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 $\frac{1}{2} < \frac{2}{3} < \frac{4}{5} < \frac{5}{6}$