Difference between (mv^2)/2 and mv.

What is the difference between kinetic energy and momentum?

((mv^2)/2)/mv = (mv^2)/2mv = mv/2

Why is kinetic energy momentum squared and divided by 2?

in >>1 something is not right

(mv^2)/2mv = mv/2

mv^2
----
2mv

you reckon that equals mv/2? cause i don't.