4.190 Выполните сложение: a) $$\frac{4}{7} + (-\frac{2}{7})$$; б) $$\frac{3}{7} + (-\frac{3}{4})$$; в) $$\frac{5}{9} + (-\frac{7}{8})$$; г) $$-2\frac{2}{9} + (-5\frac{5}{18})$$; д) $$-3\frac{3}{5} + (-5,9)$$; e) $$-2\frac{1}{6} + (-4,75)$$.

Решение:

a) $$\frac{4}{7} + (-\frac{2}{7}) = \frac{4}{7} - \frac{2}{7} = \frac{4-2}{7} = \frac{2}{7}$$.

б) $$\frac{3}{7} + (-\frac{3}{4}) = \frac{3}{7} - \frac{3}{4} = \frac{3 \cdot 4}{7 \cdot 4} - \frac{3 \cdot 7}{4 \cdot 7} = \frac{12}{28} - \frac{21}{28} = \frac{12-21}{28} = -\frac{9}{28}$$.

в) $$\frac{5}{9} + (-\frac{7}{8}) = \frac{5}{9} - \frac{7}{8} = \frac{5 \cdot 8}{9 \cdot 8} - \frac{7 \cdot 9}{8 \cdot 9} = \frac{40}{72} - \frac{63}{72} = \frac{40 - 63}{72} = -\frac{23}{72}$$.

г) $$-2\frac{2}{9} + (-5\frac{5}{18}) = -2\frac{2}{9} - 5\frac{5}{18} = -2\frac{2 \cdot 2}{9 \cdot 2} - 5\frac{5}{18} = -2\frac{4}{18} - 5\frac{5}{18} = -7\frac{9}{18} = -7\frac{1}{2}$$.

д) $$-3\frac{3}{5} + (-5,9) = -3\frac{3}{5} - 5,9 = -3,6 - 5,9 = -9,5$$.

e) $$-2\frac{1}{6} + (-4,75) = -2\frac{1}{6} - 4,75 = -2\frac{1}{6} - 4\frac{75}{100} = -2\frac{1}{6} - 4\frac{3}{4} = -2\frac{1 \cdot 2}{6 \cdot 2} - 4\frac{3 \cdot 3}{4 \cdot 3} = -2\frac{2}{12} - 4\frac{9}{12} = -6\frac{11}{12}$$.

Ответ: a) $$\frac{2}{7}$$; б) $$\frac{-9}{28}$$; в) $$\frac{-23}{72}$$; г) $$-7\frac{1}{2}$$; д) -9,5; e) $$-6\frac{11}{12}$$.