Вычислите: 2/3 : 5/7 1/4 : 1/2 2/5 : 2/3 3/4 : 1/2 3/7 : 3/5 4/8 : 9/9 5/7 : 6/12 4/9 : 2/5 2/13 : 3/24 2/9 : 4/3 36/6 : 7/49 3/10 : 7/100 3/5 : 9/25 3/16 : 5/12 1/4 : 3/4 15/16 : 3/8 1/57 : 1/19

Решение:

• \( \frac{2}{3} : \frac{5}{7} = \frac{2}{3} \cdot \frac{7}{5} = \frac{14}{15} \)
• \( \frac{1}{4} : \frac{1}{2} = \frac{1}{4} \cdot \frac{2}{1} = \frac{1}{2} \)
• \( \frac{2}{5} : \frac{2}{3} = \frac{2}{5} \cdot \frac{3}{2} = \frac{3}{5} \)
• \( \frac{3}{4} : \frac{1}{2} = \frac{3}{4} \cdot \frac{2}{1} = \frac{3}{2} \)
• \( \frac{3}{7} : \frac{3}{5} = \frac{3}{7} \cdot \frac{5}{3} = \frac{5}{7} \)
• \( \frac{4}{8} : \frac{9}{9} = \frac{1}{2} : 1 = \frac{1}{2} \)
• \( \frac{5}{7} : \frac{6}{12} = \frac{5}{7} : \frac{1}{2} = \frac{5}{7} \cdot \frac{2}{1} = \frac{10}{7} \)
• \( \frac{4}{9} : \frac{2}{5} = \frac{4}{9} \cdot \frac{5}{2} = \frac{10}{9} \)
• \( \frac{2}{13} : \frac{3}{24} = \frac{2}{13} \cdot \frac{24}{3} = \frac{2 \cdot 8}{13} = \frac{16}{13} \)
• \( \frac{2}{9} : \frac{4}{3} = \frac{2}{9} \cdot \frac{3}{4} = \frac{1}{6} \)
• \( \frac{36}{6} : \frac{7}{49} = 6 : \frac{1}{7} = 6 \cdot 7 = 42 \)
• \( \frac{3}{10} : \frac{7}{100} = \frac{3}{10} \cdot \frac{100}{7} = \frac{30}{7} \)
• \( \frac{3}{5} : \frac{9}{25} = \frac{3}{5} \cdot \frac{25}{9} = \frac{5}{3} \)
• \( \frac{3}{16} : \frac{5}{12} = \frac{3}{16} \cdot \frac{12}{5} = \frac{9}{20} \)
• \( \frac{1}{4} : \frac{3}{4} = \frac{1}{4} \cdot \frac{4}{3} = \frac{1}{3} \)
• \( \frac{15}{16} : \frac{3}{8} = \frac{15}{16} \cdot \frac{8}{3} = \frac{5}{2} \)
• \( \frac{1}{57} : \frac{1}{19} = \frac{1}{57} \cdot \frac{19}{1} = \frac{1}{3} \)

Ответ: \( \frac{14}{15}, \frac{1}{2}, \frac{3}{5}, \frac{3}{2}, \frac{5}{7}, \frac{1}{2}, \frac{10}{7}, \frac{10}{9}, \frac{16}{13}, \frac{1}{6}, 42, \frac{30}{7}, \frac{5}{3}, \frac{9}{20}, \frac{1}{3}, \frac{5}{2}, \frac{1}{3} \).