Вычислить: \(\dfrac{3.75:1\frac{1}{2}+(1.5:3\frac{3}{4})\cdot2\frac{1}{2}+(1\frac{1}{7}-\dfrac{23}{49}):\dfrac{22}{147}}{2:3\frac{1}{5}+(3\frac{1}{4}:13):\dfrac{2}{3}-(2\frac{5}{18}-\dfrac{17}{36})\cdot\dfrac{18}{65}}\).

Question

Вычислить: \(\dfrac{3.75:1\frac{1}{2}+(1.5:3\frac{3}{4})\cdot2\frac{1}{2}+(1\frac{1}{7}-\dfrac{23}{49}):\dfrac{22}{147}}{2:3\frac{1}{5}+(3\frac{1}{4}:13):\dfrac{2}{3}-(2\frac{5}{18}-\dfrac{17}{36})\cdot\dfrac{18}{65}}\).

Accepted Answer

Числитель:

\(3.75:1\frac{1}{2}=\dfrac{15}{4}:\dfrac{3}{2}=\dfrac{5}{2}\).

\((1.5:3\frac{3}{4})\cdot2\frac{1}{2}=\left(\dfrac{3}{2}:\dfrac{15}{4}\right)\cdot\dfrac{5}{2}=\dfrac{2}{5}\cdot\dfrac{5}{2}=1\).

\(\left(1\frac{1}{7}-\dfrac{23}{49}\right):\dfrac{22}{147}=\left(\dfrac{8}{7}-\dfrac{23}{49}\right):\dfrac{22}{147}=\dfrac{33}{49}\cdot\dfrac{147}{22}=\dfrac{9}{2}\).

Числитель: \(\dfrac{5}{2}+1+\dfrac{9}{2}=8\).

Знаменатель:

\(2:3\frac{1}{5}=2:\dfrac{16}{5}=\dfrac{5}{8}\).

\((3\frac{1}{4}:13):\dfrac{2}{3}=\left(\dfrac{13}{4}:13\right):\dfrac{2}{3}=\dfrac{1}{4}\cdot\dfrac{3}{2}=\dfrac{3}{8}\).

\(\left(2\frac{5}{18}-\dfrac{17}{36}\right)\cdot\dfrac{18}{65}=\left(\dfrac{41}{18}-\dfrac{17}{36}\right)\cdot\dfrac{18}{65}=\dfrac{65}{36}\cdot\dfrac{18}{65}=\dfrac{1}{2}\).

Знаменатель: \(\dfrac{5}{8}+\dfrac{3}{8}-\dfrac{1}{2}=\dfrac{1}{2}\).

\(8:\dfrac{1}{2}=16\).

Ответ: \(16\).