7. Найдите неизвестный член пропорции: а) 13 : x = 17 : 8; б) 20/x = 190/114; г) x : 2 1/12 = 15 : 4 1/2; д) 3,75 : 10,4 = 3 11/13 : x; е) 9 1/6 : 4 = 51/5 : x

Решение:

а) \( 13:x = 17:8 \)

1. \( 17x = 13 \cdot 8 \)
2. \( 17x = 104 \)
3. \( x = \frac{104}{17} \)

б) \( \frac{20}{x} = \frac{190}{114} \)

1. \( 190x = 20 \cdot 114 \)
2. \( 190x = 2280 \)
3. \( x = \frac{2280}{190} \)
4. \( x = 12 \)

г) \( x : 2\frac{1}{12} = 15 : 4\frac{1}{2} \)

1. \( x : \frac{25}{12} = 15 : \frac{9}{2} \)
2. \( \frac{9}{2}x = 15 \cdot \frac{25}{12} \)
3. \( \frac{9}{2}x = \frac{375}{12} \)
4. \( x = \frac{375}{12} \cdot \frac{2}{9} \)
5. \( x = \frac{375}{54} = \frac{125}{18} \)

д) \( 3,75:10,4 = 3\frac{11}{13} : x \)

1. \( 3,75 : 10,4 = \frac{50}{13} : x \)
2. \( 3,75x = 10,4 \cdot \frac{50}{13} \)
3. \( \frac{15}{4}x = \frac{104}{10} \cdot \frac{50}{13} \)
4. \( \frac{15}{4}x = \frac{5200}{130} \)
5. \( \frac{15}{4}x = 40 \)
6. \( x = 40 \cdot \frac{4}{15} \)
7. \( x = \frac{160}{15} = \frac{32}{3} \)

е) \( 9\frac{1}{6} : 4 = 51:5 : x \)

1. \( \frac{55}{6} : 4 = \frac{51}{5} : x \)
2. \( \frac{55}{6}x = 4 \cdot \frac{51}{5} \)
3. \( \frac{55}{6}x = \frac{204}{5} \)
4. \( x = \frac{204}{5} \cdot \frac{6}{55} \)
5. \( x = \frac{1224}{275} \)

Ответ: а) \( \frac{104}{17} \); б) 12; г) \( \frac{125}{18} \); д) \( \frac{32}{3} \); е) \( \frac{1224}{275} \).