6} + \frac{5}{18} = \frac{1 \cdot 3}{6 \cdot 3} + \frac{5}{18} = \frac{3}{18} + \frac{5}{18} = \frac{8}{18} = \frac{4}{9}$$ 2) $$\frac{1}{18} + \frac{1}{24} = \frac{1 \cdot 4}{18 \cdot 4} + \frac{1 \cdot 3}{24 \cdot 3} = \frac{4}{72} + \frac{3}{72} = \frac{7}{72}$$ 3) $$\frac{4}{9} - \frac{7}{72} = \frac{4 \cdot 8}{9 \cdot 8} - \frac{7}{72} = \frac{32}{72} - \frac{7}{72} = \frac{25}{72}$$ 6. $$4 - 2\frac{4}{7}$$ $$4 - 2\frac{4}{7} = \frac{4}{1} - \frac{18}{7} = \frac{28}{7} - \frac{18}{7} = \frac{10}{7} = 1\frac{3}{7}$$ 7. $$2,5 + 1\frac{2}{3} - 3\frac{1}{6}$$ 1) $$2,5 + 1\frac{2}{3} = 2\frac{1}{2} + 1\frac{2}{3} = \frac{5}{2} + \frac{5}{3} = \frac{15}{6} + \frac{10}{6} = \frac{25}{6}$$ 2) $$\frac{25}{6} - 3\frac{1}{6} = \frac{25}{6} - \frac{19}{6} = \frac{6}{6} = 1$$ 8. $$0,36 - \frac{9}{75} + \frac{2}{15}$$ 1) $$0,36 - \frac{9}{75} = \frac{36}{100} - \frac{9}{75} = \frac{9}{25} - \frac{3}{25} = \frac{6}{25}$$ 2) $$\frac{6}{25} + \frac{2}{15} = \frac{6 \cdot 3}{25 \cdot 3} + \frac{2 \cdot 5}{15 \cdot 5} = \frac{18}{75} + \frac{10}{75} = \frac{28}{75}$$ 9. $$\left(\frac{1}{2} - \frac{1}{3}\right) - \left(\frac{1}{4} - \frac{1}{5}\right)$$ 1) $$\frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}$$ 2) $$\frac{1}{4} - \frac{1}{5} = \frac{5}{20} - \frac{4}{20} = \frac{1}{20}$$ 3) $$\frac{1}{6} - \frac{1}{20} = \frac{10}{60} - \frac{3}{60} = \frac{7}{60}$$ 10. $$3\frac{2}{9} + 4\frac{1}{6} - 1\frac{8}{27}$$ 1) $$3\frac{2}{9} + 4\frac{1}{6} = \frac{29}{9} + \frac{25}{6} = \frac{58}{18} + \frac{75}{18} = \frac{133}{18}$$ 2) $$\frac{133}{18} - 1\frac{8}{27} = \frac{133}{18} - \frac{35}{27} = \frac{133 \cdot 3}{18 \cdot 3} - \frac{35 \cdot 2}{27 \cdot 2} = \frac{399}{54} - \frac{70}{54} = \frac{329}{54} = 6\frac{5}{54}$$ 11. $$11 - 6\frac{2}{3} - 3\frac{5}{7}$$ 1) $$11 - 6\frac{2}{3} = \frac{11}{1} - \frac{20}{3} = \frac{33}{3} - \frac{20}{3} = \frac{13}{3}$$ 2) $$\frac{13}{3} - 3\frac{5}{7} = \frac{13}{3} - \frac{26}{7} = \frac{91}{21} - \frac{78}{21} = \frac{13}{21}$$ 12. $$\frac{27}{75} + 0,32 - \frac{7}{15}$$ 1) $$\frac{27}{75} + 0,32 = \frac{9}{25} + \frac{32}{100} = \frac{9}{25} + \frac{8}{25} = \frac{17}{25}$$ 2) $$\frac{17}{25} - \frac{7}{15} = \frac{17 \cdot 3}{25 \cdot 3} - \frac{7 \cdot 5}{15 \cdot 5} = \frac{51}{75} - \frac{35}{75} = \frac{16}{75}$$ 13. $$\left(\frac{1}{3} - \frac{1}{4}\right) - \left(\frac{1}{5} - \frac{1}{6}\right)$$ 1) $$\frac{1}{3} - \frac{1}{4} = \frac{4}{12} - \frac{3}{12} = \frac{1}{12}$$ 2) $$\frac{1}{5} - \frac{1}{6} = \frac{6}{30} - \frac{5}{30} = \frac{1}{30}$$ 3) $$\frac{1}{12} - \frac{1}{30} = \frac{5}{60} - \frac{2}{60} = \frac{3}{60} = \frac{1}{20}$$ 14. $$5\frac{7}{12} - 2\frac{4}{9} + 1\frac{5}{18}$$ 1) $$5\frac{7}{12} - 2\frac{4}{9} = \frac{67}{12} - \frac{22}{9} = \frac{67 \cdot 3}{12 \cdot 3} - \frac{22 \cdot 4}{9 \cdot 4} = \frac{201}{36} - \frac{88}{36} = \frac{113}{36}$$ 2) $$\frac{113}{36} + 1\frac{5}{18} = \frac{113}{36} + \frac{23}{18} = \frac{113}{36} + \frac{23 \cdot 2}{18 \cdot 2} = \frac{113}{36} + \frac{46}{36} = \frac{159}{36} = 4\frac{15}{36} = 4\frac{5}{12}$$ 15. $$10 - 3\frac{4}{5} - 5\frac{2}{3}$$ 1) $$10 - 3\frac{4}{5} = \frac{10}{1} - \frac{19}{5} = \frac{50}{5} - \frac{19}{5} = \frac{31}{5}$$ 2) $$\frac{31}{5} - 5\frac{2}{3} = \frac{31}{5} - \frac{17}{3} = \frac{93}{15} - \frac{85}{15} = \frac{8}{15}$$ 16. $$\frac{3}{4} \cdot \frac{8}{9}$$ $$\frac{3}{4} \cdot \frac{8}{9} = \frac{3 \cdot 8}{4 \cdot 9} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3}$$ 17. $$1\frac{7}{8} \cdot 0,4$$ $$1\frac{7}{8} \cdot 0,4 = \frac{15}{8} \cdot \frac{4}{10} = \frac{15}{8} \cdot \frac{2}{5} = \frac{3 \cdot 1}{4 \cdot 1} = \frac{3}{4}$$ 18. $$1\frac{1}{3} \cdot \frac{3}{7} + \frac{4}{7} \cdot 1\frac{1}{3}$$ $$1\frac{1}{3} \cdot \frac{3}{7} + \frac{4}{7} \cdot 1\frac{1}{3} = 1\frac{1}{3} \cdot \left(\frac{3}{7} + \frac{4}{7}\right) = 1\frac{1}{3} \cdot \frac{7}{7} = 1\frac{1}{3} \cdot 1 = 1\frac{1}{3}$$ 19. $$\frac{5}{7} \cdot \frac{21}{25}$$ $$\frac{5}{7} \cdot \frac{21}{25} = \frac{5 \cdot 21}{7 \cdot 25} = \frac{1 \cdot 3}{1 \cdot 5} = \frac{3}{5}$$ 20. $$2\frac{1}{12} \cdot 0,8$$ $$2\frac{1}{12} \cdot 0,8 = \frac{25}{12} \cdot \frac{8}{10} = \frac{25}{12} \cdot \frac{4}{5} = \frac{5 \cdot 1}{3 \cdot 1} = \frac{5}{3} = 1\frac{2}{3}$$ 21. $$2\frac{1}{4} \cdot \frac{7}{9} + \frac{2}{9} \cdot 2\frac{1}{4}$$ $$2\frac{1}{4} \cdot \frac{7}{9} + \frac{2}{9} \cdot 2\frac{1}{4} = 2\frac{1}{4} \cdot \left(\frac{7}{9} + \frac{2}{9}\right) = 2\frac{1}{4} \cdot \frac{9}{9} = 2\frac{1}{4} \cdot 1 = 2\frac{1}{4}$$