Hesitant fuzzy sets (HFSs), interval-valued hesitant fuzzy sets (IVHFSs) and typical dual hesitant fuzzy sets (T-DHFSs) are new extensions of classical fuzzy sets (FSs) that have attracted more and more scholars attention nowadays. Although several contributions exist regarding basic operations on HFSs, IVHFSs and T-DHFSs, most of them are focused on the multiplication and the addition operations and do not refer extensively to the division and the subtraction operations. Thus, the main purpose of the present paper is to develop division and subtraction formulas for HFSs, IVHFSs and T-DHFSs, which provides more choices for the decision makers.