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2. Quotition and partition - Wikipedia

   en.wikipedia.org/wiki/Quotition_and_partition

   Quotition and partition. 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?" In general, a quotient where Q, N, and D are integers or rational numbers, can be conceived of in either ...

3. Field of fractions - Wikipedia

   en.wikipedia.org/wiki/Field_of_fractions

   The field of fractions of an integral domain is sometimes denoted by ⁡ or ⁡ (), and the construction is sometimes also called the fraction field, field of quotients, or quotient field of . All four are in common usage, but are not to be confused with the quotient of a ring by an ideal , which is a quite different concept.

4. Quotient - Wikipedia

   en.wikipedia.org/wiki/Quotient

   In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced / ˈkwoʊʃənt /) is a quantity produced by the division of two numbers. [1] The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division) [2] or a fraction or ratio (in the ...

5. Euclidean algorithm - Wikipedia

   en.wikipedia.org/wiki/Euclidean_algorithm

   Each quotient polynomial is chosen such that each remainder is either zero or has a degree that is smaller than the degree of its predecessor: deg[r k (x)] < deg[r k−1 (x)]. Since the degree is a nonnegative integer, and since it decreases with every step, the Euclidean algorithm concludes in a finite number of steps.

6. Division (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Division_(mathematics)

   Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other possible interpretations ...

7. Field extension - Wikipedia

   en.wikipedia.org/wiki/Field_extension

   Field extension. In mathematics, particularly in algebra, a field extension (denoted ) is a pair of fields , such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. [1] [2] [3] For example, under the usual notions of addition and multiplication, the complex numbers are ...