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

Question

Вопрос: $Фото задания: 2.276. Выполните действия: а) $\left(\frac{4}{9}+\frac{5}{12}\right)\cdot\frac{18}{31}$; б)…$ Фото задания

Accepted Answer

$\left(\frac{4}{9}+\frac{5}{12}\right)\cdot\frac{18}{31}=\left(\frac{16}{36}+\frac{15}{36}\right)\cdot\frac{18}{31}=\frac{31}{36}\cdot\frac{18}{31}=\frac{1}{2}$.
$\frac{6}{25}\cdot\left(\frac{11}{15}-\frac{9}{20}\right)=\frac{6}{25}\cdot\left(\frac{44}{60}-\frac{27}{60}\right)=\frac{6}{25}\cdot\frac{17}{60}=\frac{17}{250}$.
$\left(4-3\frac{7}{15}\right)\cdot\frac{5}{8}=\left(\frac{60}{15}-\frac{52}{15}\right)\cdot\frac{5}{8}=\frac{8}{15}\cdot\frac{5}{8}=\frac{1}{3}$.
$\left(5-4\frac{4}{7}\right)\cdot\left(7\frac{1}{6}-6\frac{5}{12}\right)=\frac{3}{7}\cdot\left(\frac{43}{6}-\frac{77}{12}\right)=\frac{3}{7}\cdot\frac{3}{4}=\frac{9}{28}$.
$\left(1\frac{1}{24}-\frac{5}{12}\right)\cdot\left(4\frac{1}{8}-3\frac{5}{24}\right)=\left(\frac{25}{24}-\frac{10}{24}\right)\cdot\left(\frac{99}{24}-\frac{77}{24}\right)=\frac{5}{8}\cdot\frac{11}{12}=\frac{55}{96}$.
$\left(1\frac{2}{15}-\frac{11}{15}\right)\cdot\left(5\frac{3}{18}-4\frac{1}{27}\right)=\left(\frac{17}{15}-\frac{11}{15}\right)\cdot\left(\frac{31}{6}-\frac{109}{27}\right)=\frac{2}{5}\cdot\frac{61}{54}=\frac{61}{135}$.

Ответ: а) $\frac{1}{2}$; б) $\frac{17}{250}$; в) $\frac{1}{3}$; г) $\frac{9}{28}$; д) $\frac{55}{96}$; е) $\frac{61}{135}$.