Вопрос:

Вычислите: 8/15 * (7/8 + 11/16)

Фотография

Ответ ассистента

11. $\frac{8}{15} \cdot (\frac{7}{8} + \frac{11}{16}) = \frac{8}{15} \cdot (\frac{14}{16} + \frac{11}{16}) = \frac{8}{15} \cdot \frac{25}{16} = \frac{1 \cdot 5}{3 \cdot 2} = \frac{5}{6}$ 12. $\frac{9}{10} \cdot (\frac{11}{12} - \frac{2}{9}) = \frac{9}{10} \cdot (\frac{33}{36} - \frac{8}{36}) = \frac{9}{10} \cdot \frac{25}{36} = \frac{1 \cdot 5}{2 \cdot 4} = \frac{5}{8}$ 13. $\frac{7}{39} \cdot (\frac{11}{14} - \frac{1}{6}) = \frac{7}{39} \cdot (\frac{33}{42} - \frac{7}{42}) = \frac{7}{39} \cdot \frac{26}{42} = \frac{1 \cdot 2}{3 \cdot 6} = \frac{2}{18} = \frac{1}{9}$ 14. $\frac{24}{49} : \frac{6}{7} + \frac{1}{14} = \frac{24}{49} \cdot \frac{7}{6} + \frac{1}{14} = \frac{4}{7} + \frac{1}{14} = \frac{8}{14} + \frac{1}{14} = \frac{9}{14}$ 15. $\frac{5}{6} - \frac{4}{9} : \frac{16}{21} = \frac{5}{6} - \frac{4}{9} \cdot \frac{21}{16} = \frac{5}{6} - \frac{1 \cdot 7}{3 \cdot 4} = \frac{5}{6} - \frac{7}{12} = \frac{10}{12} - \frac{7}{12} = \frac{3}{12} = \frac{1}{4}$ 16. $\frac{8}{9} : \frac{3}{8} : \frac{27}{28} = \frac{8}{9} \cdot \frac{8}{3} \cdot \frac{28}{27} = \frac{1792}{729} = 2\frac{334}{729}$ 17. $\frac{16}{21} : \frac{12}{35} - 2 = \frac{16}{21} \cdot \frac{35}{12} - 2 = \frac{4 \cdot 5}{3 \cdot 3} - 2 = \frac{20}{9} - 2 = 2\frac{2}{9} - 2 = \frac{2}{9}$ 18. $\frac{35}{24} : \frac{15}{32} - 3 = \frac{35}{24} \cdot \frac{32}{15} - 3 = \frac{7 \cdot 4}{3 \cdot 3} - 3 = \frac{28}{9} - 3 = 3\frac{1}{9} - 3 = \frac{1}{9}$ 19. $2 - \frac{15}{28} : \frac{10}{21} = 2 - \frac{15}{28} \cdot \frac{21}{10} = 2 - \frac{3 \cdot 3}{4 \cdot 2} = 2 - \frac{9}{8} = 2 - 1\frac{1}{8} = \frac{7}{8}$ 20. $18 \cdot \frac{5}{81} - \frac{2}{3} = \frac{18 \cdot 5}{81} - \frac{2}{3} = \frac{2 \cdot 5}{9} - \frac{2}{3} = \frac{10}{9} - \frac{6}{9} = \frac{4}{9}$

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