Rational numbers are numbers that can be expressed as fractions p/q, where q ≠ 0. Rational numbers have several key properties: Addition, subtraction, and multiplication of rational numbers is closed, meaning the result is also a rational number. Division of rational numbers is not closed as the result can sometimes be an irrational number. The additive and multiplicative identities for rational numbers are 0 and 1 respectively. Rational numbers also follow properties like commutativity, associativity, and distributivity, except for subtraction and division which are not commutative.