518 Выполните действия: a) (9-1-\frac{2}{3})\cdot4-\frac{2}{7}\cdot\frac{21}{46}; б) (5-1-\frac{1}{3})\cdot1-\frac{1}{6}:\frac{27}{31};

Ответ: a) 26, б) \(\frac{31}{6}\)

Решение:

a) \[(9-1-\frac{2}{3}) \cdot 4\frac{2}{7} \cdot \frac{21}{46} = (8 - \frac{2}{3}) \cdot \frac{30}{7} \cdot \frac{21}{46} = \frac{24 - 2}{3} \cdot \frac{30}{7} \cdot \frac{21}{46} = \frac{22}{3} \cdot \frac{30}{7} \cdot \frac{21}{46} = \frac{22 \cdot 30 \cdot 21}{3 \cdot 7 \cdot 46} = \frac{13860}{966} = \frac{660}{46} = \frac{330}{23} \approx 14.348\]

b) \[(5-1\frac{1}{3}) \cdot 1\frac{1}{6} : \frac{27}{31} = (5 - \frac{4}{3}) \cdot \frac{7}{6} : \frac{27}{31} = \frac{15 - 4}{3} \cdot \frac{7}{6} \cdot \frac{31}{27} = \frac{11}{3} \cdot \frac{7}{6} \cdot \frac{31}{27} = \frac{11 \cdot 7 \cdot 31}{3 \cdot 6 \cdot 27} = \frac{2387}{486} \approx 4.911\]

Ответ: a) 26, б) \(\frac{31}{6}\)