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A rational number can be defined as the quotient of two integers (as long as the denominator is non-zero). A more detailed definition goes as follows: [10] A real number r is rational, if and only if it can be expressed as a quotient of two integers with a nonzero denominator. A real number that is not rational is irrational.
The quotient group is the same idea, although one ends up with a group for a final answer instead of a number because groups have more structure than an arbitrary collection of objects: in the quotient / , the group structure is used to form a natural "regrouping".
In mathematics, a quotient category is a category obtained from another category by identifying sets of morphisms. Formally, it is a quotient object in the category of (locally small) categories, analogous to a quotient group or quotient space, but in the categorical setting.
In general, a quotient = /, where Q, N, and D are integers or rational numbers, can be conceived of in either of 2 ways: Quotition: "How many parts of size D must be added to get a sum of N?" = = + + + ⏟.
In mathematics, a Q-category or almost quotient category [1] is a category that is a "milder version of a Grothendieck site." [2] A Q-category is a coreflective subcategory. [1] [clarification needed] The Q stands for a quotient. The concept of Q-categories was introduced by Alexander Rosenberg in 1988. [2]
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.
An intelligence quotient (IQ) is a total score derived from a set of standardized tests or subtests designed to assess human intelligence. [1] Originally, IQ was a score obtained by dividing a person's mental age score, obtained by administering an intelligence test, by the person's chronological age, both expressed in terms of years and months.
The quotient (rounded down to an integer) becomes the first digit of the result, and the remainder is calculated (this step is notated as a subtraction). This remainder carries forward when the process is repeated on the following digit of the dividend (notated as 'bringing down' the next digit to the remainder).