Вариант 3. 1. Найдите значение выражения: a) \(4\frac{1}{11}:1\frac{3}{22}\) б) \(\frac{2\frac{2}{5}}{1\frac{1}{15}}\) в) \(\frac{4.2}{25.2}\) г) \(1\frac{56}{2\frac{2}{6}}\)

Решение:

1. \(4\frac{1}{11}:1\frac{3}{22} = \frac{45}{11} : \frac{25}{22} = \frac{45}{11} \cdot \frac{22}{25} = \frac{45 \cdot 2 \cdot 11}{11 \cdot 25} = \frac{45 \cdot 2}{25} = \frac{9 \cdot 5 \cdot 2}{5 \cdot 5} = \frac{18}{5} = 3\frac{3}{5}\)
2. \(\frac{2\frac{2}{5}}{1\frac{1}{15}} = \frac{\frac{12}{5}}{\frac{16}{15}} = \frac{12}{5} \cdot \frac{15}{16} = \frac{12 \cdot 15}{5 \cdot 16} = \frac{3 \cdot 4 \cdot 3 \cdot 5}{5 \cdot 4 \cdot 4} = \frac{9}{4} = 2\frac{1}{4}\)
3. \(\frac{4.2}{25.2} = \frac{42}{252} = \frac{1}{6}\)
4. \(1\frac{56}{2\frac{2}{6}} = \frac{1 \frac{56}{6}}{ \frac{14}{6} } = \frac{1 \frac{28}{3}}{ \frac{7}{3} } = \frac{\frac{31}{3}}{ \frac{7}{3} } = \frac{31}{3} \cdot \frac{3}{7} = \frac{31}{7} = 4\frac{3}{7}\)

Ответ: а) \(3\frac{3}{5}\), б) \(2\frac{1}{4}\), в) \(\frac{1}{6}\), г) \(4\frac{3}{7}\).