3. Решите уравнение: a) x: 1 7/9 = 6 3/4; 6) x * 3 5/7 = 2 |a) x: 1 7/8 = 2 2/9; 5) x * 2 6/7 = 4

Ответ: Вариант 1: a) 11 \(\frac{1}{3}\); б) \(\frac{14}{27}\). Вариант 2: a) \(\frac{65}{72}\); б) \(\frac{14}{20}\)

Решение:

Вариант 1:

• a) \(x : 1\frac{7}{9} = 6\frac{3}{4}\)
• \(x = 6\frac{3}{4} \cdot 1\frac{7}{9}\)
• \(x = \frac{27}{4} \cdot \frac{16}{9}\)
• \(x = \frac{27 \cdot 16}{4 \cdot 9}\)
• \(x = \frac{432}{36}\)
• \(x = 12\)

• б) \(x \cdot 3\frac{5}{7} = 2\)
• \(x = 2 : 3\frac{5}{7}\)
• \(x = 2 : \frac{26}{7}\)
• \(x = 2 \cdot \frac{7}{26}\)
• \(x = \frac{2 \cdot 7}{26}\)
• \(x = \frac{14}{26}\)
• \(x = \frac{7}{13}\)

Вариант 2:

• a) \(x : 1\frac{7}{8} = 2\frac{2}{9}\)
• \(x = 2\frac{2}{9} \cdot 1\frac{7}{8}\)
• \(x = \frac{20}{9} \cdot \frac{15}{8}\)
• \(x = \frac{20 \cdot 15}{9 \cdot 8}\)
• \(x = \frac{300}{72}\)
• \(x = \frac{25}{6}\)

• б) \(x \cdot 2\frac{6}{7} = 4\)
• \(x = 4 : 2\frac{6}{7}\)
• \(x = 4 : \frac{20}{7}\)
• \(x = 4 \cdot \frac{7}{20}\)
• \(x = \frac{4 \cdot 7}{20}\)
• \(x = \frac{28}{20}\)
• \(x = \frac{7}{5}\)

Ответ: Вариант 1: a) 12; б) \(\frac{7}{13}\). Вариант 2: a) \(\frac{25}{6}\); б) \(\frac{7}{5}\)