1.014. Вычислите: \(\dfrac{(4,5\cdot1\frac{2}{3}-6,75)\cdot\frac{2}{3}}{(3\frac{1}{3}-0,3+3\frac{1}{3}\cdot\frac{1}{8}):2\frac{2}{3}}+\dfrac{1\frac{4}{11}-0,22:0,3-0,96}{(0,2-\frac{3}{40})\cdot1,6}\).

Question

Вопрос:

Accepted Answer

Вычислим первую дробь:

\[4.5\cdot1\frac{2}{3}-6.75=4.5\cdot\frac{5}{3}-6.75=7.5-6.75=0.75.\]

\[0.75\cdot\frac{2}{3}=0.5.\]

\[3\frac{1}{3}-0.3+3\frac{1}{3}\cdot\frac{1}{8}=\frac{10}{3}-\frac{3}{10}+\frac{5}{12}=\frac{69}{20}.\]

\[\frac{69}{20}:2\frac{2}{3}=\frac{69}{20}:\frac{8}{3}=\frac{207}{160}.\]

\[\frac{0.5}{207/160}=\frac{80}{207}.\]

Вычислим вторую дробь:

\[1\frac{4}{11}-0.22:0.3-0.96=\frac{15}{11}-\frac{11}{15}-\frac{24}{25}=-\frac{272}{825}.\]

\[(0.2-\frac{3}{40})\cdot1.6=\left(\frac{1}{5}-\frac{3}{40}\right)\cdot\frac{8}{5}=\frac{1}{5}.\]

\[-\frac{272}{825}:\frac{1}{5}=-\frac{272}{165}.\]

\[\frac{80}{207}-\frac{272}{165}=\frac{400-1632}{1035}=-\frac{1232}{1035}.\]

Ответ: \(-\frac{1232}{1035}\).