4.180 Выполните сложение:

Краткое пояснение:

Пошаговое решение:

1. a) \( -1\frac{1}{2} + \left(-2\frac{1}{2}\right) = -\left(1\frac{1}{2} + 2\frac{1}{2}\right) = -\left(\frac{3}{2} + \frac{5}{2}\right) = -\frac{8}{2} = -4 \)
2. б) \( -4\frac{9}{14} + \left(-1\frac{1}{7}\right) = -\left(4\frac{9}{14} + 1\frac{1}{7}\right) = -\left(4\frac{9}{14} + 1\frac{2}{14}\right) = -\left(\frac{58}{14} + \frac{16}{14}\right) = -\frac{74}{14} = -\frac{37}{7} = -5\frac{2}{7} \)
3. в) \( -5\frac{7}{12} + \left(-2\frac{3}{4}\right) = -\left(5\frac{7}{12} + 2\frac{3}{4}\right) = -\left(5\frac{7}{12} + 2\frac{9}{12}\right) = -\left(\frac{79}{12} + \frac{33}{12}\right) = -\frac{112}{12} = -\frac{28}{3} = -9\frac{1}{3} \)
4. г) \( -5\frac{12}{17} + \left(-\frac{15}{24}\right) + \left(-1\frac{3}{8}\right) + \left(-\frac{5}{17}\right) = -\left(5\frac{12}{17} + \frac{15}{24} + 1\frac{3}{8} + \frac{5}{17}\right) \). Приведем к общему знаменателю. \( = -\left(5\frac{12+5}{17} + \frac{15}{24} + 1\frac{3}{8}\right) = -\left(5\frac{17}{17} + \frac{15}{24} + 1\frac{3}{8}\right) = -\left(6 + \frac{15}{24} + 1\frac{9}{24}\right) = -\left(6 + \frac{24}{24} + 1\right) = -(6+1+1) = -8 \)
5. д) \( -\frac{9}{28} + \left(-4\frac{9}{35}\right) + \left(-2\frac{5}{28}\right) + \left(-\frac{12}{35}\right) = -\left(\frac{9}{28} + 4\frac{9}{35} + 2\frac{5}{28} + \frac{12}{35}\right) = -\left(\left(\frac{9}{28} + 2\frac{5}{28}\right) + \left(4\frac{9}{35} + \frac{12}{35}\right)\right) = -\left(2\frac{14}{28} + 4\frac{21}{35}\right) = -\left(2\frac{1}{2} + 4\frac{3}{5}\right) = -\left(\frac{5}{2} + \frac{23}{5}\right) = -\left(\frac{25}{10} + \frac{46}{10}\right) = -\frac{71}{10} = -7\frac{1}{10} \)