3.58 Найдите неизвестный член пропорции: a) 3\(\frac{1}{2}\) : 2 = 2\(\frac{1}{7}\) : t; б) 3\(\frac{1}{3}\) : s = 4\(\frac{2}{3}\) : 1\(\frac{1}{6}\); в) y : \(\frac{2}{3}\) = 8\(\frac{1}{6}\) : 2\(\frac{1}{3}\); г) 5\(\frac{1}{7}\) : \(\frac{6}{7}\) = z : \(\frac{12}{17}\).

a) 3\(\frac{1}{2}\) : 2 = 2\(\frac{1}{7}\) : t

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

t = \(\frac{2 \cdot 15}{7} : \frac{7}{2}\) = \(\frac{2 \cdot 15 \cdot 2}{7 \cdot 7}\) = \(\frac{60}{49}\) = 1\(\frac{11}{49}\)

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 = \(\frac{10}{3} : (\frac{14}{3} : \frac{7}{6})\) = \(\frac{10}{3} : (\frac{14 \cdot 6}{3 \cdot 7})\) = \(\frac{10}{3} : \frac{4}{1}\) = \(\frac{10}{3} \cdot \frac{1}{4}\) = \(\frac{5}{6}\)

в) y : \(\frac{2}{3}\) = 8\(\frac{1}{6}\) : 2\(\frac{1}{3}\)

y : \(\frac{2}{3}\) = \(\frac{49}{6}\) : \(\frac{7}{3}\)

y = \(\frac{2}{3} \cdot (\frac{49}{6} : \frac{7}{3})\) = \(\frac{2}{3} \cdot (\frac{49 \cdot 3}{6 \cdot 7})\) = \(\frac{2}{3} \cdot \frac{7}{2}\) = \(\frac{7}{3}\) = 2\(\frac{1}{3}\)

г) 5\(\frac{1}{7}\) : \(\frac{6}{7}\) = z : \(\frac{12}{17}\)

\(\frac{36}{7}\) : \(\frac{6}{7}\) = z : \(\frac{12}{17}\)

z = \(\frac{12}{17} \cdot (\frac{36}{7} : \frac{6}{7})\) = \(\frac{12}{17} \cdot (\frac{36 \cdot 7}{7 \cdot 6})\) = \(\frac{12}{17} \cdot 6\) = \(\frac{72}{17}\) = 4\(\frac{4}{17}\)

Ответ: a) t = 1\(\frac{11}{49}\); б) s = \(\frac{5}{6}\); в) y = 2\(\frac{1}{3}\); г) z = 4\(\frac{4}{17}\).