For rational numbers to be closed under division, then any rational number divided by another rational number would have to be a rational number. This works for every rational number except when the second number is 0. Since division by 0 is undefined, dividing any rational number by the rational number zero will not give you a rational number. In order to make the rational numbers closed under division, you can choose any rational number you want except 0.
In other words, the set of rational numbers is not closed under division. The problem occurs only with division by zero. The set of rational numbers from which zero is removed is closed under division.
Every nonzero rational number is closed under division.
