76. Выполните действия: а) $(\frac{4}{9}+\frac{5}{12})\cdot\frac{18}{31}$; б) $\frac{6}{25}\cdot(\frac{11}{15}-\frac{9}{20})$; в) $(4-3\frac{7}{15})\cdot\frac{5}{8}$; г) $(5-4\frac{4}{7})\cdot(7\frac{1}{6}-6\frac{5}{12})$; д) $(1\frac{1}{24}-\frac{5}{12})\cdot(4\frac{1}{8}-3\frac{5}{24})$; е) $(1\frac{2}{15}-\frac{11}{15})\cdot(5\frac{3}{18}-4\frac{1}{27})$.

Question

Вопрос: $Фото задания: 76. Выполните действия: а) $(\frac{4}{9}+\frac{5}{12})\cdot\frac{18}{31}$; б)…$ Фото задания

Accepted Answer

а) $(\frac{4}{9}+\frac{5}{12})\cdot\frac{18}{31}=(\frac{16}{36}+\frac{15}{36})\cdot\frac{18}{31}=\frac{31}{36}\cdot\frac{18}{31}=\frac{1}{2}$.
б) $\frac{6}{25}\cdot(\frac{11}{15}-\frac{9}{20})=\frac{6}{25}\cdot(\frac{44}{60}-\frac{27}{60})=\frac{6}{25}\cdot\frac{17}{60}=\frac{17}{250}$.
в) $(4-3\frac{7}{15})\cdot\frac{5}{8}=(\frac{60}{15}-\frac{52}{15})\cdot\frac{5}{8}=\frac{8}{15}\cdot\frac{5}{8}=\frac{1}{3}$.
г) $(5-4\frac{4}{7})\cdot(7\frac{1}{6}-6\frac{5}{12})=(\frac{35}{7}-\frac{32}{7})\cdot(\frac{43}{6}-\frac{77}{12})=\frac{3}{7}\cdot\frac{3}{4}=\frac{9}{28}$.
д) $(1\frac{1}{24}-\frac{5}{12})\cdot(4\frac{1}{8}-3\frac{5}{24})=(\frac{25}{24}-\frac{10}{24})\cdot(\frac{99}{24}-\frac{77}{24})=\frac{5}{8}\cdot\frac{11}{12}=\frac{55}{96}$.
е) $(1\frac{2}{15}-\frac{11}{15})\cdot(5\frac{3}{18}-4\frac{1}{27})=(\frac{17}{15}-\frac{11}{15})\cdot(\frac{33}{6}-\frac{109}{27})=\frac{2}{5}\cdot\frac{37}{54}=\frac{37}{135}$.

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