3.161 Решите уравнение: a) \(3\frac{2}{3}:a=4\frac{8}{9}:1\frac{5}{7}\); б) \(1\frac{7}{8}:2\frac{1}{3}=3\frac{3}{4}:b\); в) \(8\frac{1}{4}:c=13\frac{3}{4}:2\frac{1}{3}\); г) \(5\frac{2}{3}:2\frac{5}{6}=2\frac{1}{7}:d\).

1. Решим уравнение а):

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

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

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

\(\frac{11}{3}:a=\frac{11 \cdot 7}{9 \cdot 3}\)

\(\frac{11}{3}:a=\frac{77}{27}\)

\(a=\frac{11}{3}: \frac{77}{27}\)

\(a=\frac{11}{3} \cdot \frac{27}{77}\)

\(a=\frac{1 \cdot 9}{1 \cdot 7}\)

\(a=\frac{9}{7}=1\frac{2}{7}\)

Ответ: \(a=1\frac{2}{7}\)

2. Решим уравнение б):

\(1\frac{7}{8}:2\frac{1}{3}=3\frac{3}{4}:b\)

\(\frac{15}{8}:\frac{7}{3}=\frac{15}{4}:b\)

\(\frac{15}{8} \cdot \frac{3}{7}=\frac{15}{4}:b\)

\(\frac{45}{56}=\frac{15}{4}:b\)

\(b=\frac{15}{4}:\frac{45}{56}\)

\(b=\frac{15}{4} \cdot \frac{56}{45}\)

\(b=\frac{1 \cdot 14}{1 \cdot 3}\)

\(b=\frac{14}{3}=4\frac{2}{3}\)

Ответ: \(b=4\frac{2}{3}\)

3. Решим уравнение в):

\(8\frac{1}{4}:c=13\frac{3}{4}:2\frac{1}{3}\)

\(\frac{33}{4}:c=\frac{55}{4}:\frac{7}{3}\)

\(\frac{33}{4}:c=\frac{55}{4} \cdot \frac{7}{3}\)

\(\frac{33}{4}:c=\frac{385}{12}\)

\(c=\frac{33}{4}: \frac{385}{12}\)

\(c=\frac{33}{4} \cdot \frac{12}{385}\)

\(c=\frac{3 \cdot 3}{1 \cdot 35}\)

\(c=\frac{9}{35}\)

Ответ: \(c=\frac{9}{35}\)

4. Решим уравнение г):

\(5\frac{2}{3}:2\frac{5}{6}=2\frac{1}{7}:d\)

\(\frac{17}{3}:\frac{17}{6}=\frac{15}{7}:d\)

\(\frac{17}{3} \cdot \frac{6}{17}=\frac{15}{7}:d\)

\(2=\frac{15}{7}:d\)

\(d=\frac{15}{7}: 2\)

\(d=\frac{15}{7} \cdot \frac{1}{2}\)

\(d=\frac{15}{14}=1\frac{1}{14}\)

Ответ: \(d=1\frac{1}{14}\)