25. Найдите значение выражения: а) 6 6/11 · 3/4 : 2 2/5 · 2 1/5; б) 9 1/3 : 7/8 · 7/16 : 14/27; в) 5/14 + 18/35 + (1 1/4 − 5/14) : (5/12)^2; г) (7/12 − 8/15)^2 + 4/5 · (7/10 − 9/16).

Question

Вопрос:

Accepted Answer

а) \(6\frac{6}{11}\cdot\frac{3}{4}:2\frac{2}{5}\cdot2\frac{1}{5}=\frac{72}{11}\cdot\frac{3}{4}\cdot\frac{5}{12}\cdot\frac{11}{5}=\frac{9}{2}=4\frac{1}{2}\).
б) \(9\frac{1}{3}:\frac{7}{8}\cdot\frac{7}{16}:\frac{14}{27}=\frac{28}{3}\cdot\frac{8}{7}\cdot\frac{7}{16}\cdot\frac{27}{14}=\frac{2304}{49}=47\frac{1}{49}\).
в) \(\frac{5}{14}+\frac{18}{35}+\left(\frac{5}{4}-\frac{5}{14}\right):\frac{25}{144}=\frac{61}{70}+\frac{25}{28}\cdot\frac{144}{25}=\frac{61}{70}+\frac{36}{7}=\frac{421}{70}=6\frac{1}{70}\).
г) \(\left(\frac{7}{12}-\frac{8}{15}\right)^2+\frac{4}{5}\cdot\left(\frac{7}{10}-\frac{9}{16}\right)=\left(\frac{1}{20}\right)^2+\frac{4}{5}\cdot\frac{11}{80}=\frac{1}{400}+\frac{11}{100}=\frac{9}{80}\).

Ответ: а) 4 1/2; б) 47 1/49; в) 6 1/70; г) 9/80.