1. Вычислите: a) 3/4 * 5/7; д) 4/5 * 3/7; б) 4/11 * 3/4; е) 15/8 * 5/4; в) 5/7 * 14/19; ж) 4/9 : 2; г) (3/5)^2; з) 6 : 3/5. 2. Вычислите: a) 2 * (14/15 : 2/3); б) 12/11 * 3/4 * 11/24; в) 1/2 * 2/3 * 3/4 * 4/5.

1. Вычислите:

a) \(\frac{3}{4} \cdot \frac{5}{7} = \frac{3 \cdot 5}{4 \cdot 7} = \frac{15}{28}\)

б) \(\frac{4}{11} \cdot \frac{3}{4} = \frac{4 \cdot 3}{11 \cdot 4} = \frac{12}{44} = \frac{3}{11}\)

в) \(\frac{5}{7} \cdot \frac{14}{19} = \frac{5 \cdot 14}{7 \cdot 19} = \frac{70}{133} = \frac{10}{19}\)

г) \((\frac{3}{5})^2 = \frac{3^2}{5^2} = \frac{9}{25}\)

д) \(\frac{4}{5} \cdot \frac{3}{7} = \frac{4 \cdot 3}{5 \cdot 7} = \frac{12}{35}\)

е) \(\frac{15}{8} : \frac{5}{4} = \frac{15}{8} \cdot \frac{4}{5} = \frac{15 \cdot 4}{8 \cdot 5} = \frac{60}{40} = \frac{3}{2} = 1\frac{1}{2}\)

ж) \(\frac{4}{9} : 2 = \frac{4}{9} : \frac{2}{1} = \frac{4}{9} \cdot \frac{1}{2} = \frac{4 \cdot 1}{9 \cdot 2} = \frac{4}{18} = \frac{2}{9}\)

з) \(6 : \frac{3}{5} = \frac{6}{1} : \frac{3}{5} = \frac{6}{1} \cdot \frac{5}{3} = \frac{6 \cdot 5}{1 \cdot 3} = \frac{30}{3} = 10\)

2. Вычислите:

a) \(2 \cdot (\frac{14}{15} : \frac{2}{3}) = 2 \cdot (\frac{14}{15} \cdot \frac{3}{2}) = 2 \cdot \frac{14 \cdot 3}{15 \cdot 2} = 2 \cdot \frac{42}{30} = 2 \cdot \frac{7}{5} = \frac{2 \cdot 7}{5} = \frac{14}{5} = 2\frac{4}{5}\)

б) \(\frac{12}{11} \cdot \frac{3}{4} \cdot \frac{11}{24} = \frac{12 \cdot 3 \cdot 11}{11 \cdot 4 \cdot 24} = \frac{396}{1056} = \frac{3}{8}\)

в) \(\frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5} = \frac{1 \cdot 2 \cdot 3 \cdot 4}{2 \cdot 3 \cdot 4 \cdot 5} = \frac{24}{120} = \frac{1}{5}\)