Вычислите: $\frac{7}{39} \cdot \left( \frac{11}{14} - \frac{1}{6} \right)$

13. $$ \frac{7}{39} \cdot \left( \frac{11}{14} - \frac{1}{6} \right) = \frac{7}{39} \cdot \left( \frac{11 \cdot 3}{14 \cdot 3} - \frac{1 \cdot 7}{6 \cdot 7} \right) = \frac{7}{39} \cdot \left( \frac{33}{42} - \frac{7}{42} \right) = \frac{7}{39} \cdot \frac{33 - 7}{42} = \frac{7}{39} \cdot \frac{26}{42} = \frac{7 \cdot 26}{39 \cdot 42} = \frac{7 \cdot (2 \cdot 13)}{(3 \cdot 13) \cdot (6 \cdot 7)} = \frac{2 \cdot 13}{3 \cdot 13 \cdot 6} = \frac{2}{3 \cdot 6} = \frac{2}{18} = \frac{1}{9} $$ **Ответ: $\frac{1}{9}$** 14. $$ \frac{24}{49} : \frac{6}{7} + \frac{1}{14} = \frac{24}{49} \cdot \frac{7}{6} + \frac{1}{14} = \frac{24 \cdot 7}{49 \cdot 6} + \frac{1}{14} = \frac{(4 \cdot 6) \cdot 7}{(7 \cdot 7) \cdot 6} + \frac{1}{14} = \frac{4}{7} + \frac{1}{14} = \frac{4 \cdot 2}{7 \cdot 2} + \frac{1}{14} = \frac{8}{14} + \frac{1}{14} = \frac{8 + 1}{14} = \frac{9}{14} $$ **Ответ: $\frac{9}{14}$** 15. $$ \frac{5}{6} - \frac{4}{9} : \frac{16}{21} = \frac{5}{6} - \frac{4}{9} \cdot \frac{21}{16} = \frac{5}{6} - \frac{4 \cdot 21}{9 \cdot 16} = \frac{5}{6} - \frac{4 \cdot (3 \cdot 7)}{(3 \cdot 3) \cdot (4 \cdot 4)} = \frac{5}{6} - \frac{7}{3 \cdot 4} = \frac{5}{6} - \frac{7}{12} = \frac{5 \cdot 2}{6 \cdot 2} - \frac{7}{12} = \frac{10}{12} - \frac{7}{12} = \frac{10 - 7}{12} = \frac{3}{12} = \frac{1}{4} $$ **Ответ: $\frac{1}{4}$** 16. $$ \frac{8}{9} - \frac{3}{8} : \frac{27}{28} = \frac{8}{9} - \frac{3}{8} \cdot \frac{28}{27} = \frac{8}{9} - \frac{3 \cdot 28}{8 \cdot 27} = \frac{8}{9} - \frac{3 \cdot (4 \cdot 7)}{(2 \cdot 4) \cdot (9 \cdot 3)} = \frac{8}{9} - \frac{7}{2 \cdot 9} = \frac{8}{9} - \frac{7}{18} = \frac{8 \cdot 2}{9 \cdot 2} - \frac{7}{18} = \frac{16}{18} - \frac{7}{18} = \frac{16 - 7}{18} = \frac{9}{18} = \frac{1}{2} $$ **Ответ: $\frac{1}{2}$** 17. $$ \frac{16}{21} : \frac{12}{35} - 2 = \frac{16}{21} \cdot \frac{35}{12} - 2 = \frac{16 \cdot 35}{21 \cdot 12} - 2 = \frac{(4 \cdot 4) \cdot (5 \cdot 7)}{(3 \cdot 7) \cdot (3 \cdot 4)} - 2 = \frac{4 \cdot 5}{3 \cdot 3} - 2 = \frac{20}{9} - 2 = \frac{20}{9} - \frac{2 \cdot 9}{9} = \frac{20}{9} - \frac{18}{9} = \frac{20 - 18}{9} = \frac{2}{9} $$ **Ответ: $\frac{2}{9}$** 18. $$ \frac{35}{24} : \frac{15}{32} - 3 = \frac{35}{24} \cdot \frac{32}{15} - 3 = \frac{35 \cdot 32}{24 \cdot 15} - 3 = \frac{(7 \cdot 5) \cdot (4 \cdot 8)}{(3 \cdot 8) \cdot (3 \cdot 5)} - 3 = \frac{7 \cdot 4}{3 \cdot 3} - 3 = \frac{28}{9} - 3 = \frac{28}{9} - \frac{3 \cdot 9}{9} = \frac{28}{9} - \frac{27}{9} = \frac{28 - 27}{9} = \frac{1}{9} $$ **Ответ: $\frac{1}{9}$**