Rational numbers are those that express the quotient between two integers. The notion of rational comes from cooperation (part of a set). Rational numbers are formed by whole numbers (which can be expressed as a quotient: 5 = 5/1, 38 = 38/1) and fractions (non-rational integers: 2/5, 8/12, 69/253).
It is important to mention that while in whole numbers each number has a following (-1, 0, 1, 2, 3, 4...), there are an infinite number of numbers between each rational number.
Rational numbers to express measures. Comparing a quantity with his unit, there are, in general, a fractional result. For example: dividing / sharing a pizza into two parts, one obtains two halves. Each portion will be 1/2 pizza (part two). If we take the two portions, there again the whole pizza (2/2 = 1).
Rational numbers can be added, subtracted, multiplied, or divided (except zero). The result of these operations is always another rational number. Because integers can be positive or negative, the sign rule is applied. How to perform operations varies according to the presence or absence of a (equal) common denominator in fractions.
It is noted that the rationals are already used in ancient Egypt. The mathematicians of that time used unit fractions, which are those whose denominators are positive integers. In cases where they need fractions with non-unitary numerators, the Egyptians had recourse to the sum of different unit fractions (called Egyptian fractions).