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In [[mathematics]], a '''quotient''' (from {{lang-lat|quotient}}) is the result of [[division (mathematics)|division]].<ref>http://dictionary.reference.com/browse/quotient</ref> For example, when dividing 6 by 3, the quotient is 2, while 6 is called the [[division (mathematics)|dividend]], and 3 the [[divisor]]. The quotient further is expressed as the number of times the divisor divides into the dividend, e.g. 3 |
In [[mathematics]], a '''quotient''' (from {{lang-lat|quotient}}) is the result of [[division (mathematics)|division]].<ref>http://dictionary.reference.com/browse/quotient</ref> For example, when dividing 6 by 3, the quotient is 2, while 6 is called the [[division (mathematics)|dividend]], and 3 the [[divisor]]. The quotient further is expressed as the number of times the divisor divides into the dividend, e.g. 3 d vdivides 2 times into 6. A quotient can also mean just the [[integer]] part of the result of dividing two integers. For example, the quotient of 13 and 5 would be 2 while the [[remainder]] would be 3. For more, see the [[division algorithm]]. |
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In more abstract branches of mathematics, the word ''quotient'' is often used to describe [[Set (mathematics)|sets]], [[Space (mathematics)|spaces]], or [[algebraic structure]]s whose elements are the [[equivalence class]]es of some [[equivalence relation]] on another set, space, or algebraic structure. See: |
In more abstract branches of mathematics, the word ''quotient'' is often used to describe [[Set (mathematics)|sets]], [[Space (mathematics)|spaces]], or [[algebraic structure]]s whose elements are the [[equivalence class]]es of some [[equivalence relation]] on another set, space, or algebraic structure. See: |
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Revision as of 09:13, 28 March 2012
In mathematics, a quotient (from Latin: quotient) is the result of division.[1] 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 d vdivides 2 times into 6. A quotient can also mean just the integer part of the result of dividing two integers. For example, the quotient of 13 and 5 would be 2 while the remainder would be 3. For more, see the division algorithm.
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)
The quotient rule is a method for finding derivatives in calculus.
Other meanings
Quotients also come up in certain tests, like the IQ 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.