Question

See, I got an answer but my teacher showed us the websites answer and I'm confused.

Answer 1

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):

`(a)/(b)`

Where "a" is the numerator and "b" is the denominator.

Integers include negative numbers and, positive numbers and zero. For example, these are Integers:

`4,2,-3,-8`

An Integer is always a Rational number, because it can be written as a fraction with denominator 1:

`(4)/(1),(2)/(1),(-3)/(1),\text{ }(-8)/(1)`

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:

`(1)/(2)`

but the second one can written showing only the numerator (because it is know that all Integers have denominator 1):

`4=(4)/(1)`

Therefore, all Integers are Rational numbers, but a Rational number is not always an Integer.