In
arithmetic
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
, 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:
* "How many parts of the size of 2 must be added to get the amount of 6?" (Quotition division)
: One can write
::
: Since it takes 3 parts, the conclusion is that
::
* "What is the size of 2 equal parts whose sum is that of 6?". (Partition division)
: One can write
::
: Since the size of each part is 3, the conclusion is that
::
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
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of ...
of
multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...
in multiplication arithmetic.
Division
Division or divider may refer to:
Mathematics
*Division (mathematics), the inverse of multiplication
*Division algorithm, a method for computing the result of mathematical division
Military
*Division (military), a formation typically consisting ...
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.
See also
*
List of partition topics
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are
* partition of a set or an ordered partition of a set,
* partition of a graph,
* partition of an integer,
* ...
References
*
*
{{Refend
External links
A University of Melbourne web pageshows what to do when the fraction is a
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of
integers
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language o ...
or
rational
Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abi ...
.
Operations on numbers