Starting with the structure $(N_0,+,\cdot,\leq)$ of natural numbers with zero, one way of introducing structures of nonegative rational numbers $(Q_+,+,\cdot,\leq)$ and of rational numbers $(Q,+,\cdot,\leq)$ is presented, together with proving all of their main properties. In particular, generalized commutative and associative laws are proved. Also, it is proved that the introduced structures are minimal ones that satisfy the given lists of properties.