1163. Представьте в виде \(\frac{a}{b}\) (где \(a\) – целое число, а \(b\) – нату. ральное число): а) суммы: -\(\frac{3}{7}\) + \(\frac{5}{14}\); \(\frac{3}{11}\) - \(\frac{9}{22}\); \(\frac{4}{9}\) + \(\frac{5}{18}\); 0,5 – 3,1; б) произведения \(\frac{3}{8}\) \(\cdot\) (-\(\frac{4}{9}\)); -8\(\frac{1}{3}\) \(\cdot\) 0,9; -2\(\frac{1}{5}\) \(\cdot\) \(\frac{10}{11}\); -1\(\frac{5}{12}\) \(\cdot\) \(\frac{1}{17}\); в) частные \(\frac{2}{3}\) : (-\(\frac{7}{9}\)); 0,27 : 0,9; -0,26 : (-0,13); -\(\frac{3}{5}\) : 0,6.

Ответ:

1. Суммы:

   • \[-\frac{3}{7} + \frac{5}{14} = -\frac{3 \cdot 2}{7 \cdot 2} + \frac{5}{14} = -\frac{6}{14} + \frac{5}{14} = \frac{-6+5}{14} = \frac{-1}{14} = -\frac{1}{14}\]

   • \[\frac{3}{11} - \frac{9}{22} = \frac{3 \cdot 2}{11 \cdot 2} - \frac{9}{22} = \frac{6}{22} - \frac{9}{22} = \frac{6-9}{22} = \frac{-3}{22} = -\frac{3}{22}\]

   • \[\frac{4}{9} + \frac{5}{18} = \frac{4 \cdot 2}{9 \cdot 2} + \frac{5}{18} = \frac{8}{18} + \frac{5}{18} = \frac{8+5}{18} = \frac{13}{18}\]

   • \[0.5 - 3.1 = \frac{5}{10} - \frac{31}{10} = \frac{5-31}{10} = \frac{-26}{10} = -\frac{13}{5}\]

2. Произведения:

   • \[\frac{3}{8} \cdot (-\frac{4}{9}) = -\frac{3 \cdot 4}{8 \cdot 9} = -\frac{12}{72} = -\frac{1}{6}\]

   • \[-8\frac{1}{3} \cdot 0.9 = -\frac{25}{3} \cdot \frac{9}{10} = -\frac{25 \cdot 9}{3 \cdot 10} = -\frac{225}{30} = -\frac{15}{2} = -7\frac{1}{2}\]

   • \[-2\frac{1}{5} \cdot \frac{10}{11} = -\frac{11}{5} \cdot \frac{10}{11} = -\frac{11 \cdot 10}{5 \cdot 11} = -\frac{110}{55} = -2\]

   • \[-1\frac{5}{12} \cdot \frac{1}{17} = -\frac{17}{12} \cdot \frac{1}{17} = -\frac{17 \cdot 1}{12 \cdot 17} = -\frac{17}{204} = -\frac{1}{12}\]

3. Частные:

   • \[\frac{2}{3} : (-\frac{7}{9}) = \frac{2}{3} \cdot (-\frac{9}{7}) = -\frac{2 \cdot 9}{3 \cdot 7} = -\frac{18}{21} = -\frac{6}{7}\]

   • \[0.27 : 0.9 = \frac{27}{100} : \frac{9}{10} = \frac{27}{100} \cdot \frac{10}{9} = \frac{27 \cdot 10}{100 \cdot 9} = \frac{270}{900} = \frac{3}{10} = 0.3\]

   • \[-0.26 : (-0.13) = \frac{-26}{100} : \frac{-13}{100} = \frac{-26}{100} \cdot \frac{100}{-13} = \frac{-26 \cdot 100}{100 \cdot -13} = \frac{-2600}{-1300} = 2\]

   • \[-\frac{3}{5} : 0.6 = -\frac{3}{5} : \frac{6}{10} = -\frac{3}{5} \cdot \frac{10}{6} = -\frac{3 \cdot 10}{5 \cdot 6} = -\frac{30}{30} = -1\]

Ответ: