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?"
where Q, N, and D are integers or rational numbers, can be conceived of in either of 2 ways: For example, the quotient
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.
Thought of quotitively, a division problem can be solved by repeatedly subtracting groups of the size of the divisor.
If the last group is a remainder smaller than the divisor, it can be thought of as forming an additional smaller group.
The answer to the question "How many cartons are needed to fit 45 eggs?"
Quotition is the concept of division most used in measurement.
For example, measuring the length of a table using a measuring tape involves comparing the table to the markings on the tape.
This is conceptually equivalent to dividing the length of the table by a unit of length, the distance between markings.
Thought of partitively, a division problem might be solved by sorting the initial quantity into a specific number of groups by adding items to each group in turn.
If there is a remainder in solving a partition problem, the parts will end up with unequal sizes.