Solve the following fraction problems: 1. 5/7 : 21/15 : 9/24 = 2. 4/5 : 8/10 : 20/2 = 3. 6/7 : 3/9 : 28/30 = 4. 40/50 : 20/5 : 3/4 = 5. 17/20 : 10/34 : 5/2 = 6. 15/20 : 150/200 : 2/3 = 7. 14/63 : 18/28 : 2/6 = 8. 77/25 : 11/13 : 65/7 = 9. 81/90 : 2/3 : 18/20 = 10. 42/60 : 7/12 : 3/21 =

Решение:

1. \( \frac{5}{7} : \frac{21}{15} : \frac{9}{24} = \frac{5}{7} \cdot \frac{15}{21} \cdot \frac{24}{9} = \frac{5 \cdot 15 \cdot 24}{7 \cdot 21 \cdot 9} = \frac{5 \cdot (3 \cdot 5) \cdot (3 \cdot 8)}{7 \cdot (3 \cdot 7) \cdot (3 \cdot 3)} = \frac{5 \cdot 5 \cdot 8}{7 \cdot 7 \cdot 3} = \frac{200}{147} \)


2. \( \frac{4}{5} : \frac{8}{10} : \frac{20}{2} = \frac{4}{5} \cdot \frac{10}{8} \cdot \frac{2}{20} = \frac{4 \cdot 10 \cdot 2}{5 \cdot 8 \cdot 20} = \frac{80}{800} = \frac{1}{10} \)


3. \( \frac{6}{7} : \frac{3}{9} : \frac{28}{30} = \frac{6}{7} \cdot \frac{9}{3} \cdot \frac{30}{28} = \frac{6 \cdot 9 \cdot 30}{7 \cdot 3 \cdot 28} = \frac{6 \cdot 3 \cdot 30}{7 \cdot 28} = \frac{18 \cdot 30}{7 \cdot 28} = \frac{540}{196} = \frac{135}{49} \)


4. \( \frac{40}{50} : \frac{20}{5} : \frac{3}{4} = \frac{40}{50} \cdot \frac{5}{20} \cdot \frac{4}{3} = \frac{40 \cdot 5 \cdot 4}{50 \cdot 20 \cdot 3} = \frac{800}{3000} = \frac{8}{30} = \frac{4}{15} \)


5. \( \frac{17}{20} : \frac{10}{34} : \frac{5}{2} = \frac{17}{20} \cdot \frac{34}{10} \cdot \frac{2}{5} = \frac{17 \cdot 34 \cdot 2}{20 \cdot 10 \cdot 5} = \frac{1156}{1000} = \frac{289}{250} \)


6. \( \frac{15}{20} : \frac{150}{200} : \frac{2}{3} = \frac{15}{20} \cdot \frac{200}{150} \cdot \frac{3}{2} = \frac{15 \cdot 200 \cdot 3}{20 \cdot 150 \cdot 2} = \frac{9000}{6000} = \frac{3}{2} \)


7. \( \frac{14}{63} : \frac{18}{28} : \frac{2}{6} = \frac{14}{63} \cdot \frac{28}{18} \cdot \frac{6}{2} = \frac{14 \cdot 28 \cdot 6}{63 \cdot 18 \cdot 2} = \frac{2352}{2268} = \frac{98}{94.5} = \frac{196}{189} = \frac{28}{27} \)


8. \( \frac{77}{25} : \frac{11}{13} : \frac{65}{7} = \frac{77}{25} \cdot \frac{13}{11} \cdot \frac{7}{65} = \frac{77 \cdot 13 \cdot 7}{25 \cdot 11 \cdot 65} = \frac{7007}{17875} = \frac{91}{225} \)


9. \( \frac{81}{90} : \frac{2}{3} : \frac{18}{20} = \frac{81}{90} \cdot \frac{3}{2} \cdot \frac{20}{18} = \frac{81 \cdot 3 \cdot 20}{90 \cdot 2 \cdot 18} = \frac{4860}{3240} = \frac{486}{324} = \frac{3}{2} \)


10. \( \frac{42}{60} : \frac{7}{12} : \frac{3}{21} = \frac{42}{60} \cdot \frac{12}{7} \cdot \frac{21}{3} = \frac{42 \cdot 12 \cdot 21}{60 \cdot 7 \cdot 3} = \frac{10584}{1260} = \frac{84}{10} = \frac{42}{5} \)

Ответ: 1. 200/147, 2. 1/10, 3. 135/49, 4. 4/15, 5. 289/250, 6. 3/2, 7. 28/27, 8. 91/225, 9. 3/2, 10. 42/5.