Calculate the following expressions: 1) \((-9.7+7.1):(-1\frac{4}{9})\) 2) \((3\frac{1}{8}-2\frac{5}{12})\cdot(-1\frac{3}{17})\)

Решение:

1. \(\( -9.7 + 7.1 = -2.6 \)
2. \( -2.6 = -\frac{26}{10} = -\frac{13}{5} \)
3. \( 1\frac{4}{9} = \frac{9 \cdot 1 + 4}{9} = \frac{13}{9} \)
4. \( -\frac{13}{5} : (-\frac{13}{9}) = -\frac{13}{5} \cdot (-\frac{9}{13}) = \frac{9}{5} = 1\frac{4}{5} \)
5. \( 3\frac{1}{8} = \frac{3 \cdot 8 + 1}{8} = \frac{25}{8} \)
6. \( 2\frac{5}{12} = \frac{2 \cdot 12 + 5}{12} = \frac{29}{12} \)
7. \( \frac{25}{8} - \frac{29}{12} = \frac{25 \cdot 3}{24} - \frac{29 \cdot 2}{24} = \frac{75 - 58}{24} = \frac{17}{24} \)
8. \( 1\frac{3}{17} = \frac{17 \cdot 1 + 3}{17} = \frac{20}{17} \)
9. \( \frac{17}{24} \cdot (-\frac{20}{17}) = -\frac{20}{24} = -\frac{5}{6} \)

Ответ: 1) \(1\frac{4}{5}\); 2) \(-\frac{5}{6}\)