4.191 Выполните действия: a) \left(-4,75 + \left(-2\frac{1}{4}\right)\right) + \left(-\frac{5}{9} + \left(-1\frac{1}{3}\right)\right); б) (-\frac{1}{3} + \left(-2\frac{2}{15}\right)) + (-2,43 + (-2,77)).

a) \[ \left(-4,75 + \left(-2\frac{1}{4}\right)\right) + \left(-\frac{5}{9} + \left(-1\frac{1}{3}\right)\right) = \left(-4.75 - 2.25\right) + \left(-\frac{5}{9} - \frac{4}{3}\right) = -7 + \left(-\frac{5}{9} - \frac{4 \cdot 3}{3 \cdot 3}\right) = -7 + \left(-\frac{5}{9} - \frac{12}{9}\right) = -7 + \left(-\frac{17}{9}\right) = -7 - \frac{17}{9} = -7 - 1\frac{8}{9} = -8\frac{8}{9} \]

б)

\[ \left(-\frac{1}{3} + \left(-2\frac{2}{15}\right)\right) + (-2,43 + (-2,77)) = \left(-\frac{1}{3} - 2\frac{2}{15}\right) + (-2.43 - 2.77) = \left(-\frac{1 \cdot 5}{3 \cdot 5} - 2\frac{2}{15}\right) + (-5.2) = \left(-\frac{5}{15} - 2\frac{2}{15}\right) - 5.2 = -2\frac{7}{15} - 5.2 = -2\frac{7}{15} - 5\frac{2}{10} = -2\frac{7}{15} - 5\frac{1}{5} = -2\frac{7}{15} - 5\frac{1 \cdot 3}{5 \cdot 3} = -2\frac{7}{15} - 5\frac{3}{15} = -7\frac{10}{15} = -7\frac{2}{3} \]

Ответ: a) -8\frac{8}{9}; б) -7\frac{2}{3}