29. Найдите значение выражения: a) \(\frac{6}{5} : (\frac{9}{10} - \frac{1}{5}) = \) b) \((\frac{7}{25} + \frac{1}{5}) : \frac{3}{50} = \) в) \(1 - \frac{3}{7} \cdot \frac{15}{28} = \) r) \(\frac{34}{9} : \frac{17}{54} : \frac{5}{6} = \)

Решение:

а)

\[ \frac{6}{5} : (\frac{9}{10} - \frac{2}{10}) = \frac{6}{5} : \frac{7}{10} = \frac{6}{5} \cdot \frac{10}{7} = \frac{6 \cdot 2}{7} = \frac{12}{7} \]

б)

\[ (\frac{7}{25} + \frac{5}{25}) : \frac{3}{50} = \frac{12}{25} : \frac{3}{50} = \frac{12}{25} \cdot \frac{50}{3} = \frac{4 \cdot 2}{1} = 8 \]

в)

\[ 1 - \frac{3}{7} \cdot \frac{15}{28} = 1 - \frac{3 \cdot 15}{7 \cdot 28} = 1 - \frac{45}{196} = \frac{196 - 45}{196} = \frac{151}{196} \]

г)

\[ \frac{34}{9} : \frac{17}{54} : \frac{5}{6} = \frac{34}{9} \cdot \frac{54}{17} : \frac{5}{6} = \frac{2 \cdot 6}{1} : \frac{5}{6} = 12 : \frac{5}{6} = 12 \cdot \frac{6}{5} = \frac{72}{5} \]

Ответ: а) \(\frac{12}{7}\); б) 8; в) \(\frac{151}{196}\); г) \(\frac{72}{5}\).