2.463 Найдите значение выражения: a) 4 : 1 + 1 - 1 : 1 ; б) 2 : ( + ) + ( : 5 ); в) :1 + 2 - 1 : ; г) (2 :3+3:2). :9; д) (10 -7):6; e) ((1 ):):8.

a) $$4\frac{1}{5} \div 1\frac{1}{3} + 1\frac{3}{7} - 1\frac{1}{8} = \frac{21}{5} \div \frac{4}{3} + \frac{10}{7} - \frac{9}{8} = \frac{21}{5} \cdot \frac{3}{4} + \frac{10}{7} - \frac{9}{8} = \frac{63}{20} + \frac{10}{7} - \frac{9}{8} = \frac{63 \cdot 14 + 10 \cdot 40 - 9 \cdot 35}{280} = \frac{882 + 400 - 315}{280} = \frac{967}{280} = 3\frac{127}{280} \approx 3.454$$

б) $$2\frac{1}{6} \div (\frac{1}{15} + \frac{1}{21}) + (2\frac{1}{3} + \frac{3}{4}) \div 5\frac{3}{5} = \frac{13}{6} \div (\frac{7 + 5}{105}) + (\frac{7}{3} + \frac{3}{4}) \div \frac{28}{5} = \frac{13}{6} \div \frac{12}{105} + \frac{28 + 9}{12} \div \frac{28}{5} = \frac{13}{6} \cdot \frac{105}{12} + \frac{37}{12} \cdot \frac{5}{28} = \frac{13 \cdot 35}{2 \cdot 12} + \frac{37 \cdot 5}{12 \cdot 28} = \frac{455}{24} + \frac{185}{336} = \frac{455 \cdot 14 + 185}{336} = \frac{6370 + 185}{336} = \frac{6555}{336} = 19\frac{171}{336} = 19\frac{57}{112} \approx 19.509$$

в) $$\frac{1}{4} + 11\frac{14}{57} \div 2\frac{1}{6} - 3\frac{7}{32} = \frac{1}{4} + \frac{641}{57} \div \frac{13}{6} - \frac{103}{32} = \frac{1}{4} + \frac{641}{57} \cdot \frac{6}{13} - \frac{103}{32} = \frac{1}{4} + \frac{641 \cdot 2}{19 \cdot 13} - \frac{103}{32} = \frac{1}{4} + \frac{1282}{247} - \frac{103}{32} = \frac{1}{4} + 5\frac{37}{247} - 3\frac{7}{32} = \frac{247 \cdot 8 + 1282 \cdot 64 - 103 \cdot 247}{8 \cdot 247 \cdot 4} = \frac{1976 + 82048 - 25441}{1976} = \frac{58583}{7904} \approx 7.412$$

г) $$(2\frac{1}{2} \div 3 + 3\frac{1}{3} \div 2\frac{1}{2}) \cdot \frac{3}{5} = (\frac{5}{2} \div 3 + \frac{10}{3} \div \frac{5}{2}) \cdot \frac{3}{5} = (\frac{5}{2} \cdot \frac{1}{3} + \frac{10}{3} \cdot \frac{2}{5}) \cdot \frac{3}{5} = (\frac{5}{6} + \frac{20}{15}) \cdot \frac{3}{5} = (\frac{5}{6} + \frac{4}{3}) \cdot \frac{3}{5} = (\frac{5 + 8}{6}) \cdot \frac{3}{5} = \frac{13}{6} \cdot \frac{3}{5} = \frac{13}{2} \cdot \frac{1}{5} = \frac{13}{10} = 1.3$$

д) $$(10\frac{5}{13} - 7\frac{23}{26}) \div 6\frac{2}{5} = (\frac{135}{13} - \frac{205}{26}) \div \frac{32}{5} = (\frac{270 - 205}{26}) \div \frac{32}{5} = \frac{65}{26} \cdot \frac{5}{32} = \frac{5}{2} \cdot \frac{5}{32} = \frac{25}{64} \approx 0.391$$

e) $$((\frac{11}{2})^3 \div \frac{3}{4}) \div 8\frac{7}{8} = (\frac{1331}{8} \cdot \frac{4}{3}) \div \frac{71}{8} = (\frac{1331}{2} \cdot \frac{1}{3}) \div \frac{71}{8} = \frac{1331}{6} \cdot \frac{8}{71} = \frac{1331}{3} \cdot \frac{4}{71} = \frac{5324}{213} = 24\frac{212}{213} \approx 25.00$$

Ответ: а) 3.454; б) 19.509; в) 7.412; г) 1.3; д) 0.391; e) 25.00