Quotition and partition

In arithmetic, quotition is one of two ways of viewing fractions and division, the other being partition.

In quotition division one asks how many parts there are; in partition division one asks what the size of each part is.

For example, the expression

$6\div 2\,$

can be construed in either of two ways:

• "How many parts of size 2 must be added to get 6?" (Quotition division)

We can write

$6=\underbrace {2+2+2} _{\text{3 parts}}.$

Since it takes 3 parts, we conclude that

$6\div 2=3.\,$

• "What is the size of 2 equal parts whose sum is 6?". (Partition division)

We can write

$6=\underbrace {3+3} _{\text{2 parts}}.$

Since the size of each part is 3, we conclude that

$6\div 2=3.\,$

It is a fact of elementary theoretical mathematics that the numerical answer is the same either way: 6 ÷ 2 = 3. This is essentially equivalent to the commutativity of multiplication.

Division involves thinking about a whole in terms of its parts. One frequent division notion, a natural number of equal parts, is known as partition to educators. The basic concept behind partition is sharing. In sharing a whole entity becomes an integer number of equal parts. What quotition concerns is explained by removing the word integer in the last sentence. Allow number to be any fraction and you have quotition instead of partition.

See also

• List of partition topics

External links

• A University of Melbourne web page shows what to do when the fraction is a ratio of integers or rational.