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

1. $$ \frac{5}{6} - \frac{3}{22} = \frac{5 \cdot 11}{6 \cdot 11} - \frac{3 \cdot 3}{22 \cdot 3} = \frac{55}{66} - \frac{9}{66} = \frac{46}{66} = \frac{23}{33} $$ **Ответ:** $\frac{23}{33}$ 2. $$ 0,75 - \left(\frac{3}{16} + \frac{1}{24}\right) = \frac{3}{4} - \left(\frac{3 \cdot 3}{16 \cdot 3} + \frac{1 \cdot 2}{24 \cdot 2}\right) = \frac{3}{4} - \left(\frac{9}{48} + \frac{2}{48}\right) = \frac{3}{4} - \frac{11}{48} = \frac{3 \cdot 12}{4 \cdot 12} - \frac{11}{48} = \frac{36}{48} - \frac{11}{48} = \frac{25}{48} $$ **Ответ:** $\frac{25}{48}$ 3. $$ \frac{9}{16} + \left(0,25 - \frac{5}{24}\right) = \frac{9}{16} + \left(\frac{1}{4} - \frac{5}{24}\right) = \frac{9}{16} + \left(\frac{1 \cdot 6}{4 \cdot 6} - \frac{5}{24}\right) = \frac{9}{16} + \left(\frac{6}{24} - \frac{5}{24}\right) = \frac{9}{16} + \frac{1}{24} = \frac{9 \cdot 3}{16 \cdot 3} + \frac{1 \cdot 2}{24 \cdot 2} = \frac{27}{48} + \frac{2}{48} = \frac{29}{48} $$ **Ответ:** $\frac{29}{48}$ 4. $$ 0,88 - \frac{2}{15} = \frac{88}{100} - \frac{2}{15} = \frac{22}{25} - \frac{2}{15} = \frac{22 \cdot 3}{25 \cdot 3} - \frac{2 \cdot 5}{15 \cdot 5} = \frac{66}{75} - \frac{10}{75} = \frac{56}{75} $$ **Ответ:** $\frac{56}{75}$ 5. $$ \left(\frac{1}{6} + \frac{5}{18}\right) - \left(\frac{1}{18} + \frac{1}{24}\right) = \left(\frac{3}{18} + \frac{5}{18}\right) - \left(\frac{4}{72} + \frac{3}{72}\right) = \frac{8}{18} - \frac{7}{72} = \frac{4}{9} - \frac{7}{72} = \frac{4 \cdot 8}{9 \cdot 8} - \frac{7}{72} = \frac{32}{72} - \frac{7}{72} = \frac{25}{72} $$ **Ответ:** $\frac{25}{72}$ 6. $$ 4 - 2\frac{4}{7} = 4 - \frac{18}{7} = \frac{28}{7} - \frac{18}{7} = \frac{10}{7} = 1\frac{3}{7} $$ **Ответ:** $1\frac{3}{7}$ 7. $$ 2,5 + 1\frac{2}{3} - 3\frac{1}{6} = 2\frac{1}{2} + 1\frac{2}{3} - 3\frac{1}{6} = \frac{5}{2} + \frac{5}{3} - \frac{19}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{5 \cdot 2}{3 \cdot 2} - \frac{19}{6} = \frac{15}{6} + \frac{10}{6} - \frac{19}{6} = \frac{15+10-19}{6} = \frac{6}{6} = 1 $$ **Ответ:** $1$ 8. $$ 0,36 - \frac{9}{75} + \frac{2}{15} = \frac{36}{100} - \frac{9}{75} + \frac{2}{15} = \frac{9}{25} - \frac{9}{75} + \frac{2}{15} = \frac{9 \cdot 3}{25 \cdot 3} - \frac{9}{75} + \frac{2 \cdot 5}{15 \cdot 5} = \frac{27}{75} - \frac{9}{75} + \frac{10}{75} = \frac{27-9+10}{75} = \frac{28}{75} $$ **Ответ:** $\frac{28}{75}$ 9. $$ \left(\frac{1}{2} - \frac{1}{3}\right) - \left(\frac{1}{4} - \frac{1}{5}\right) = \left(\frac{3}{6} - \frac{2}{6}\right) - \left(\frac{5}{20} - \frac{4}{20}\right) = \frac{1}{6} - \frac{1}{20} = \frac{1 \cdot 10}{6 \cdot 10} - \frac{1 \cdot 3}{20 \cdot 3} = \frac{10}{60} - \frac{3}{60} = \frac{7}{60} $$ **Ответ:** $\frac{7}{60}$ 10. $$ 3\frac{2}{9} + 4\frac{1}{6} - 1\frac{8}{27} = \frac{29}{9} + \frac{25}{6} - \frac{35}{27} = \frac{29 \cdot 6}{9 \cdot 6} + \frac{25 \cdot 9}{6 \cdot 9} - \frac{35 \cdot 2}{27 \cdot 2} = \frac{174}{54} + \frac{225}{54} - \frac{70}{54} = \frac{174+225-70}{54} = \frac{329}{54} = 6\frac{5}{54} $$ **Ответ:** $6\frac{5}{54}$ 11. $$ 11 - 6\frac{2}{3} - 3\frac{5}{7} = 11 - \frac{20}{3} - \frac{26}{7} = \frac{11 \cdot 21}{21} - \frac{20 \cdot 7}{3 \cdot 7} - \frac{26 \cdot 3}{7 \cdot 3} = \frac{231}{21} - \frac{140}{21} - \frac{78}{21} = \frac{231 - 140 - 78}{21} = \frac{13}{21} $$ **Ответ:** $\frac{13}{21}$ 12. $$ \frac{27}{75} + 0,32 - \frac{7}{15} = \frac{9}{25} + \frac{32}{100} - \frac{7}{15} = \frac{9}{25} + \frac{8}{25} - \frac{7}{15} = \frac{17}{25} - \frac{7}{15} = \frac{17 \cdot 3}{25 \cdot 3} - \frac{7 \cdot 5}{15 \cdot 5} = \frac{51}{75} - \frac{35}{75} = \frac{16}{75} $$ **Ответ:** $\frac{16}{75}$ 13. $$ \left(\frac{1}{3} - \frac{1}{4}\right) - \left(\frac{1}{5} - \frac{1}{6}\right) = \left(\frac{4}{12} - \frac{3}{12}\right) - \left(\frac{6}{30} - \frac{5}{30}\right) = \frac{1}{12} - \frac{1}{30} = \frac{1 \cdot 5}{12 \cdot 5} - \frac{1 \cdot 2}{30 \cdot 2} = \frac{5}{60} - \frac{2}{60} = \frac{3}{60} = \frac{1}{20} $$ **Ответ:** $\frac{1}{20}$ 14. $$ 5\frac{7}{12} - 2\frac{4}{9} + 1\frac{5}{18} = \frac{67}{12} - \frac{22}{9} + \frac{23}{18} = \frac{67 \cdot 3}{12 \cdot 3} - \frac{22 \cdot 4}{9 \cdot 4} + \frac{23 \cdot 2}{18 \cdot 2} = \frac{201}{36} - \frac{88}{36} + \frac{46}{36} = \frac{201-88+46}{36} = \frac{159}{36} = \frac{53}{12} = 4\frac{5}{12} $$ **Ответ:** $4\frac{5}{12}$ 15. $$ 10 - 3\frac{4}{5} - 5\frac{2}{3} = 10 - \frac{19}{5} - \frac{17}{3} = \frac{10 \cdot 15}{15} - \frac{19 \cdot 3}{5 \cdot 3} - \frac{17 \cdot 5}{3 \cdot 5} = \frac{150}{15} - \frac{57}{15} - \frac{85}{15} = \frac{150-57-85}{15} = \frac{8}{15} $$ **Ответ:** $\frac{8}{15}$ 16. $$ \frac{3}{4} \cdot \frac{8}{9} = \frac{3 \cdot 8}{4 \cdot 9} = \frac{24}{36} = \frac{2}{3} $$ **Ответ:** $\frac{2}{3}$ 17. $$ 1\frac{7}{8} \cdot 0,4 = \frac{15}{8} \cdot \frac{4}{10} = \frac{15}{8} \cdot \frac{2}{5} = \frac{15 \cdot 2}{8 \cdot 5} = \frac{30}{40} = \frac{3}{4} $$ **Ответ:** $\frac{3}{4}$ 18. $$ 1\frac{1}{3} \cdot \frac{3}{7} + \frac{4}{7} \cdot 1\frac{1}{3} = 1\frac{1}{3} \cdot \left(\frac{3}{7} + \frac{4}{7}\right) = 1\frac{1}{3} \cdot \frac{7}{7} = 1\frac{1}{3} \cdot 1 = 1\frac{1}{3} $$ **Ответ:** $1\frac{1}{3}$ 19. $$ \frac{5}{7} \cdot \frac{21}{25} = \frac{5 \cdot 21}{7 \cdot 25} = \frac{1 \cdot 3}{1 \cdot 5} = \frac{3}{5} $$ **Ответ:** $\frac{3}{5}$ 20. $$ 2\frac{1}{12} \cdot 0,8 = \frac{25}{12} \cdot \frac{8}{10} = \frac{25}{12} \cdot \frac{4}{5} = \frac{25 \cdot 4}{12 \cdot 5} = \frac{5 \cdot 1}{3 \cdot 1} = \frac{5}{3} = 1\frac{2}{3} $$ **Ответ:** $1\frac{2}{3}$ 21. $$ 2\frac{1}{4} \cdot \frac{7}{9} + 2\frac{1}{4} \cdot 2\frac{1}{4} = 2\frac{1}{4} \cdot \left(\frac{7}{9} + 2\frac{1}{4}\right) = \frac{9}{4} \cdot \left(\frac{7}{9} + \frac{9}{4}\right) = \frac{9}{4} \cdot \left(\frac{7 \cdot 4}{9 \cdot 4} + \frac{9 \cdot 9}{4 \cdot 9}\right) = \frac{9}{4} \cdot \left(\frac{28}{36} + \frac{81}{36}\right) = \frac{9}{4} \cdot \frac{109}{36} = \frac{1 \cdot 109}{4 \cdot 4} = \frac{109}{16} = 6\frac{13}{16} $$ **Ответ:** $6\frac{13}{16}$