Question

Answer 1

Ta có:

\(\dfrac{a}{b}< \dfrac{c}{d}\Rightarrow\dfrac{a\cdot d}{b\cdot d}< \dfrac{c\cdot b}{d\cdot b}\)

\(\Rightarrow\dfrac{ab}{bd}< \dfrac{bc}{bd}\)

Mà: \(b,d>0\Rightarrow bd>0\)

\(\Rightarrow\dfrac{ad}{bd}< \dfrac{bc}{bd}\Rightarrow ad< bc\)

⇒ Đpcm 

Answer 2

Ta có :

\(\dfrac{a}{b}< \dfrac{c}{d}\)

\(\Leftrightarrow\dfrac{a}{b}-\dfrac{c}{d}< 0\)

\(\Leftrightarrow\dfrac{ad-bc}{bd}< 0\)

mà \(bd>0\left(b>0;d>0\right)\)

\(\Leftrightarrow ad-bc< 0\)

\(\Leftrightarrow ad< bc\left(dpcm\right)\)