Ordering fractions

Problem:

 

Solution:

$ \frac{3}{4} $, $ \frac{2}{9} $, $ \frac{13}{18} $, $ \frac{11}{12} $ = $ \frac{27}{36} $, $ \frac{8}{36} $, $ \frac{26}{36} $, $ \frac{33}{36} $

Therefore the correct order is $ \frac{2}{9} < \frac{13}{18} < \frac{3}{4} < \frac{11}{12} $


$ \frac{3}{7} $, $ \frac{4}{9} $, $ \frac{4}{5} $, $ \frac{5}{8} $ = $ \frac{1080}{2520} $, $ \frac{1120}{2520} $, $ \frac{2016}{2520} $, $ \frac{1575}{2520} $

Therefore the correct order is $ \frac{3}{7} < \frac{4}{9} < \frac{5}{8} < \frac{4}{5} $

$ \frac{2}{3} $, $ \frac{3}{7} $, $ \frac{6}{11} $, $ \frac{1}{5} $ = $ \frac{770}{1155} $, $ \frac{495}{1155} $, $ \frac{630}{1155} $, $ \frac{231}{1155} $

Therefore the correct order is $ \frac{1}{5} < \frac{3}{7} < \frac{6}{11} < \frac{2}{3} $

$ \frac{1}{2} $, $ \frac{5}{12} $, $ \frac{7}{6} $, $ \frac{9}{4} $ = $ \frac{6}{12} $, $ \frac{5}{12} $, $ \frac{14}{12} $, $ \frac{27}{12} $

Therefore the correct order is $ \frac{5}{12} < \frac{1}{2} < \frac{7}{6} < \frac{9}{4} $

$ \frac{4}{5} $, $ \frac{5}{6} $, $ \frac{1}{2} $, $ \frac{2}{3} $ = $ \frac{24}{30} $, $ \frac{25}{30} $, $ \frac{15}{30} $, $ \frac{20}{30} $

Therefore the correct order is $ \frac{1}{2} < \frac{2}{3} < \frac{4}{5} < \frac{5}{6} $