№5. Вычислите: 1) 13/30-(-7/6)+(-11/10)-11/15; 2) −(1/50)−47/2+(-3/5+7/10); 3) 23/44 −1/2+3/4+31/88+9/11; 4) −46/4−3/120+61/30−7/12.

Ответ: 1) -23/15; 2) -24,55; 3) 1; 4) -5,375

Решение:

1. \[\frac{13}{30} -\left(-\frac{7}{6}\right) + \left(-\frac{11}{10}\right) - \frac{11}{15} = \frac{13}{30} + \frac{7}{6} - \frac{11}{10} - \frac{11}{15} = \frac{13 + 35 - 33 - 22}{30} = \frac{-7}{30}\]
2. \[-\left(\frac{1}{50}\right) - \frac{47}{2} + \left(-\frac{3}{5} + \frac{7}{10}\right) = -\frac{1}{50} - \frac{47}{2} - \frac{3}{5} + \frac{7}{10} = -\frac{1}{50} - \frac{1175}{50} - \frac{30}{50} + \frac{35}{50} = \frac{-1 - 1175 - 30 + 35}{50} = \frac{-1171}{50} = -23.42\]
3. \[\frac{23}{44} - \frac{1}{2} + \frac{3}{4} + \frac{31}{88} + \frac{9}{11} = \frac{46 - 44 + 66 + 31 + 72}{88} = \frac{171}{88}\]
4. \[-\frac{46}{4} - \frac{3}{120} + \frac{61}{30} - \frac{7}{12} = -\frac{1380}{120} - \frac{3}{120} + \frac{244}{120} - \frac{70}{120} = \frac{-1380 - 3 + 244 - 70}{120} = \frac{-1209}{120} = -10.075\]

Ответ: 1) -7/30; 2) -1171/50; 3) 171/88; 4) -1209/120