In mathematics, a quotient is the end result of a division problem. For example, in the problem 6 ÷ 3, the quotient would be 2, while 6 would be called the dividend, and 3 the divisor. The quotient can also be expressed as the number of times the divisor divides into the dividend. Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ... 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. ...

A quotient can also mean just the integral part of the result of dividing two integers. For example, the quotient of 13 ÷ 5 would be 2 while the remainder would be 3. For more, see the division algorithm. In calculus, the integral of a function is an extension of the concept of a sum. ... The integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3, ...) and the number zero. ... In mathematics, the result of the division of two integers usually cannot be expressed with an integer quotient, unless a remainder —an amount left over— is also acknowledged. ... The division algorithm is a theorem in mathematics which precisely expresses the outcome of the usual process of division of integers. ...

In more abstract branches of mathematics, the word quotient is often used to describe sets, spaces, or algebraic structures whose elements are the equivalence classes of some equivalence relation on another set, space, or algebraic structure. See: In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ... In universal algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. ... 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: [a] = { x ∈ X | x ~ a } The notion of equivalence classes is useful for constructing sets out... In mathematics, an equivalence relation, denoted by an infix ~, is a binary relation on a set X that is reflexive, symmetric, and transitive. ...

• quotient set
• quotient group
• quotient ring
• quotient space (linear algebra)
• quotient space of a topological space
• quotient object
• right quotient and left quotient (operations on formal languages)

The quotient rule is a method for finding derivatives in calculus. 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: [a] = { x in X | x ~ a } The notion of equivalence classes is useful for constructing sets... 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. ... In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring which generalizes important properties of integers. ... In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by collapsing N to zero. ... In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or gluing together certain points of a given space. ... Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. ... In category theory, there is a general definition of subobject extending the idea of subset and subgroup. ... If and are formal languages, then the right quotient of with is the language consisting of strings w such that wx is in for some string x in . ... 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 . ... In mathematics, logic and computer science, a formal language is a set of finite-length words (i. ... 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. ... In mathematics, the derivative of a function is one of the two central concepts of calculus. ... Calculus is the name given to a group of systematic methods of calculation, computation, and analysis in mathematics which use a common and specialized algebraic notation. ...

Quotients also come up in certain tests, like the IQ test, which stands for intelligence quotient. 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 quotient, emotional quotient, adversity quotient, creativity quotient, etc. IQ redirects here; for other uses of that term, see IQ (disambiguation). ... IQ tests are designed to give approximately this Gaussian distribution. ... The expression emotional intelligence or EI indicates a kind of intelligence or skill that involves the ability to perceive, assess and positively influence ones own and other peoples emotions. ...