Reciprocity is the exchange of gifts in favors in order to pressure someone into doing or purchasing something.
It also has a more general meaning; you have two people or parties involved in a transaction, and each gives something and each gets something; there is an exchange. This is in comparison to a transaction in which only one party gives, and the other only receives. If someone asks me to donate to their cause (whatever that cause may be) and I do, there is no reciprocity (unless you count the receipt which I might use to claim a tax deduction - and even so, that is a very feeble form of reciprocity).
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The number by which a given number must be multiplied to get aresult of one. The reciprocal of one-half, for example, is two.