All Topics  
Quotient

 

 
   Email Print
   Bookmark   Link
 

 

Quotient
 
 
  Topics Quotient Topic Home

In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, a quotient is the result of a division
Division (mathematics)

In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication.Specifically, if c times b equals a, written:...
. For example, when dividing 6 by 3, the quotient is 2, while 6 is called the dividend
Division (mathematics)

In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication.Specifically, if c times b equals a, written:...
, and 3 the divisor
Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder....
. The quotient can also be expressed as the number of times the divisor divides into the dividend.

A quotient can also mean just the integer
Integer

The integers are natural numbers including 0 and their negative and non-negative numberss . They are numbers that can be written without a fractional or decimal component, and fall within the set ....
 part of the result of dividing two integers. For example, the quotient of 13 ÷ 5 would be 2 while the remainder
Remainder

In arithmetic, when the result of the division of two integers cannot be expressed with an integer quotient, the remainder is the amount "left over."...
 would be 3. For more, see the division algorithm
Division algorithm

The division algorithm is a theorem in mathematics which precisely expresses the outcome of the usual process of division of integers. The name is something of a misnomer, as it is a theorem, not an algorithm, i.e....
.

In more abstract branches of mathematics, the word quotient is often used to describe sets, spaces, or algebraic structure
Algebraic structure

In algebra, a branch of pure mathematics, an algebraic structure consists of one or more Set Closure under one or more Operation , satisfying some axiom....
s whose elements are the equivalence class
Equivalence class

In mathematics, given a Set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a:...
es of some equivalence relation
Equivalence relation

In mathematics, an equivalence relation is, loosely, a binary relation on a Set that specifies how to split up the set into subsets such that every element of the larger set is in exactly one of the subsets....
 on another set, space, or algebraic structure.






Discussion
Ask a question about 'Quotient'
Start a new discussion about 'Quotient'
Answer questions from other users
Full Discussion Forum



Encyclopedia


In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, a quotient is the result of a division
Division (mathematics)

In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication.Specifically, if c times b equals a, written:...
. For example, when dividing 6 by 3, the quotient is 2, while 6 is called the dividend
Division (mathematics)

In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication.Specifically, if c times b equals a, written:...
, and 3 the divisor
Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder....
. The quotient can also be expressed as the number of times the divisor divides into the dividend.

A quotient can also mean just the integer
Integer

The integers are natural numbers including 0 and their negative and non-negative numberss . They are numbers that can be written without a fractional or decimal component, and fall within the set ....
 part of the result of dividing two integers. For example, the quotient of 13 ÷ 5 would be 2 while the remainder
Remainder

In arithmetic, when the result of the division of two integers cannot be expressed with an integer quotient, the remainder is the amount "left over."...
 would be 3. For more, see the division algorithm
Division algorithm

The division algorithm is a theorem in mathematics which precisely expresses the outcome of the usual process of division of integers. The name is something of a misnomer, as it is a theorem, not an algorithm, i.e....
.

In more abstract branches of mathematics, the word quotient is often used to describe sets, spaces, or algebraic structure
Algebraic structure

In algebra, a branch of pure mathematics, an algebraic structure consists of one or more Set Closure under one or more Operation , satisfying some axiom....
s whose elements are the equivalence class
Equivalence class

In mathematics, given a Set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a:...
es of some equivalence relation
Equivalence relation

In mathematics, an equivalence relation is, loosely, a binary relation on a Set that specifies how to split up the set into subsets such that every element of the larger set is in exactly one of the subsets....
 on another set, space, or algebraic structure. See:
  • quotient set
  • quotient group
    Quotient group

    In mathematics, given a group G and a normal subgroup N of G, the quotient group, or factor group, of G over N is intuitively a group that "collapses" the normal subgroup N to the identity element....
  • quotient ring
    Quotient ring

    In mathematics a quotient ring, also known as factor ring or residue class ring, is a construction in ring theory, quite similar to the factor groups of group theory and the quotient space s of linear algebra....
  • quotient space (linear algebra)
    Quotient space (linear algebra)

    In linear algebra, the quotient of a vector space V by a linear subspace N is a vector space obtained by "collapsing" N to zero. The space obtained is called a quotient space and is denoted V/N ....
  • quotient space
    Quotient space

    In topology and related areas of mathematics, a quotient space is, intuitively speaking, the result of identifying or "gluing together" certain points of a given space....
     of a topological space
    Topological space

    Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connected space, and Continuous function ....
  • quotient object
  • right quotient
    Right quotient

    The right quotient of a formal language with a formal language is the language consisting of strings w such that wx is in for some string x in ....
     and left quotient
    Left quotient

    If and are formal languages, then the left quotient of with is the language consisting of strings w such that xw is in for some string x in ....
     (operations on formal languages)


The quotient rule
Quotient rule

In calculus, the quotient rule is a method of finding the derivative of a function that is the quotient of two other functions for which derivatives exist....
 is a method for finding derivatives in calculus
Calculus

Calculus is a branch of mathematics that includes the study of limit , derivatives, integrals, and infinite series, and constitutes a major part of modern university education....
.

Quotients also come up in certain tests, like the IQ test, which stands for intelligence quotient
Intelligence quotient

An Intelligence Quotient or IQ is a score derived from one of several different standardized tests attempting to measure intelligence. The term "IQ," a calque of the German language Intelligenz-Quotient, was coined by the German psychologist William Stern in 1912 as a proposed method of scoring early modern children's intelligenc...
. In this case, your quotient is basically your score. In recent decades, as people begin to emphasize on full personal development, other similar quotients appeared. These include moral
Moral

A moral is a message conveyed or a lesson to be learned from a story or event. The moral may be left to the hearer, reader or viewer to determine for themselves, or may be explicitly encapsulated in a maxim....
 quotient, emotional quotient, adversity
Adversity

Sorry, no overview for this topic
 quotient, creativity
Creativity

Creativity is a mental and social process involving the generation of new ideas or concepts, or new associations of the creative mind between existing ideas or concepts....
 quotient, etc.

See also

  • Ratio
    Ratio

    A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities, but in theory any number of quantities can be compared....