In arithmetic, quotition and partition are two ways of viewing fractions and division. In quotitive division one asks "how many parts are there?" while in partitive division one asks "what is the size of each part?"
In general, a quotient where Q, N, and D are integers or rational numbers, can be conceived of in either of 2 ways:
For example, the quotient can be conceived of as representing either of the decompositions:
In the rational number system used in elementary mathematics, the numerical answer is always the same no matter which way you put it, as a consequence of the commutativity of multiplication.
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