Full Idea
One reason to introduce the rational numbers is that it simplifes the theory of division, since every rational number is divisible by every nonzero rational number, while the analogous statement is false for the natural numbers.
Gist of Idea
Every rational number, unlike every natural number, is divisible by some other number
Source
Shaughan Lavine (Understanding the Infinite [1994], VI.3)
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.198
A Reaction
That is, with rations every division operation has an answer.