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 :

6 \div 2

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 ::

6 = \underbrace_.

: Since it takes 3 parts, the conclusion is that ::

6 \div 2 = 3.

* "What is the size of 2 equal parts whose sum is that of 6?". (Partition division) : One can write ::

6 = \underbrace_.

: Since the size of each part is 3, the conclusion is that ::

6 \div 2 = 3.

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 ...

multiplication Multiplication (often denoted by the Multiplication sign, cross symbol , by the mid-line #Notation and terminology, dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four Elementary arithmetic, elementary Op ...

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.

References

* * {{Refend

External links

A University of Melbourne web page
shows 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 or rational. Operations on numbers

See also

References

External links