105. Найдите значение выражения: а) \(\left(6\frac{1}{8}\cdot1\frac{2}{7}-2\frac{11}{14}\cdot1\frac{8}{13}\right)\cdot1\frac{3}{5}\); б) \(\left(2\frac{7}{15}+1\frac{7}{12}\right)\cdot1\frac{1}{9}-1\frac{7}{8}\); в) \(\left(4\frac{3}{10}-3\frac{3}{5}\cdot\frac{5}{12}\right)\cdot\frac{5}{6}\); г) \(\left(4\frac{1}{3}-3\frac{4}{9}\right)^2\cdot\left(2\frac{1}{4}\right)^2\); д) \(\left(5\frac{8}{15}-4\frac{7}{10}\right)\cdot2\frac{2}{3}-\frac{5}{9}\); е) \(\left(\frac{5}{24}+\frac{5}{16}\right)\left(1\frac{2}{3}-\frac{3}{5}\right)\cdot1\frac{4}{5}\).

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Фото задания: 105. Найдите значение выражения: а)…

105. Найдите значение выражения: а) \(\left(6\frac{1}{8}\cdot1\frac{2}{7}-2\frac{11}{14}\cdot1\frac{8}{13}\right)\cdot1\frac{3}{5}\); б) \(\left(2\frac{7}{15}+1\frac{7}{12}\right)\cdot1\frac{1}{9}-1\frac{7}{8}\); в) \(\left(4\frac{3}{10}-3\frac{3}{5}\cdot\frac{5}{12}\right)\cdot\frac{5}{6}\); г) \(\left(4\frac{1}{3}-3\frac{4}{9}\right)^2\cdot\left(2\frac{1}{4}\right)^2\); д) \(\left(5\frac{8}{15}-4\frac{7}{10}\right)\cdot2\frac{2}{3}-\frac{5}{9}\); е) \(\left(\frac{5}{24}+\frac{5}{16}\right)\left(1\frac{2}{3}-\frac{3}{5}\right)\cdot1\frac{4}{5}\).

Accepted Answer

а)

Переведём смешанные числа в неправильные дроби:

\(6\frac{1}{8}=\frac{49}{8}\), \(1\frac{2}{7}=\frac{9}{7}\), \(2\frac{11}{14}=\frac{39}{14}\), \(1\frac{8}{13}=\frac{21}{13}\), \(1\frac{3}{5}=\frac{8}{5}\).

\(\left(\frac{49}{8}\cdot\frac{9}{7}-\frac{39}{14}\cdot\frac{21}{13}\right)\cdot\frac{8}{5}=\left(\frac{63}{8}-\frac{9}{2}\right)\cdot\frac{8}{5}=\frac{27}{8}\cdot\frac{8}{5}=\frac{27}{5}=5\frac{2}{5}\).

б)

\(2\frac{7}{15}=\frac{37}{15}\), \(1\frac{7}{12}=\frac{19}{12}\), \(1\frac{1}{9}=\frac{10}{9}\), \(1\frac{7}{8}=\frac{15}{8}\).

\(\left(\frac{37}{15}+\frac{19}{12}\right)\cdot\frac{10}{9}-\frac{15}{8}=\frac{81}{20}\cdot\frac{10}{9}-\frac{15}{8}=\frac{9}{2}-\frac{15}{8}=\frac{21}{8}=2\frac{5}{8}\).

в)

\(4\frac{3}{10}=\frac{43}{10}\), \(3\frac{3}{5}=\frac{18}{5}\).

\(\left(\frac{43}{10}-\frac{18}{5}\cdot\frac{5}{12}\right)\cdot\frac{5}{6}=\left(\frac{43}{10}-\frac{3}{4}\right)\cdot\frac{5}{6}=\frac{71}{20}\cdot\frac{5}{6}=\frac{71}{24}=2\frac{23}{24}\).

г)

\(4\frac{1}{3}=\frac{13}{3}\), \(3\frac{4}{9}=\frac{31}{9}\), \(2\frac{1}{4}=\frac{9}{4}\).

\(\left(\frac{13}{3}-\frac{31}{9}\right)^2\cdot\left(\frac{9}{4}\right)^2=\left(\frac{8}{9}\right)^2\cdot\frac{81}{16}=\frac{64}{81}\cdot\frac{81}{16}=4\).

д)

\(5\frac{8}{15}=\frac{83}{15}\), \(4\frac{7}{10}=\frac{47}{10}\), \(2\frac{2}{3}=\frac{8}{3}\).

\(\left(\frac{83}{15}-\frac{47}{10}\right)\cdot\frac{8}{3}-\frac{5}{9}=\frac{5}{6}\cdot\frac{8}{3}-\frac{5}{9}=\frac{20}{9}-\frac{5}{9}=\frac{5}{3}\).

е)

\(1\frac{2}{3}=\frac{5}{3}\), \(1\frac{4}{5}=\frac{9}{5}\).

\(\left(\frac{5}{24}+\frac{5}{16}\right)\left(\frac{5}{3}-\frac{3}{5}\right)\cdot\frac{9}{5}=\frac{25}{48}\cdot\frac{16}{15}\cdot\frac{9}{5}=\frac{5}{9}\cdot\frac{9}{5}=1\).

Ответ: а) \(5\frac{2}{5}\); б) \(2\frac{5}{8}\); в) \(2\frac{23}{24}\); г) \(4\); д) \(\frac{5}{3}\); е) \(1\).