Ordering more fractions

Problem:



Solution:

$ \frac{2}{7} $, $ \frac{1}{3} $, $ \frac{3}{4} $, $ \frac{4}{9} $ = $ \frac{72}{252} $, $ \frac{84}{252} $, $ \frac{189}{252} $, $ \frac{112}{252} $

Therefore the correct order is $\frac{2}{7} < \frac{1}{3}  < \frac{4}{9}  < \frac{3}{4} $

$ \frac{5}{8} $, $ \frac{11}{12} $, $ \frac{7}{4} $, $ \frac{9}{16} $ = $ \frac{30}{48} $, $ \frac{44}{48} $, $ \frac{84}{48} $, $ \frac{27}{48} $

Therefore the correct order is $\frac{9}{16} < \frac{5}{8}  < \frac{11}{12}  < \frac{7}{4} $

$ \frac{1}{6} $, $ \frac{1}{2} $, $ \frac{1}{3} $, $ \frac{1}{9} $ = $ \frac{3}{18} $, $ \frac{9}{18} $, $ \frac{6}{18} $, $ \frac{2}{18} $

Therefore the correct order is $\frac{1}{9} < \frac{1}{6}  < \frac{1}{3}  < \frac{1}{2} $

$ \frac{2}{5} $, $ \frac{5}{12} $, $ \frac{3}{10} $, $ \frac{1}{6} $ = $ \frac{24}{60} $, $ \frac{25}{60} $, $ \frac{18}{60} $, $ \frac{10}{60} $

Therefore the correct order is $\frac{1}{6} < \frac{3}{10}  < \frac{2}{5}  < \frac{5}{12} $

$ \frac{3}{14} $, $ \frac{5}{18} $, $ \frac{7}{16} $, $ \frac{1}{12} $ = $ \frac{216}{1008} $, $ \frac{280}{1008} $, $ \frac{441}{1008} $, $ \frac{84}{1008} $

Therefore the correct order is $\frac{1}{12} < \frac{3}{14}  < \frac{5}{18}  < \frac{7}{16} $

$ \frac{9}{8} $, $ \frac{7}{2} $, $ \frac{13}{6} $, $ \frac{5}{4} $ = $ \frac{27}{24} $, $ \frac{84}{24} $, $ \frac{52}{24} $, $ \frac{30}{24} $

Therefore the correct order is $\frac{9}{8} < \frac{5}{4}  < \frac{13}{6}  < \frac{7}{2} $

$ \frac{9}{40} $, $ \frac{13}{20} $, $ \frac{11}{10} $, $ \frac{17}{30} $ = $ \frac{27}{120} $, $ \frac{78}{120} $, $ \frac{132}{120} $, $ \frac{68}{120} $

Therefore the correct order is $\frac{9}{40} < \frac{17}{30}  < \frac{13}{20}  < \frac{11}{10} $