\(\dfrac{a}{b}< \dfrac{c}{d}\\ \Leftrightarrow\dfrac{a}{b}-\dfrac{c}{d}< 0\\ \Leftrightarrow\dfrac{ad-bc}{bd}< 0\)
Vì \(b>0;d>0\)
\(\Rightarrow ad-bc< 0\\ \Leftrightarrow ab< bc\left(đpcm\right)\)
Ngược lại : \(ad< bc\)
Vì \(b>0;d>0\Rightarrow bd>0\)
Chia cả hai vế cho \(bd\)
\(ad< bc\\ \Leftrightarrow\dfrac{ad}{bd}< \dfrac{bc}{bd}\\ \Leftrightarrow\dfrac{a}{b}< \dfrac{c}{d}\left(đpcm\right)\)