3.58 Найдите неизвестный член пропорции: a) $$3\frac{1}{2}:2\frac{1}{7}=2\frac{1}{3}:t$$; б) $$3\frac{1}{3}:s=4\frac{2}{3}:1\frac{1}{6}$$; в) $$y:\frac{2}{3}=8:2\frac{1}{3}$$; г) $$5\frac{1}{7}:\frac{6}{7}=z:12\frac{1}{7}$$.

a) $$3\frac{1}{2}:2\frac{1}{7}=2\frac{1}{3}:t$$ $$\frac{7}{2}:\frac{15}{7}=\frac{7}{3}:t$$ $$t=\frac{\frac{7}{3} \cdot \frac{15}{7}}{\frac{7}{2}}=\frac{15}{3} \cdot \frac{2}{7}=\frac{10}{7}=1\frac{3}{7}$$. б) $$3\frac{1}{3}:s=4\frac{2}{3}:1\frac{1}{6}$$ $$\frac{10}{3}:s=\frac{14}{3}:\frac{7}{6}$$ $$s=\frac{\frac{10}{3} \cdot \frac{7}{6}}{\frac{14}{3}}=\frac{70}{18} \cdot \frac{3}{14}=\frac{5}{3}=1\frac{2}{3}$$. в) $$y:\frac{2}{3}=8:2\frac{1}{3}$$ $$y=\frac{8 \cdot \frac{2}{3}}{2\frac{1}{3}}=\frac{8 \cdot \frac{2}{3}}{\frac{7}{3}}=\frac{16}{3} \cdot \frac{3}{7}=\frac{16}{7}=2\frac{2}{7}$$. г) $$5\frac{1}{7}:\frac{6}{7}=z:12\frac{1}{7}$$ $$\frac{36}{7}:\frac{6}{7}=z:\frac{85}{7}$$ $$z=\frac{\frac{36}{7} \cdot \frac{85}{7}}{\frac{6}{7}}=\frac{36}{7} \cdot \frac{85}{7} \cdot \frac{7}{6}=\frac{6 \cdot 85}{7}=\frac{510}{7}=72\frac{6}{7}$$. Ответ: a) $$t=1\frac{3}{7}$$, б) $$s=1\frac{2}{3}$$, в) $$y=2\frac{2}{7}$$, г) $$z=72\frac{6}{7}$$.