9) 1 \frac{1}{2} = \frac{x}{1 \frac{2}{3}} ; \frac{2}{6 \frac{2}{3}} = x ; 13) 2 \frac{16}{8} = \frac{6 \frac{1}{4}}{3 \frac{15}{x}} ; 14) \frac{x}{1 \frac{23}{49}} = \frac{15 \frac{2}{5}}{12 \frac{6}{7}} ; 11) 1 \frac{11}{24} = \frac{x}{1 \frac{7}{9}} ; \frac{4}{21} 15) 4 \frac{25}{6 \frac{2}{15}} = \frac{x}{15 \frac{2}{3}} ; 12) 1 \frac{17}{25} = \frac{1 \frac{1}{5}}{1 \frac{5}{16}} ; x 16) 5 \frac{5}{18} = \frac{9 \frac{1}{2}}{x} ;\frac{2}{5 \frac{2}{3}}

Решим данные пропорции. Для этого выразим неизвестную переменную x. Используем основное свойство пропорции: произведение крайних членов равно произведению средних членов. 9) \( 1 \frac{1}{2} = \frac{x}{1 \frac{2}{3}} \) \( 1 \frac{1}{2} = \frac{3}{2} \) \( 1 \frac{2}{3} = \frac{5}{3} \) \( \frac{3}{2} = \frac{x}{\frac{5}{3}} \) Чтобы найти делимое, нужно делитель умножить на частное. \( x = \frac{3}{2} \cdot \frac{5}{3} = \frac{3 \cdot 5}{2 \cdot 3} = \frac{5}{2} \) \( x = 2 \frac{1}{2} \) \( \frac{2}{6 \frac{2}{3}} = x \) \( 6 \frac{2}{3} = \frac{20}{3} \) \( \frac{2}{\frac{20}{3}} = x \) Чтобы разделить число на дробь, нужно это число умножить на дробь, обратную данной. \( x = 2 \cdot \frac{3}{20} = \frac{2 \cdot 3}{20} = \frac{6}{20} = \frac{3}{10} \) \( x = 0.3 \) 13) \( 2 \frac{16}{8} = \frac{6 \frac{1}{4}}{3 \frac{15}{x}} \) \( 2 \frac{16}{8} = 2 + \frac{16}{8} = 2 + 2 = 4 \) \( 6 \frac{1}{4} = \frac{25}{4} \) \( \frac{25}{4} : 4 = \frac{25}{4} \cdot \frac{1}{4} = \frac{25}{16} = 1 \frac{9}{16} \) \( 3 \frac{15}{x} = 1 \frac{9}{16} \) \( \frac{15}{x} = 1 \frac{9}{16} - 3 = \frac{25}{16} - 3 = \frac{25}{16} - \frac{48}{16} = -\frac{23}{16} \) \( \frac{15}{x} = - \frac{23}{16} \) \( x = 15 : (- \frac{23}{16}) = 15 \cdot (- \frac{16}{23}) = -\frac{15 \cdot 16}{23} = -\frac{240}{23} = -10 \frac{10}{23} \) 14) \( \frac{x}{1 \frac{23}{49}} = \frac{15 \frac{2}{5}}{12 \frac{6}{7}} \) \( 1 \frac{23}{49} = \frac{72}{49} \) \( 15 \frac{2}{5} = \frac{77}{5} \) \( 12 \frac{6}{7} = \frac{90}{7} \) \( \frac{\frac{77}{5}}{\frac{90}{7}} = \frac{77 \cdot 7}{5 \cdot 90} = \frac{539}{450} = 1 \frac{89}{450} \) \( \frac{x}{\frac{72}{49}} = 1 \frac{89}{450} \) \( x = \frac{72}{49} \cdot \frac{539}{450} = \frac{72 \cdot 539}{49 \cdot 450} = \frac{38808}{22050} = \frac{4312}{2450} = \frac{2156}{1225} = 1 \frac{931}{1225} \) 11) \( 1 \frac{11}{24} = \frac{x}{1 \frac{7}{9}} \) \( 1 \frac{11}{24} = \frac{35}{24} \) \( 1 \frac{7}{9} = \frac{16}{9} \) \( \frac{35}{24} = \frac{x}{\frac{16}{9}} \) \( x = \frac{35}{24} \cdot \frac{16}{9} = \frac{35 \cdot 16}{24 \cdot 9} = \frac{560}{216} = \frac{280}{108} = \frac{140}{54} = \frac{70}{27} = 2 \frac{16}{27} \) \( \frac{x}{\frac{4}{21}} = 2 \frac{16}{27} \) \( x = \frac{4}{21} \cdot \frac{70}{27} = \frac{4 \cdot 70}{21 \cdot 27} = \frac{280}{567} = \frac{40}{81} \) 15) \( 4 \frac{2}{6 \frac{2}{15}} = \frac{x}{15 \frac{2}{3}} \) \( 4 \frac{2}{\frac{92}{15}} = \frac{4 \cdot 92}{15} = \frac{368}{15} = 24 \frac{8}{15} \) \( 6 \frac{2}{15} = \frac{92}{15} \) \( 15 \frac{2}{3} = \frac{47}{3} \) \( \frac{24 \frac{8}{15}}{x} = \frac{47}{3} \) \( \frac{\frac{368}{15}}{x} = \frac{47}{3} \) \( x = \frac{368}{15} : \frac{47}{3} = \frac{368 \cdot 3}{15 \cdot 47} = \frac{1104}{705} = \frac{368}{235} = 1 \frac{133}{235} \) 12) \( 1 \frac{17}{25} = \frac{1 \frac{1}{5}}{1 \frac{5}{16}} ; x \) \( 1 \frac{17}{25} = \frac{42}{25} \) \( 1 \frac{1}{5} = \frac{6}{5} \) \( 1 \frac{5}{16} = \frac{21}{16} \) \( \frac{42}{25} = \frac{\frac{6}{5}}{x} : \frac{21}{16} \) \( \frac{6}{5} : \frac{21}{16} = \frac{6 \cdot 16}{5 \cdot 21} = \frac{96}{105} \) \( \frac{42}{25} = \frac{\frac{96}{105}}{x} \) \( x = \frac{96}{105} : \frac{42}{25} = \frac{96 \cdot 25}{105 \cdot 42} = \frac{2400}{4410} = \frac{240}{441} = \frac{80}{147} \) 16) \( 5 \frac{5}{18} = \frac{9 \frac{1}{2}}{x} ; \frac{2}{5 \frac{2}{3}} \) \( 5 \frac{5}{18} = \frac{95}{18} \) \( 9 \frac{1}{2} = \frac{19}{2} \) \( 5 \frac{2}{3} = \frac{17}{3} \) \( \frac{95}{18} = \frac{\frac{19}{2}}{x} : \frac{2}{\frac{17}{3}} \) \( \frac{2}{\frac{17}{3}} = \frac{2 \cdot 3}{17} = \frac{6}{17} \) \( \frac{19}{2} : \frac{6}{17} = \frac{19 \cdot 17}{2 \cdot 6} = \frac{323}{12} \) \( \frac{95}{18} = \frac{\frac{323}{12}}{x} \) \( x = \frac{323}{12} : \frac{95}{18} = \frac{323 \cdot 18}{12 \cdot 95} = \frac{5814}{1140} = \frac{2907}{570} = \frac{969}{190} = 5 \frac{19}{190} \)

Ответ: См. решение