2.463 Найдите значение выражения: a) 4/5 : 1 1/3 + 2 1/7 - 1 : 1 3/8; б) 2 1/6 : (1/15 - 1/5) + (2 1/4 + 3/8) : 5 3/4; в) (1/4 + 11/14) : 14/57 - 2/3 : 1 7/6 \cdot 3/32; г) (2 1/2 : 3 1/3 + 3 1/2 : 2 1/2) ∙ 9 3/5; д) (10 5/13 - 7 23/26) : 5/6; е) (1 1/2 : 3/4) : 7/8.

• а) $$\frac{4}{5} : 1\frac{1}{3} + 2\frac{1}{7} - 1 : 1\frac{3}{8} = \frac{4}{5} : \frac{4}{3} + \frac{15}{7} - 1 : \frac{11}{8} = \frac{4}{5} \cdot \frac{3}{4} + \frac{15}{7} - 1 \cdot \frac{8}{11} = \frac{4 \cdot 3}{5 \cdot 4} + \frac{15}{7} - \frac{8}{11} = \frac{3}{5} + \frac{15}{7} - \frac{8}{11} = \frac{3 \cdot 77 + 15 \cdot 55 - 8 \cdot 35}{385} = \frac{231+825-280}{385} = \frac{776}{385} = 2\frac{6}{35}$$
• б) $$2\frac{1}{6} : (\frac{1}{15} - \frac{1}{5}) + (2\frac{1}{4} + \frac{3}{8}) : 5\frac{3}{4} = \frac{13}{6} : (\frac{1}{15} - \frac{3}{15}) + (\frac{9}{4} + \frac{3}{8}) : \frac{23}{4} = \frac{13}{6} : (\frac{-2}{15}) + (\frac{18}{8} + \frac{3}{8}) : \frac{23}{4} = \frac{13}{6} : (\frac{-2}{15}) + \frac{21}{8} : \frac{23}{4} = \frac{13}{6} \cdot (\frac{-15}{2}) + \frac{21}{8} \cdot \frac{4}{23} = -\frac{13 \cdot 15}{6 \cdot 2} + \frac{21 \cdot 4}{8 \cdot 23} = -\frac{13 \cdot 5}{2 \cdot 2} + \frac{21 \cdot 1}{2 \cdot 23} = -\frac{65}{4} + \frac{21}{46} = \frac{-65 \cdot 23 + 21 \cdot 2}{92} = \frac{-1495 + 42}{92} = \frac{-1453}{92} = -15\frac{73}{92}$$
• в) $$\left(\frac{1}{4} + \frac{11}{14}\right) : \frac{14}{57} - \frac{2}{3} : 1\frac{7}{6} \cdot \frac{3}{32} = \left(\frac{7}{28} + \frac{22}{28}\right) : \frac{14}{57} - \frac{2}{3} : \frac{13}{6} \cdot \frac{3}{32} = \frac{29}{28} : \frac{14}{57} - \frac{2}{3} \cdot \frac{6}{13} \cdot \frac{3}{32} = \frac{29}{28} \cdot \frac{57}{14} - \frac{2 \cdot 6 \cdot 3}{3 \cdot 13 \cdot 32} = \frac{29 \cdot 57}{28 \cdot 14} - \frac{1 \cdot 2 \cdot 1}{1 \cdot 13 \cdot 16} = \frac{1653}{392} - \frac{2}{208} = \frac{1653 \cdot 26 - 2 \cdot 49}{10192} = \frac{42978 - 98}{10192} = \frac{42880}{10192} = \frac{5360}{1274} = 4\frac{264}{1274}$$
• г) $$\left(2\frac{1}{2} : 3\frac{1}{3} + 3\frac{1}{2} : 2\frac{1}{2}\right) \cdot 9\frac{3}{5} = \left(\frac{5}{2} : \frac{10}{3} + \frac{7}{2} : \frac{5}{2}\right) \cdot \frac{48}{5} = \left(\frac{5}{2} \cdot \frac{3}{10} + \frac{7}{2} \cdot \frac{2}{5}\right) \cdot \frac{48}{5} = \left(\frac{5 \cdot 3}{2 \cdot 10} + \frac{7 \cdot 2}{2 \cdot 5}\right) \cdot \frac{48}{5} = \left(\frac{3}{4} + \frac{7}{5}\right) \cdot \frac{48}{5} = \left(\frac{15}{20} + \frac{28}{20}\right) \cdot \frac{48}{5} = \frac{43}{20} \cdot \frac{48}{5} = \frac{43 \cdot 48}{20 \cdot 5} = \frac{43 \cdot 12}{5 \cdot 5} = \frac{516}{25} = 20\frac{16}{25}$$
• д) $$\left(10\frac{5}{13} - 7\frac{23}{26}\right) : \frac{5}{6} = \left(\frac{135}{13} - \frac{205}{26}\right) : \frac{5}{6} = \left(\frac{270}{26} - \frac{205}{26}\right) : \frac{5}{6} = \frac{65}{26} : \frac{5}{6} = \frac{65}{26} \cdot \frac{6}{5} = \frac{65 \cdot 6}{26 \cdot 5} = \frac{13 \cdot 3}{13 \cdot 1} = 3$$
• е) $$\left(1\frac{1}{2} : \frac{3}{4}\right) : \frac{7}{8} = \left(\frac{3}{2} : \frac{3}{4}\right) : \frac{7}{8} = \left(\frac{3}{2} \cdot \frac{4}{3}\right) : \frac{7}{8} = \frac{3 \cdot 4}{2 \cdot 3} : \frac{7}{8} = 2 : \frac{7}{8} = 2 \cdot \frac{8}{7} = \frac{2 \cdot 8}{7} = \frac{16}{7} = 2\frac{2}{7}$$

Ответ: а) $$2\frac{6}{35}$$; б) $$-15\frac{73}{92}$$; в) $$4\frac{264}{1274}$$; г) $$20\frac{16}{25}$$; д) 3; е) $$2\frac{2}{7}$$