191. Вычислите, применив законы сложения: a) (\frac{1}{2}+\frac{13}{15})+(- \frac{13}{15}) = \frac{1}{2}+(\frac{13}{15}+(- \frac{13}{15})) = \frac{1}{2} +0 = \frac{1}{2}; б) (- \frac{2}{3}+\frac{5}{17})+(- \frac{5}{17}) = в) \frac{8}{7}+(\frac{3}{11}+(- \frac{8}{7})) = г) -\frac{3}{22}+(\frac{5}{7}+\frac{3}{22}) = д) \frac{3}{71}+(\frac{2}{17}+(- \frac{3}{71})) = е) -\frac{13}{21}+(\frac{13}{21}+\frac{1}{2}) = 192. Вычислите, применив законы умножения: a) -\frac{5}{2} \cdot (- \frac{15}{22}) \cdot (- \frac{2}{5}) = -\frac{5}{2} \cdot (- \frac{2}{5}) \cdot (- \frac{15}{22}) = 1 \cdot (- \frac{15}{22}) = - \frac{15}{22}; б) \frac{7}{3} \cdot (- \frac{2}{3}) \cdot (- \frac{3}{7}) = в) -\frac{3}{4} \cdot \frac{5}{13} \cdot (- \frac{8}{3}) = г) \frac{11}{12} \cdot (- \frac{13}{27} \cdot \frac{12}{11}) = д) (- \frac{19}{18}) \cdot (- \frac{18}{19} \cdot \frac{2}{5}) = е) \frac{14}{15} \cdot (- \frac{13}{22} \cdot \frac{15}{14}) = 193. Вычислите, применив распределительный закон: a) \frac{1}{2} \cdot (- \frac{3}{7})+ \frac{1}{2} \cdot (- \frac{4}{7}) = \frac{1}{2} \cdot (- \frac{3}{7}+(- \frac{4}{7})) = \frac{1}{2} \cdot (-1) = -\frac{1}{2}; б) \frac{3}{4} \cdot \frac{4}{17} - \frac{3}{4} \cdot \frac{21}{17} =

Ответ: смотри ниже построчное решение.

191.

а) \[(\frac{1}{2}+\frac{13}{15})+(- \frac{13}{15}) = \frac{1}{2}+(\frac{13}{15}+(- \frac{13}{15})) = \frac{1}{2} +0 = \frac{1}{2};\]

б) \[(-\frac{2}{3}+\frac{5}{17})+(-\frac{5}{17}) = -\frac{2}{3} + (\frac{5}{17} - \frac{5}{17}) = -\frac{2}{3} + 0 = -\frac{2}{3}.\]

в) \[\frac{8}{7}+(\frac{3}{11}+(-\frac{8}{7})) = (\frac{8}{7} - \frac{8}{7}) + \frac{3}{11} = 0 + \frac{3}{11} = \frac{3}{11}.\]

г) \[-\frac{3}{22}+(\frac{5}{7}+\frac{3}{22}) = (-\frac{3}{22} + \frac{3}{22}) + \frac{5}{7} = 0 + \frac{5}{7} = \frac{5}{7}.\]

д) \[\frac{3}{71}+(\frac{2}{17}+(-\frac{3}{71})) = (\frac{3}{71} - \frac{3}{71}) + \frac{2}{17} = 0 + \frac{2}{17} = \frac{2}{17}.\]

е) \[-\frac{13}{21}+(\frac{13}{21}+\frac{1}{2}) = (-\frac{13}{21} + \frac{13}{21}) + \frac{1}{2} = 0 + \frac{1}{2} = \frac{1}{2}.\]

192.

а) \[-\frac{5}{2} \cdot (-\frac{15}{22}) \cdot (-\frac{2}{5}) = -\frac{5}{2} \cdot (-\frac{2}{5}) \cdot (-\frac{15}{22}) = 1 \cdot (-\frac{15}{22}) = -\frac{15}{22}.\]

б) \[\frac{7}{3} \cdot (-\frac{2}{3}) \cdot (-\frac{3}{7}) = \frac{7}{3} \cdot (-\frac{3}{7}) \cdot (-\frac{2}{3}) = -1 \cdot (-\frac{2}{3}) = \frac{2}{3}.\]

в) \[-\frac{3}{4} \cdot \frac{5}{13} \cdot (-\frac{8}{3}) = -\frac{3}{4} \cdot (-\frac{8}{3}) \cdot \frac{5}{13} = 2 \cdot \frac{5}{13} = \frac{10}{13}.\]

г) \[\frac{11}{12} \cdot (-\frac{13}{27}) \cdot \frac{12}{11} = \frac{11}{12} \cdot \frac{12}{11} \cdot (-\frac{13}{27}) = 1 \cdot (-\frac{13}{27}) = -\frac{13}{27}.\]

д) \[(-\frac{19}{18}) \cdot (-\frac{18}{19}) \cdot \frac{2}{5} = 1 \cdot \frac{2}{5} = \frac{2}{5}.\]

е) \[\frac{14}{15} \cdot (-\frac{13}{22}) \cdot \frac{15}{14} = \frac{14}{15} \cdot \frac{15}{14} \cdot (-\frac{13}{22}) = 1 \cdot (-\frac{13}{22}) = -\frac{13}{22}.\]

193.

а) \[\frac{1}{2} \cdot (-\frac{3}{7})+ \frac{1}{2} \cdot (-\frac{4}{7}) = \frac{1}{2} \cdot (-\frac{3}{7}+(-\frac{4}{7})) = \frac{1}{2} \cdot (-1) = -\frac{1}{2}.\]

б) \[\frac{3}{4} \cdot \frac{4}{17} - \frac{3}{4} \cdot \frac{21}{17} = \frac{3}{4} \cdot (\frac{4}{17} - \frac{21}{17}) = \frac{3}{4} \cdot (\frac{-17}{17}) = \frac{3}{4} \cdot (-1) = -\frac{3}{4}.\]