1. Вычислите: a) \(\frac{3}{7} \cdot \frac{2}{5}\); б) \(\frac{6}{16} \cdot \frac{8}{9}\); в) \(\frac{3}{10} \cdot 3\); г) \(\frac{2}{9} \cdot 6\); д) \(1\frac{1}{3} \cdot 4\); e) \(1\frac{3}{4} \cdot 1\frac{2}{5}\); ж) \((\frac{4}{7})^2\); з) \((\frac{1}{3})^3\)

Ответ:

• а) \(\frac{3}{7} \cdot \frac{2}{5} = \frac{3 \cdot 2}{7 \cdot 5} = \frac{6}{35}\)
• б) \(\frac{6}{16} \cdot \frac{8}{9} = \frac{6 \cdot 8}{16 \cdot 9} = \frac{48}{144} = \frac{1}{3}\)
• в) \(\frac{3}{10} \cdot 3 = \frac{3 \cdot 3}{10} = \frac{9}{10}\)
• г) \(\frac{2}{9} \cdot 6 = \frac{2 \cdot 6}{9} = \frac{12}{9} = \frac{4}{3} = 1\frac{1}{3}\)
• д) \(1\frac{1}{3} \cdot 4 = \frac{4}{3} \cdot 4 = \frac{4 \cdot 4}{3} = \frac{16}{3} = 5\frac{1}{3}\)
• е) \(1\frac{3}{4} \cdot 1\frac{2}{5} = \frac{7}{4} \cdot \frac{7}{5} = \frac{7 \cdot 7}{4 \cdot 5} = \frac{49}{20} = 2\frac{9}{20}\)
• ж) \((\frac{4}{7})^2 = \frac{4}{7} \cdot \frac{4}{7} = \frac{4 \cdot 4}{7 \cdot 7} = \frac{16}{49}\)
• з) \((\frac{1}{3})^3 = \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} = \frac{1 \cdot 1 \cdot 1}{3 \cdot 3 \cdot 3} = \frac{1}{27}\)

Ответ: a) \(\frac{6}{35}\); б) \(\frac{1}{3}\); в) \(\frac{9}{10}\); г) \(1\frac{1}{3}\); д) \(5\frac{1}{3}\); e) \(2\frac{9}{20}\); ж) \(\frac{16}{49}\); з) \(\frac{1}{27}\)