1. (6 баллов) Выполните действия: a) \(\frac{5}{7} \cdot \frac{3}{11}\); б) \(\frac{5}{6}:\frac{5}{18}\); в) \(\frac{12}{25}\cdot\frac{6}{5}\); г) \(6:\frac{12}{13}\); c) \(4:\frac{6}{13}\)

Ответ:

1. а) \(\frac{5}{7} \cdot \frac{3}{11} = \frac{5 \cdot 3}{7 \cdot 11} = \frac{15}{77}\)
2. б) \(\frac{5}{6}:\frac{5}{18} = \frac{5}{6} \cdot \frac{18}{5} = \frac{5 \cdot 18}{6 \cdot 5} = \frac{90}{30} = 3\)
3. в) \(\frac{12}{25}\cdot\frac{6}{5} = \frac{12 \cdot 6}{25 \cdot 5} = \frac{72}{125}\)
4. г) \(6:\frac{12}{13} = \frac{6}{1} \cdot \frac{13}{12} = \frac{6 \cdot 13}{1 \cdot 12} = \frac{78}{12} = \frac{13}{2} = 6\frac{1}{2}\)
5. с) \(4:\frac{6}{13} = \frac{4}{1} \cdot \frac{13}{6} = \frac{4 \cdot 13}{1 \cdot 6} = \frac{52}{6} = \frac{26}{3} = 8\frac{2}{3}\)

Ответ: а) \(\frac{15}{77}\); б) 3; в) \(\frac{72}{125}\); г) \(6\frac{1}{2}\); c) \(8\frac{2}{3}\)