3.58 Найдите неизвестный член пропорции: a) 3 1/2 : 2 1/7 = 2 1/3 : t б) 3 1/3 : s = 4 2/3 : 1 1/6 в) y : 2/3 = 8 1/6 : 2 1/3 г) 5 1/7 : 6/7 = z : 12/17

Решение:

1. a) 3 1/2 : 2 1/7 = 2 1/3 : t
   7/2 : 15/7 = 7/3 : t
   t = (15/7 * 7/3) / (7/2) = (15/3) / (7/2) = 5 / (7/2) = 5 * 2/7 = 10/7
   Ответ: t = 10/7
2. б) 3 1/3 : s = 4 2/3 : 1 1/6
   10/3 : s = 14/3 : 7/6
   s = (10/3 * 7/6) / (14/3) = (70/18) / (14/3) = (35/9) * (3/14) = 105 / 126 = 5/6
   Ответ: s = 5/6
3. в) y : 2/3 = 8 1/6 : 2 1/3
   y : 2/3 = 49/6 : 7/3
   y = (2/3 * 49/6) / (7/3) = (98/18) / (7/3) = (49/9) * (3/7) = 147 / 63 = 7/3
   Ответ: y = 7/3
4. г) 5 1/7 : 6/7 = z : 12/17
   36/7 : 6/7 = z : 12/17
   6 = z : 12/17
   z = 6 * 12/17 = 72/17
   Ответ: z = 72/17