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In mathematics, a quotient (from Latin: quotiens "how many times", pronounced ˈkwoʊʃənt) is the result of division. For example, when dividing 6 by 3, the quotient is 2, while 6 is called the dividend, and 3 the divisor. The quotient further is expressed as the number of times the divisor divides into the dividend, e.g., 3 divides 2 times into 6. A quotient can also mean the integer part of the result of dividing two integers. For example, the quotient of 13 divided by 5 would be 2 while the remainder would be 3. For more, see the Euclidean division.
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:
- quotient set
- quotient group
- quotient ring
- quotient module
- quotient space (linear algebra)
- quotient space of a topological space
- quotient object
- quotient category
- right quotient and left quotient (operations on formal languages)
- quotient type
Quotients also come up in certain tests, like the IQ or SAT test, which stands for intelligence quotient. In recent decades, as more emphasis has been placed on full personal development, other similar quotients have appeared. These include moral quotient, emotional quotient, adversity quotient, social quotient, creativity quotient, etc.