However, it is not closed under division of subtraction. If you divide 3 by 4, you get 0.75, which is not a natural number. Notice that the whole numbers don't include negative numbers. Like natural numbers, the whole numbers are closed under addition and multiplication, but not under subtraction and division. The integers are positive and negative whole numbers.
Rational numbers can be positive or negative.
Rational numbers are closed under addition, subtraction, multiplication, and division. A number which is not rational is called irrational. As a matter of fact, many early mathematicians like Pythagoras were unwilling to accept that such numbers could exist. Decimal numbers that don't repeat or terminate. There are many other examples.