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In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced / ˈ k w oʊ ʃ ən t /) is a quantity produced by the division of two numbers. [1] The quotient has widespread use throughout mathematics.
The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of ...
2. Denotes a quotient structure. For example, quotient set, quotient group, quotient category, etc. 3. In number theory and field theory, / denotes a field extension, where F is an extension field of the field E. 4. In probability theory, denotes a conditional probability.
For example, the quotient / = can be conceived of as ... The math we need to know and do in grades preK–5 : concepts, skills, standards, and assessments (2nd ed.).
The process is begun by dividing the left-most digit of the dividend by the divisor. 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 ...
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative; however, the usual representative is the least positive residue, the smallest non-negative integer that belongs to that class (i.e., the remainder of the Euclidean division). [2]
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".