Let's use the example of a credit card bill:
The most responsible attitude would be to pay as much as possible on the due date. Making the minimum payment should be avoided.
The holder of a credit card signs a contract with the card supplier that allows the first to spend a certain amount of money, during a period of time, under the promise to return it to the second in the established terms. The credit card bills arrive when a certain amount is due for repayment.
Therefore the most resposible way of dealing with the bill is paying the whole amount due on time or, if not possible, at least pay as much as possible so that most part of the debt is met.
