4) \(\frac{3{,}75:1\frac{1}{2}+(1{,}5:3\frac{3}{4})\cdot2\frac{1}{2}+(1\frac{1}{7}-\frac{23}{49}):\frac{22}{147}}{2:3\frac{1}{6}+(3\frac{1}{4}:13):\frac{2}{3}-(2\frac{5}{18}-\frac{17}{36})\cdot\frac{18}{65}}\)

Question

Вопрос:

4) \(\frac{3{,}75:1\frac{1}{2}+(1{,}5:3\frac{3}{4})\cdot2\frac{1}{2}+(1\frac{1}{7}-\frac{23}{49}):\frac{22}{147}}{2:3\frac{1}{6}+(3\frac{1}{4}:13):\frac{2}{3}-(2\frac{5}{18}-\frac{17}{36})\cdot\frac{18}{65}}\)

Accepted Answer

Числитель: \(3{,}75:1\frac{1}{2}=\frac{15}{4}:\frac{3}{2}=\frac{5}{2}\).

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

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

Числитель: \(\frac{5}{2}+\frac{1}{2}+\frac{9}{2}=\frac{15}{2}\).

Знаменатель: \(2:3\frac{1}{6}=2:\frac{19}{6}=\frac{12}{19}\).

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

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

Знаменатель: \(\frac{12}{19}+\frac{3}{8}-\frac{1}{2}=\frac{12}{19}-\frac{1}{8}=\frac{77}{152}\).

\(\frac{15}{2}:\frac{77}{152}=\frac{15}{2}\cdot\frac{152}{77}=\frac{570}{77}=7\frac{31}{77}\).

Ответ: \(\frac{570}{77}=7\frac{31}{77}\).