# Math Help - order axioms proof.

1. ## order axioms proof.

Hello all,
Can someone please help me with the following proof? i have an exam on monday and cant figure out this one question i found online:

Use order axioms to show that 0 < a < b & 0 < c < d implies that
a/d < b/c. Thanks in advance.

I hope I remember: $\frac{a}{d}<\frac{b}{c} \Longleftrightarrow ac $\Longleftrightarrow ac-bd <0 \Longleftrightarrow ac-ad+ad-bd<0$ $\Longleftrightarrow a(c-d)+d(a-b)<0$, and since the last inequality is exactly the opposite that we have by the given data ( $c and everybody's positive here, the correct inequality should be $\frac {a}{d}>\frac{b}{c}$