4.283 Выполните действия: a) (3-5) (6-9); 6) 11-2 -\frac{5}{14} \cdot \frac{7}{9}; B) 17,5 - 27.(-);

Ответ:

a)

\[\left(\frac{3}{16}-5\right) \cdot \left(6\frac{26}{29}-9\right) = \left(\frac{3}{16}-\frac{80}{16}\right) \cdot \left(\frac{174}{29}+\frac{26}{29}-\frac{261}{29}\right) = \]

\[=-\frac{77}{16} \cdot \left(-\frac{61}{29}\right) = \frac{77 \cdot 61}{16 \cdot 29} = \frac{4697}{464} = 10\frac{57}{464}\]

б)

\[11\frac{1}{5} \cdot \frac{7}{8}-2\frac{5}{14} \cdot \frac{7}{9} = \frac{56}{5} \cdot \frac{7}{8} - \frac{33}{14} \cdot \frac{7}{9} = \frac{7 \cdot 7}{5} - \frac{11}{2} \cdot \frac{1}{9} = \frac{49}{5} - \frac{11}{18} = \frac{49 \cdot 18 - 11 \cdot 5}{90} = \]

\[= \frac{882 - 55}{90} = \frac{827}{90} = 9\frac{17}{90}\]

в)

\[17,5 - 27 \cdot \left(\frac{5}{12} - \frac{3}{4}\right) = 17,5 - 27 \cdot \left(\frac{5}{12} - \frac{9}{12}\right) = 17,5 - 27 \cdot \left(-\frac{4}{12}\right) = \]

\[= 17,5 + 27 \cdot \frac{1}{3} = 17,5 + 9 = 26,5\]

Ответ:

а) \[10\frac{57}{464}\]

б) \[9\frac{17}{90}\]

в) \[26,5\]