М) \(\frac{1}{4}\cdot4\frac{3}{4}\cdot\frac{16}{57}+\left(4\frac{1}{4}+1\frac{2}{3}\right)\cdot\frac{16}{71}+\frac{2}{27}\cdot4\frac{1}{2}\)

Question

Вопрос:

М) \(\frac{1}{4}\cdot4\frac{3}{4}\cdot\frac{16}{57}+\left(4\frac{1}{4}+1\frac{2}{3}\right)\cdot\frac{16}{71}+\frac{2}{27}\cdot4\frac{1}{2}\)

Accepted Answer

Преобразуем смешанные числа:

\[4\frac{3}{4}=\frac{19}{4},\qquad 4\frac{1}{4}=\frac{17}{4},\qquad 1\frac{2}{3}=\frac{5}{3},\qquad 4\frac{1}{2}=\frac{9}{2}.\]

\[\frac{1}{4}\cdot\frac{19}{4}\cdot\frac{16}{57}=\frac{1}{3}.\]

\[\left(\frac{17}{4}+\frac{5}{3}\right)\cdot\frac{16}{71}=\left(\frac{51}{12}+\frac{20}{12}\right)\cdot\frac{16}{71}=\frac{71}{12}\cdot\frac{16}{71}=\frac{4}{3}.\]

\[\frac{2}{27}\cdot\frac{9}{2}=\frac{1}{3}.\]

\[\frac{1}{3}+\frac{4}{3}+\frac{1}{3}=2.\]

Ответ: \(2\).