5.459 Найдите произведение: a) \(\frac{4}{7}\) · 14; б) 2\(\frac{5}{8}\); в) 10 · \(\frac{3}{8}\); г) \(\frac{3}{7}\) · 21; д) \(\frac{9}{17}\) · 0; е) \(\frac{11}{100}\) · 1; ж) \(\frac{1}{3}\) · 24; з) \(\frac{3}{31}\) · 31.

Решение:

а) \(\frac{4}{7}\) · 14 = \(\frac{4}{7}\) · \(\frac{14}{1}\) = \(\frac{4 \cdot 14}{7 \cdot 1}\) = \(\frac{4 \cdot 2 \cdot 7}{7 \cdot 1}\) = \(\frac{4 \cdot 2}{1}\) = 8

б) 2\(\frac{5}{8}\) = \(\frac{2 \cdot 8 + 5}{8}\) = \(\frac{16+5}{8}\) = \(\frac{21}{8}\)

\(\frac{21}{8}\) = \(\frac{21}{8}\) = \(\frac{3 \cdot 7}{8}\) = 2\(\frac{5}{8}\)

в) 10 · \(\frac{3}{8}\) = \(\frac{10}{1}\) · \(\frac{3}{8}\) = \(\frac{10 \cdot 3}{1 \cdot 8}\) = \(\frac{30}{8}\) = \(\frac{2 \cdot 15}{2 \cdot 4}\) = \(\frac{15}{4}\) = 3\(\frac{3}{4}\)

г) \(\frac{3}{7}\) · 21 = \(\frac{3}{7}\) · \(\frac{21}{1}\) = \(\frac{3 \cdot 21}{7 \cdot 1}\) = \(\frac{3 \cdot 3 \cdot 7}{7 \cdot 1}\) = \(\frac{3 \cdot 3}{1}\) = 9

д) \(\frac{9}{17}\) · 0 = 0

е) \(\frac{11}{100}\) · 1 = \(\frac{11}{100}\)

ж) \(\frac{1}{3}\) · 24 = \(\frac{1}{3}\) · \(\frac{24}{1}\) = \(\frac{1 \cdot 24}{3 \cdot 1}\) = \(\frac{24}{3}\) = 8

з) \(\frac{3}{31}\) · 31 = \(\frac{3}{31}\) · \(\frac{31}{1}\) = \(\frac{3 \cdot 31}{31 \cdot 1}\) = \(\frac{3}{1}\) = 3

Ответ: a) 8; б) 2\(\frac{5}{8}\); в) 3\(\frac{3}{4}\); г) 9; д) 0; e) \(\frac{11}{100}\); ж) 8; з) 3.