The set of real numbers is made up of two different sets of numbers -- the set of rational numbers and the set of irrational numbers. This means every real number is either a rational number OR an irrational number, no number can be in both sets. There are many more irrational numbers than rational numbers.
Rational numbers are numbers that can be represented by the ratio of two integers p/q (but q CANNOT be zero!) while irrational numbers cannot be written as the ratio of two integers. We commonly call rational numbers fractions.
The numerator and denominator of a fraction have specific roles in the value of the amount being represented. The denominator names the pieces that make up the "whole." The whole will change depending on the circumstances, but the denominator identifies how the whole is being divided. The numerator of a fraction tells how many pieces we have.