I Need a Binary Operation

Define a binary operation http://www.mathhelpforum.com/math-he...7a046183-1.gif on the rationals so that the map http://www.mathhelpforum.com/math-he...9cf5ab48-1.gif defined by http://www.mathhelpforum.com/math-he...c4a92706-1.gif is an isomorphism between sets with binary operations. Prove that http://www.mathhelpforum.com/math-he...2cc525ec-1.gif is an isomorphism.

By Isomorphism i mean i need to find a binary operation such that for all u, v in http://www.mathhelpforum.com/math-he...a4249b74-1.gif,

$\displaystyle \phi(u \bullet v) = \phi(u) + \phi(v)$