1. Вычислите: a) \(\frac{5}{8} \cdot \frac{3}{7}\) b) \(\frac{7}{12} \cdot \frac{6}{11}\) в) \(\frac{28}{25} \cdot \frac{60}{49}\) г) \(\left(\frac{7}{4}\right)^2\) д) \(1,4 \cdot \frac{9}{7}\) e) \(\frac{6}{5} \cdot \frac{35}{48} \cdot \frac{18}{39}\)

Решение:

• а) \(\frac{5}{8} \cdot \frac{3}{7} = \frac{5 \cdot 3}{8 \cdot 7} = \frac{15}{56}\)
• б) \(\frac{7}{12} \cdot \frac{6}{11} = \frac{7 \cdot 6}{12 \cdot 11} = \frac{7}{2 \cdot 11} = \frac{7}{22}\)
• в) \(\frac{28}{25} \cdot \frac{60}{49} = \frac{28 \cdot 60}{25 \cdot 49} = \frac{(4 \cdot 7) \cdot (5 \cdot 12)}{(5 \cdot 5) \cdot (7 \cdot 7)} = \frac{4 \cdot 12}{5 \cdot 7} = \frac{48}{35}\)
• г) \(\left(\frac{7}{4}\right)^2 = \frac{7^2}{4^2} = \frac{49}{16}\)
• д) \(1,4 \cdot \frac{9}{7} = \frac{14}{10} \cdot \frac{9}{7} = \frac{7}{5} \cdot \frac{9}{7} = \frac{9}{5}\)
• е) \(\frac{6}{5} \cdot \frac{35}{48} \cdot \frac{18}{39} = \frac{6 \cdot 35 \cdot 18}{5 \cdot 48 \cdot 39} = \frac{6 \cdot (5 \cdot 7) \cdot (3 \cdot 6)}{(5) \cdot (6 \cdot 8) \cdot (3 \cdot 13)} = \frac{7 \cdot 6}{8 \cdot 13} = \frac{7 \cdot 3}{4 \cdot 13} = \frac{21}{52}\)

Ответ: а) rac{15}{56}; б) rac{7}{22}; в) rac{48}{35}; г) rac{49}{16}; д) rac{9}{5}; е) rac{21}{52}