5.462 Вычислите: а) \(\frac{2}{3}\) ч. 6; б) \(\frac{7}{12}\) ч. 8; в) \(\frac{5}{24}\) ч. 24; г) \(\frac{4}{15}\) ч 10; д) \(\frac{5}{6}\) ч. 12.

Решение:

а) \(\frac{2}{3}\) · 6 = \(\frac{2}{3}\) · \(\frac{6}{1}\) = \(\frac{2 \cdot 6}{3 \cdot 1}\) = \(\frac{2 \cdot 2 \cdot 3}{3 \cdot 1}\) = \(\frac{2 \cdot 2}{1}\) = 4

б) \(\frac{7}{12}\) · 8 = \(\frac{7}{12}\) · \(\frac{8}{1}\) = \(\frac{7 \cdot 8}{12 \cdot 1}\) = \(\frac{7 \cdot 2 \cdot 4}{3 \cdot 4 \cdot 1}\) = \(\frac{7 \cdot 2}{3}\) = \(\frac{14}{3}\) = 4\(\frac{2}{3}\)

в) \(\frac{5}{24}\) · 24 = \(\frac{5}{24}\) · \(\frac{24}{1}\) = \(\frac{5 \cdot 24}{24 \cdot 1}\) = \(\frac{5}{1}\) = 5

г) \(\frac{4}{15}\) · 10 = \(\frac{4}{15}\) · \(\frac{10}{1}\) = \(\frac{4 \cdot 10}{15 \cdot 1}\) = \(\frac{4 \cdot 2 \cdot 5}{3 \cdot 5 \cdot 1}\) = \(\frac{4 \cdot 2}{3}\) = \(\frac{8}{3}\) = 2\(\frac{2}{3}\)

д) \(\frac{5}{6}\) · 12 = \(\frac{5}{6}\) · \(\frac{12}{1}\) = \(\frac{5 \cdot 12}{6 \cdot 1}\) = \(\frac{5 \cdot 2 \cdot 6}{6 \cdot 1}\) = \(\frac{5 \cdot 2}{1}\) = 10

Ответ: а) 4; б) 4\(\frac{2}{3}\); в) 5; г) 2\(\frac{2}{3}\); д) 10.