Fastest way to compare fractions Which is the fastest method to compare the below fractions with minimum calculation possible and finding which is greatest and which the smallest??
$$\frac{26}{686},\quad \frac{48}{874},\quad \frac{80}{892},\quad \frac{27}{865}$$

$\dfrac{1}{30} < \dfrac{26}{686} < \dfrac{1}{20}$ because $30 \times 26 = 780 > 686$ while $20 \times 26 = 520 < 686$.
$\dfrac{1}{20} < \dfrac{48}{874} < \dfrac{1}{12}$ because $20 \times 48 = 960 > 874$ while
$12 \times 48 = 144 \times 4 = 576 < 874$
$\dfrac{1}{12} < \dfrac{80}{892}$ because $12 \times 80 = 960 > 892$.
$\dfrac{27}{865} < \dfrac{1}{30}$ because $30 \times 27 = 810 < 865$. 
So $\dfrac{27}{865} < \dfrac{26}{686} < \dfrac{48}{874}<  \dfrac{80}{892}$.
