Prove that |a/b|=|a|/|b|

Question

It is that says prove that the absolute of a over b is equal to absolute of a over absolute of b

Answer 1

prove la/bl=lal/lbl   (b≠0 and if a=0 in any case then la/bl=lal/lbl=0)

case 1 a>0, b>0

la/bl=a/b and lal/lbl=a/b

case 2 a<0, b>0

la/bl=-(a/b) and lal/lbl=-(a)/b=-(a/b)

case 3 a>0, b<0

la/bl=-(a/b) and lal/lbl=a/-(b)=-(a/b)

case 4 a<0, b<0

la/bl=a/b and lal/lbl=(-a)/(-b)=a/b