3.58 Найдите неизвестный член пропорции: a) $$\frac{3}{\frac{1}{7}}:2=\frac{2}{7}:t$$; б) $$3\frac{1}{3}:s=4\frac{2}{3}:1\frac{1}{6}$$; в) $$y:\frac{3}{2}=8:2\frac{1}{6}$$; г) $$5\frac{1}{7}:\frac{6}{7}=z:17$$.

а) $$\frac{3}{\frac{1}{7}}:2=\frac{2}{7}:t$$

Найдем t:

$$3 \cdot 7 : 2 = \frac{2}{7} : t$$

$$21:2 = \frac{2}{7}:t$$

$$10,5 = \frac{2}{7}:t$$

$$t = \frac{\frac{2}{7}}{10,5} = \frac{2}{7} : 10,5 = \frac{2}{7} : \frac{21}{2} = \frac{2}{7} \cdot \frac{2}{21} = \frac{4}{147}$$

б) $$3\frac{1}{3}:s=4\frac{2}{3}:1\frac{1}{6}$$

Найдем s:

$$\frac{10}{3} : s = \frac{14}{3} : \frac{7}{6}$$

$$\frac{10}{3} : s = \frac{14}{3} \cdot \frac{6}{7}$$

$$\frac{10}{3} : s = 4$$

$$s = \frac{10}{3} : 4 = \frac{10}{3} \cdot \frac{1}{4} = \frac{5}{6}$$

в) $$y:\frac{3}{2}=8:2\frac{1}{6}$$

Найдем y:

$$y : \frac{3}{2} = 8 : \frac{13}{6}$$

$$y : \frac{3}{2} = 8 \cdot \frac{6}{13}$$

$$y : \frac{3}{2} = \frac{48}{13}$$

$$y = \frac{48}{13} \cdot \frac{3}{2} = \frac{24}{13} \cdot \frac{3}{1} = \frac{72}{13} = 5\frac{7}{13}$$

г) $$5\frac{1}{7}:\frac{6}{7}=z:17$$

Найдем z:

$$\frac{36}{7} : \frac{6}{7} = z : 17$$

$$\frac{36}{7} \cdot \frac{7}{6} = z : 17$$

$$6 = z : 17$$

$$z = 6 \cdot 17 = 102$$

Ответ: а) $$t=\frac{4}{147}$$; б) $$s=\frac{5}{6}$$; в) $$y=5\frac{7}{13}$$; г) $$z=102$$.