1) $\frac{5}{6}+\frac{7}{33}+\frac{9}{22}$; 2) $\frac{6}{11}:\frac{5}{8}\cdot\frac{9}{40}+0{,}01$; 3) $\left(1-\frac{1}{11}+\frac{1}{121}\right):\left(\frac{8}{20}+\frac{4}{12}\right)$.

Question

$Фото задания: 1) $\frac{5}{6}+\frac{7}{33}+\frac{9}{22}$; 2) $\frac{6}{11}:\frac{5}{8}\cdot\frac{9}{40}+0{,}01$; 3)…$ Фото задания

Accepted Answer

Приведём дроби к знаменателю 66:
\[\frac{5}{6}+\frac{7}{33}+\frac{9}{22}=\frac{55}{66}+\frac{14}{66}+\frac{27}{66}=\frac{96}{66}=\frac{16}{11}.\]
Заменим десятичную дробь: $0{,}01=\frac{1}{100}$.
\[\frac{6}{11}:\frac{5}{8}\cdot\frac{9}{40}+0{,}01=\frac{6}{11}\cdot\frac{8}{5}\cdot\frac{9}{40}+\frac{1}{100}=\frac{54}{275}+\frac{1}{100}=\frac{227}{1100}.\]
\[1-\frac{1}{11}+\frac{1}{121}=\frac{121-11+1}{121}=\frac{111}{121},\quad \frac{8}{20}+\frac{4}{12}=\frac{2}{5}+\frac{1}{3}=\frac{11}{15}.\]
Тогда
\[\frac{111}{121}:\frac{11}{15}=\frac{111}{121}\cdot\frac{15}{11}=\frac{1665}{1331}.\]

Ответ: 1) $\frac{16}{11}$; 2) $\frac{227}{1100}$; 3) $\frac{1665}{1331}$.

1) \(\frac{5}{6}+\frac{7}{33}+\frac{9}{22}\); 2) \(\frac{6}{11}:\frac{5}{8}\cdot\frac{9}{40}+0{,}01\); 3) \(\left(1-\frac{1}{11}+\frac{1}{121}\right):\left(\frac{8}{20}+\frac{4}{12}\right)\).