4.283 Выполните действия: a) ($$\frac{3}{16} - 5$$) * ($$6\frac{26}{29} - 9$$); б) $$11\frac{1}{5} * \frac{7}{8} - 2\frac{5}{14} * \frac{7}{9}$$; в) $$17,5 - 27 * (\frac{5}{12} - \frac{3}{4}$$); г) ($$-\frac{1}{3} - \frac{4}{7} - \frac{20}{21}$$) * $$\frac{7}{13} + \frac{11}{25}$$; д) ($$6\frac{1}{3} - 4,2$$) * ($$-\frac{9}{16}$$) - 4,23; е) ($$-\frac{1}{4} - 0,75 - \frac{1}{5}$$) * ($$-\frac{2}{3}$$) + 4,2.

Решение: а) ($$\frac{3}{16} - 5$$) * ($$6\frac{26}{29} - 9$$) = ($$\frac{3}{16} - \frac{80}{16}$$) * ($$\frac{6*29 + 26}{29} - \frac{9*29}{29}$$) = ($$-\frac{77}{16}$$) * ($$\frac{174 + 26 - 261}{29}$$) = ($$-\frac{77}{16}$$) * ($$-\frac{61}{29}$$) = $$\frac{77*61}{16*29}$$ = $$\frac{4697}{464}$$ = $$10\frac{57}{464}$$; б) $$11\frac{1}{5} * \frac{7}{8} - 2\frac{5}{14} * \frac{7}{9}$$ = $$\frac{56}{5} * \frac{7}{8} - \frac{33}{14} * \frac{7}{9}$$ = $$\frac{7*7}{5} - \frac{11}{2} * \frac{1}{3}$$ = $$\frac{49}{5} - \frac{11}{6}$$ = $$\frac{49*6 - 11*5}{30}$$ = $$\frac{294 - 55}{30}$$ = $$\frac{239}{30}$$ = $$7\frac{29}{30}$$; в) $$17,5 - 27 * (\frac{5}{12} - \frac{3}{4}$$) = $$17,5 - 27 * (\frac{5}{12} - \frac{9}{12}$$) = $$17,5 - 27 * (-\frac{4}{12}$$) = $$17,5 - 27 * (-\frac{1}{3}$$) = $$17,5 + 9$$ = $$26,5$$; г) ($$-\frac{1}{3} - \frac{4}{7} - \frac{20}{21}$$) * $$\frac{7}{13} + \frac{11}{25}$$ = ($$-\frac{7}{21} - \frac{12}{21} - \frac{20}{21}$$) * $$\frac{7}{13} + \frac{11}{25}$$ = ($$-\frac{39}{21}$$) * $$\frac{7}{13} + \frac{11}{25}$$ = ($$-\frac{3}{21} * 13$$) * $$\frac{7}{13} + \frac{11}{25}$$ = -1 * $$\frac{7}{7} + \frac{11}{25}$$ = $$-1 + \frac{11}{25}$$ = $$\frac{-25 + 11}{25}$$ = -$$\frac{14}{25}$$ = -0,56; д) ($$6\frac{1}{3} - 4,2$$) * ($$-\frac{9}{16}$$) - 4,23 = ($$\frac{19}{3} - \frac{42}{10}$$) * ($$-\frac{9}{16}$$) - 4,23 = ($$\frac{190 - 126}{30}$$) * ($$-\frac{9}{16}$$) - 4,23 = $$\frac{64}{30}$$ * ($$-\frac{9}{16}$$) - 4,23 = $$\frac{32}{15}$$ * ($$-\frac{9}{16}$$) - 4,23 = $$\frac{2}{5}$$ * ($$\frac{-3}{1}$$) - 4,23 = -$$\frac{6}{5}$$ - 4,23 = -1,2 - 4,23 = -5,43; е) ($$-\frac{1}{4} - 0,75 - \frac{1}{5}$$) * ($$-\frac{2}{3}$$) + 4,2 = ($$-\frac{1}{4} - \frac{3}{4} - \frac{1}{5}$$) * ($$-\frac{2}{3}$$) + 4,2 = ($$-1 - \frac{1}{5}$$) * ($$-\frac{2}{3}$$) + 4,2 = ($$-\frac{6}{5}$$) * ($$-\frac{2}{3}$$) + 4,2 = $$\frac{12}{15}$$ + 4,2 = $$\frac{4}{5}$$ + 4,2 = 0,8 + 4,2 = 5;