In this paper, we examine the syntactic conditions under which Mandarin Chinese Distributive Numerals (DistNums) can associate their target DP. We argue that DistNum may associate with a DP only if it has moved across it, be this movement overt or covert. The fact that this generalization holds suggests that proposals that take these phenomena to have the same source are on the right track. Building on Nissenbaum's (2000) work on parasitic gaps, and previous analyses of DistNums and similar adverbials by Beck & von Stechow (2007) and Cable (2014), we provide an account of this generalization, with the central idea being that the kinds of predicates that DistNums modify can only be created by movement. We also provide a semantics for these adverbials that is capable of assigning the correct truth-conditions to sentences in which a DistNum associates with only one of the DPs in a coordinated structure. Finally, we use DistNum association to provide new arguments in favor of the existence of covert pied-piping in Mandarin Chinese wh-questions and null topic movement in clauses with object drop.