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

Ответ: 1) -\frac{1}{3}; 2) -1.29; 3) 1; 4) -1.64

Решение:

1. \frac{13}{30}-(-\frac{1}{6})+(- \frac{7}{10})-\frac{11}{15} = \frac{13}{30} + \frac{1}{6} - \frac{7}{10} - \frac{11}{15} = \frac{13}{30} + \frac{5}{30} - \frac{21}{30} - \frac{22}{30} = \frac{13 + 5 - 21 - 22}{30} = \frac{-25}{30} = -\frac{5}{6}
2. -(\frac{1}{2})-\frac{47}{50}+(\frac{2}{5}-\frac{3}{10}) = -\frac{1}{2} - \frac{47}{50} + \frac{2}{5} - \frac{3}{10} = -\frac{25}{50} - \frac{47}{50} + \frac{20}{50} - \frac{15}{50} = \frac{-25 - 47 + 20 - 15}{50} = \frac{-67}{50} = -1.34
3. -\frac{23}{44}-\frac{1}{2}+\frac{3}{4}+\frac{31}{88}+\frac{9}{11} = -\frac{23}{44} - \frac{22}{44} + \frac{33}{44} + \frac{31}{88} + \frac{72}{88} = -\frac{46}{88} - \frac{44}{88} + \frac{66}{88} + \frac{31}{88} + \frac{72}{88} = \frac{-46 - 44 + 66 + 31 + 72}{88} = \frac{79}{88}
4. -\frac{13}{46}-\frac{3}{4}-\frac{61}{120}+\frac{11}{30}-\frac{7}{12} = -\frac{195}{690} - \frac{517.5}{690} - \frac{351.5}{690} + \frac{253}{690} - \frac{402.5}{690} = -\frac{1234}{690} = -1.79

Ответ: 1) -\frac{1}{3}; 2) -1.29; 3) 1; 4) -1.64