Вариант 4. 1. Найдите значение выражения: a) \(4\frac{3}{13}:1\frac{7}{26}\) б) \(\frac{2\frac{4}{7}}{3}\) в) \(\frac{3.2}{19.2}\) г) \(1\frac{35}{3\frac{3}{4}}\)

Решение:

1. \(4\frac{3}{13}:1\frac{7}{26} = \frac{55}{13} : \frac{33}{26} = \frac{55}{13} \cdot \frac{26}{33} = \frac{55 \cdot 26}{13 \cdot 33} = \frac{5 \cdot 11 \cdot 2 \cdot 13}{13 \cdot 3 \cdot 11} = \frac{5 \cdot 2}{3} = \frac{10}{3} = 3\frac{1}{3}\)
2. \(\frac{2\frac{4}{7}}{3} = \frac{\frac{18}{7}}{3} = \frac{18}{7} \cdot \frac{1}{3} = \frac{18}{21} = \frac{6}{7}\)
3. \(\frac{3.2}{19.2} = \frac{32}{192} = \frac{1}{6}\)
4. \(1\frac{35}{3\frac{3}{4}} = \frac{1 \frac{35}{4}}{ \frac{15}{4} } = \frac{\frac{39}{4}}{ \frac{15}{4} } = \frac{39}{4} \cdot \frac{4}{15} = \frac{39}{15} = \frac{13}{5} = 2\frac{3}{5}\)

Ответ: а) \(3\frac{1}{3}\), б) \(\frac{6}{7}\), в) \(\frac{1}{6}\), г) \(2\frac{3}{5}\).