We deal with the extension of division operation for flexible queries in relational databases where several graded notions are involved, such as the levels of certainty, of importance, or of fulfillment of a graded property, as well as fuzzy quantifiers. We address the case where both levels of fulfillment and levels of importance are present in the specification of a requirement. Furthermore, we consider the case where a level of fulfillment may be ill-known in the available data, which is expressed by a fuzzy-valued degree. We also show that quantifiers like most can be handled by a suitable weakening of the min operation in our extension.