6. Решите уравнения: a) \(\frac{2}{7} \cdot x = \frac{1}{7}\) б) \(8 \frac{1}{2} : 2 \frac{1}{2}\) в) \(8 \cdot 2 \frac{1}{4} : 3 \frac{3}{4}\) г) \(3 \frac{1}{2} : 2 \frac{1}{3}\) д) \(3 : 2 \frac{1}{2}\) е) \(6 \frac{2}{3} : 6 \frac{3}{4}\) ж) \(4 : \frac{11}{15} \cdot \frac{5}{14}\) 6. Решите уравнения: a) \(x : \frac{4}{15} = \frac{2}{5}\)

Решение:

1. а) \(x = \frac{1}{7} : \frac{2}{7} = \frac{1}{7} \cdot \frac{7}{2} = \frac{1}{2}\)


2. б) \(8 \frac{1}{2} : 2 \frac{1}{2} = \frac{17}{2} : \frac{5}{2} = \frac{17}{2} \cdot \frac{2}{5} = \frac{17}{5} = 3 \frac{2}{5}\)


3. в) \(8 \cdot 2 \frac{1}{4} : 3 \frac{3}{4} = 8 \cdot \frac{9}{4} : \frac{15}{4} = 18 : \frac{15}{4} = 18 \cdot \frac{4}{15} = \frac{6 \cdot 3 \cdot 4}{5 \cdot 3} = \frac{24}{5} = 4 \frac{4}{5}\)


4. г) \(3 \frac{1}{2} : 2 \frac{1}{3} = \frac{7}{2} : \frac{7}{3} = \frac{7}{2} \cdot \frac{3}{7} = \frac{3}{2} = 1 \frac{1}{2}\)


5. д) \(3 : 2 \frac{1}{2} = 3 : \frac{5}{2} = 3 \cdot \frac{2}{5} = \frac{6}{5} = 1 \frac{1}{5}\)


6. е) \(6 \frac{2}{3} : 6 \frac{3}{4} = \frac{20}{3} : \frac{27}{4} = \frac{20}{3} \cdot \frac{4}{27} = \frac{80}{81}\)


7. ж) \(4 : \frac{11}{15} \cdot \frac{5}{14} = 4 \cdot \frac{15}{11} \cdot \frac{5}{14} = \frac{4 \cdot 15 \cdot 5}{11 \cdot 14} = \frac{2 \cdot 2 \cdot 3 \cdot 5 \cdot 5}{11 \cdot 2 \cdot 7} = \frac{150}{77} = 1 \frac{73}{77}\)


8. а) \(x = \frac{2}{5} \cdot \frac{4}{15} = \frac{8}{75}\)

Ответ: а) \(\frac{1}{2}\); б) \(3 \frac{2}{5}\); в) \(4 \frac{4}{5}\); г) \(1 \frac{1}{2}\); д) \(1 \frac{1}{5}\); е) \(\frac{80}{81}\); ж) \(1 \frac{73}{77}\); а) \(\frac{8}{75}\).