What is the correct ordering of the three numbers $$\dfrac{5}{6}$$, $$\dfrac{7}{8}$$, and $$\dfrac{9}{10}$$, in increasing order? (Adapted from$$2012$$ AMC $$8$$ Problem, Question \#$$4$$) 
Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering
Instead of finding the LCD, we can subtract each fraction from $$1$$ to get a common numerator. Thus,  $$1- \dfrac{5}{6}= \dfrac{1}{6}$$,  $$1- \dfrac{7}{8}= \dfrac{1}{8}$$,  $$1- \dfrac{9}{10}= \dfrac{1}{10}$$.  All three fractions have the common numerator $$1$$. Now the order of the fractions is obvious. $$\dfrac{1}{6}\textgreater\dfrac{1}{8}\textgreater\dfrac{1}{10}\Rightarrow\dfrac{5}{6}\textless\dfrac{7}{8}\textless\dfrac{9}{10}$$. Therefore, $$\dfrac{5}{6}\textless\dfrac{7}{8}\textless\dfrac{9}{10}$$. 