1.008. Вычислите: \(\left(\dfrac{3\frac13+2{,}5}{2{,}5-1\frac13}\cdot\dfrac{4{,}6-2\frac13}{4{,}6+2\frac13}\cdot5{,}2\right):\left(\dfrac{0{,}05}{\frac17-0{,}125}+5{,}7\right)\).

Question

1.008. Вычислите: \(\left(\dfrac{3\frac13+2{,}5}{2{,}5-1\frac13}\cdot\dfrac{4{,}6-2\frac13}{4{,}6+2\frac13}\cdot5{,}2\right):\left(\dfrac{0{,}05}{\frac17-0{,}125}+5{,}7\right)\).

Accepted Answer

\(\dfrac{3\frac13+2{,}5}{2{,}5-1\frac13}=\frac{35/6}{7/6}=5\).

\(\dfrac{4{,}6-2\frac13}{4{,}6+2\frac13}=\frac{68/15}{104/15}=\frac{17}{26}\), поэтому первая скобка равна \(5\cdot\frac{17}{26}\cdot\frac{26}{5}=17\).

\(\frac{0{,}05}{\frac17-0{,}125}+5{,}7=\frac{1/20}{1/56}+\frac{57}{10}=\frac{14}{5}+\frac{57}{10}=\frac{85}{10}=\frac{17}{2}\).

\(17:\frac{17}{2}=2\).

Ответ: \(2\).