Quotition and partition


In arithmetic, quotition and partition are two ways of viewing fractions and division.
In quotition division one asks, "how many parts are there?"; While in partition division one asks, "what is the size of each part?".
For example, the expression is
and it can be constructed of either two ways:
It is a fact of elementary theoretical mathematics that the numerical answer is always the same no matter which way you put it, 6 ÷ 2 = 3. This is essentially equivalent to the commutativity of multiplication in multiplication arithmetic.
Division involves thinking about a whole in terms of its parts. One frequent division notation, is that a natural number of equal parts, is known as a partition to educators who teach it.
The basic concept behind a partition is sharing. In sharing instead the whole entity becomes an integer number with equal parts.
What quotition focuses on, is explained by removing the word integer in the last sentence. Allow the number to be any fraction and you may have a quotition instead of a partition.