Вычислите, используя законы умножения:
а) $(23 * \frac{11}{25}) * \frac{5}{43} + (20 * \frac{11}{25}) * \frac{5}{43}$;
б) $(47 * \frac{1}{26}) * \frac{13}{27} - (20 * \frac{1}{26}) * \frac{13}{27}$;
в) $(\frac{1}{2} * \frac{3}{4}) * (\frac{2}{3} * \frac{4}{5}) * (\frac{5}{6} * \frac{7}{8}) * (\frac{6}{7} * \frac{8}{9})$;
г) $(\frac{2}{3} * \frac{4}{5}) * (\frac{3}{4} * \frac{5}{6}) * (\frac{6}{7} * \frac{8}{9}) * (\frac{7}{8} * \frac{9}{10})$.
$(23 * \frac{11}{25}) * \frac{5}{43} + (20 * \frac{11}{25}) * \frac{5}{43} = 23 * (\frac{11}{25} * \frac{5}{43}) + 20 * (\frac{11}{25} * \frac{5}{43}) = (\frac{11}{25} * \frac{5}{43}) * (23 + 20) = (\frac{11}{25} * \frac{5}{43}) * 43 = \frac{11}{25} * (\frac{5}{43} * 43) = \frac{11}{25} * 5 = \frac{11}{5}$
$(47 * \frac{1}{26}) * \frac{13}{27} - (20 * \frac{1}{26}) * \frac{13}{27} = 47 * (\frac{1}{26} * \frac{13}{27}) - 20 * (\frac{1}{26} * \frac{13}{27}) = (47 - 20) * (\frac{1}{26} * \frac{13}{27}) = 27 * (\frac{1}{26} * \frac{13}{27}) = (27 * \frac{13}{27}) * \frac{1}{26} = 13 * \frac{1}{26} = \frac{1}{2}$
$(\frac{1}{2} * \frac{3}{4}) * (\frac{2}{3} * \frac{4}{5}) * (\frac{5}{6} * \frac{7}{8}) * (\frac{6}{7} * \frac{8}{9}) = (\frac{1}{2} * \frac{2}{3}) * (\frac{3}{4} * \frac{4}{5}) * (\frac{5}{6} * \frac{6}{7}) * (\frac{7}{8} * \frac{8}{9}) = (\frac{1}{3} * \frac{3}{5}) * (\frac{5}{7} * \frac{7}{9}) = \frac{1}{5} * \frac{5}{9} = \frac{1}{9}$
$(\frac{2}{3} * \frac{4}{5}) * (\frac{3}{4} * \frac{5}{6}) * (\frac{6}{7} * \frac{8}{9}) * (\frac{7}{8} * \frac{9}{10}) = (\frac{2}{3} * \frac{3}{4}) * (\frac{4}{5} * \frac{5}{6}) * (\frac{6}{7} * \frac{7}{8}) * (\frac{8}{9} * \frac{9}{10}) = (\frac{2}{4}) * (\frac{6}{8} * \frac{8}{10}) = \frac{2}{6} * \frac{6}{10} = \frac{1}{1} * \frac{1}{5} = \frac{1}{5}$
Пожауйста, оцените решение
