6. Вычислите: a) \((6 - 4 \frac{1}{5}) : 1 \frac{1}{3}\) б) \(3 \frac{1}{3} \cdot 10 - 8 \frac{2}{4} : \frac{7}{4}\)

Решение:

a) \((6 - 4 \frac{1}{5}) : 1 \frac{1}{3} = (6 - \frac{4 \cdot 5 + 1}{5}) : \frac{1 \cdot 3 + 1}{3} = (6 - \frac{21}{5}) : \frac{4}{3} = (\frac{6 \cdot 5}{5} - \frac{21}{5}) : \frac{4}{3} = (\frac{30}{5} - \frac{21}{5}) : \frac{4}{3} = \frac{9}{5} : \frac{4}{3} = \frac{9}{5} \cdot \frac{3}{4} = \frac{9 \cdot 3}{5 \cdot 4} = \frac{27}{20} = 1 \frac{7}{20}\)

б) \(3 \frac{1}{3} \cdot 10 - 8 \frac{2}{4} : \frac{7}{4} = \frac{3 \cdot 3 + 1}{3} \cdot 10 - \frac{8 \cdot 4 + 2}{4} : \frac{7}{4} = \frac{10}{3} \cdot 10 - \frac{34}{4} : \frac{7}{4} = \frac{100}{3} - \frac{34}{4} \cdot \frac{4}{7} = \frac{100}{3} - \frac{34}{7} = \frac{100 \cdot 7}{3 \cdot 7} - \frac{34 \cdot 3}{7 \cdot 3} = \frac{700}{21} - \frac{102}{21} = \frac{700 - 102}{21} = \frac{598}{21} = 28 \frac{10}{21}\)

Ответ: a) \(1 \frac{7}{20}\); б) \(28 \frac{10}{21}\)