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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 ...
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 ...
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. [ 1][ 2][ 3] Let , where both f and g are differentiable and The quotient rule states that the derivative of h(x) is. It is provable in many ways by using other derivative rules .
Quotient (universal algebra) In mathematics, a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation . Quotient algebras are also called factor algebras. Here, the congruence relation must be an equivalence relation that is additionally compatible with all the operations of the algebra ...
The difference between two points, themselves, is known as their Delta (Δ P ), as is the difference in their function result, the particular notation being determined by the direction of formation: Backward difference: ∇F (P) = F (P) − F (P − ΔP). The general preference is the forward orientation, as F (P) is the base, to which ...
Quotient group. A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored out"). For example, the cyclic group of addition modulo n can be obtained from the group of integers ...
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 ...
Remainder. Integer division with remainder. In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient ( integer division ).