3.161 Решите уравнение: а) $$3\frac{2}{3}:a = 4\frac{8}{9}:1\frac{5}{7}$$; б) $$1\frac{7}{8}:2\frac{3}{4} = 3\frac{3}{4}:b$$; в) $$8\frac{1}{4}:c = 13\frac{3}{4}:2\frac{1}{3}$$; г) $$5:2\frac{5}{7} = 2\frac{1}{2}:d$$.

Применим протокол Я.

1. Определим цель задания: решить данные уравнения.
2. Составим краткий план: Решим каждое уравнение по очереди.
3. Выполним подробный анализ:
   1. Уравнение а):

$$3\frac{2}{3}:a = 4\frac{8}{9}:1\frac{5}{7}$$

$$\frac{11}{3}:a = \frac{44}{9}:\frac{12}{7}$$

$$\frac{11}{3}:a = \frac{44}{9} \cdot \frac{7}{12}$$

$$\frac{11}{3}:a = \frac{11 \cdot 4 \cdot 7}{9 \cdot 4 \cdot 3}$$

$$\frac{11}{3}:a = \frac{77}{27}$$

$$a = \frac{11}{3}:\frac{77}{27}$$

$$a = \frac{11}{3} \cdot \frac{27}{77}$$

$$a = \frac{11 \cdot 3 \cdot 9}{3 \cdot 11 \cdot 7}$$

$$a = \frac{9}{7} = 1\frac{2}{7}$$

2. Уравнение б): $$1\frac{7}{8}:2\frac{3}{4} = 3\frac{3}{4}:b$$ $$\frac{15}{8}:\frac{11}{4} = \frac{15}{4}:b$$ $$\frac{15}{8} \cdot \frac{4}{11} = \frac{15}{4}:b$$ $$\frac{15 \cdot 4}{8 \cdot 11} = \frac{15}{4}:b$$ $$\frac{15}{22} = \frac{15}{4}:b$$ $$b = \frac{15}{4}:\frac{15}{22}$$ $$b = \frac{15}{4} \cdot \frac{22}{15}$$ $$b = \frac{15 \cdot 22}{4 \cdot 15}$$ $$b = \frac{22}{4} = \frac{11}{2} = 5\frac{1}{2}$$
3. Уравнение в): $$8\frac{1}{4}:c = 13\frac{3}{4}:2\frac{1}{3}$$ $$\frac{33}{4}:c = \frac{55}{4}:\frac{7}{3}$$ $$\frac{33}{4}:c = \frac{55}{4} \cdot \frac{3}{7}$$ $$\frac{33}{4}:c = \frac{165}{28}$$ $$c = \frac{33}{4}:\frac{165}{28}$$ $$c = \frac{33}{4} \cdot \frac{28}{165}$$ $$c = \frac{33 \cdot 28}{4 \cdot 165}$$ $$c = \frac{924}{660}$$ $$c = \frac{14}{10} = \frac{7}{5} = 1\frac{2}{5}$$
4. Уравнение г): $$5:2\frac{5}{7} = 2\frac{1}{2}:d$$ $$5:\frac{19}{7} = \frac{5}{2}:d$$ $$5 \cdot \frac{7}{19} = \frac{5}{2}:d$$ $$\frac{35}{19} = \frac{5}{2}:d$$ $$d = \frac{5}{2}:\frac{35}{19}$$ $$d = \frac{5}{2} \cdot \frac{19}{35}$$ $$d = \frac{5 \cdot 19}{2 \cdot 5 \cdot 7}$$ $$d = \frac{19}{14} = 1\frac{5}{14}$$

Ответ: а) \(a = 1\frac{2}{7}\); б) \(b = 5\frac{1}{2}\); в) \(c = 1\frac{2}{5}\); г) \(d = 1\frac{5}{14}\).