First let's remember what a Rational number is. A Rational number is that one that can be written in this form (as a fraction):
[tex]\frac{a}{b}[/tex]
Where "a" is the numerator and "b" is the denominator.
Integers include negative numbers and, positive numbers and zero. For example, these are Integers:
[tex]4,2,-3,-8[/tex]
An Integer is always a Rational number, because it can be written as a fraction with denominator 1:
[tex]\frac{4}{1},\frac{2}{1},\frac{-3}{1},\text{ }\frac{-8}{1}[/tex]
Then:
A Rational number that is not an Integer is different from a Rational number that is an Integer, because the first one must be written with a denominator. For example:
[tex]\frac{1}{2}[/tex]
but the second one can written showing only the numerator (because it is know that all Integers have denominator 1):
[tex]4=\frac{4}{1}[/tex]
Therefore, all Integers are Rational numbers, but a Rational number is not always an Integer.
