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division, fundamental operation in arithmetic; the inverse of multiplication. Division may be indicated by the symbol ÷, as in 15 ÷ 3, or simply by a fraction, 15/3. The number that is being divided, e.g. 15, is called the dividend and the number dividing into it, e.g. 3, the divisor. The result of division is called the quotient. If the dividend is an exact (integral) multiple of the divisor, then the division will be exact, the quotient being the factor by which the divisor must be multiplied to yield the dividend (in the above example the quotient 5 multiplied by the divisor 3 equals the dividend 15). If the dividend is not an exact multiple of the divisor there will be a remainder expressed as a fraction with the divisor as the denominator; e.g., 16/3 = 51/3, where 1/3 is the remainder. A division in which the divisor *b* is larger than the dividend *a* is simply indicated by the fraction *a/b,* with no actual operation being carried out. In terms of multiplication either of the symbols 1/*b* or *b*^{-1} is called the multiplicative inverse of *b* with the property that the product of a number and its inverse equals 1, or *b* · *b*^{-1} =1. The division of *a* by *b* is equivalent to the multiplication of *a* by the multiplicative inverse of *b,* i.e., *a* ÷ *b* = *a* · (1/*b*) = *a* · *b*^{-1}; for example, when *a* = 25 and *b* = 5, then 1/*b* = 1/5 and 25 ÷ 5 = 25 · (1/5) = 5.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

division, in taxonomy: see classification.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

(German *panzer*, “armoured”) Self-contained military unit of the German army, built around the capabilities of armoured vehicles. In World War II, it consisted of a tank brigade with four battalions; a motorized infantry brigade with four rifle battalions; an artillery regiment; and reconnaissance, antitank, and military-engineering battalions and service units. Germany had six panzer divisions in 1939 and 20 by 1941. It remains the principal offensive element of the German army.

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Specialization in the production process. Complex jobs can usually be less expensively completed by a large number of people each performing a small number of specialized tasks than by one person attempting to complete the entire job. The idea that specialization reduces costs, and thereby the price the consumer pays, is embedded in the principle of comparative advantage. Division of labour is the basic principle underlying the assembly line in mass production systems. *See* Émile Durkheim.

Learn more about division of labour with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Division may refer to:## See also

Processes:

- Cell division, the process in which biological cells multiply.
- Continental divide, the geographical term for separation between watersheds.
- Diairesis, Plato's method of definition by division.
- Division (fallacy), a fallacy of ambiguation in which one assumes that various parts have a property solely because the whole has that same property.
- Division (digital), digital implementation of mathematical division.
- Division (horticulture), a method of vegetative plant propagation, or the plants created by using this method.
- Division in relational algebra.
- Division (mathematics), an arithmetic operation that serves as the inverse of multiplication.
- Division (politics), the process of changing national borders or separating political entities.
- Division (vote), a manner by which the votes of legislators are recorded.
- Fair division, the problem of dividing a resource so recipients believe they have received a fair amount
- North-South divide, the geopolitical term for the division between wealthy nations and poor nations.
- Segmentation

Units/ Entities:

- Census division
- county constituency or a Parliamentary seat in the United Kingdom Parliament.
- Division (botany), a classification of plants or fungi (the botanical/mycological counterpart to zoology's phylum).
- Division (business), a separate named business operated as a part of an organization.
- Division (country subdivision), a name for a subsidiary state or prefecture of a country.
- Division (military), a unit typically consisting of between 10,000 to 20,000 troops.
- Division (naval), a unit typically consisting of two or four ships.
- Division (organisation), a subsidiary of a larger organisation.
- Division (sport), a group of compatible teams in organised sport who compete amongst themselves for a Divisional title.
- hundred (division) (a subpart of a former administrative unit in England and Wales.
- Police division, a large territorial unit (now often referred to as a Basic Command Unit) of the British police.

Music:

- A grouping of pipe ranks in a pipe organ, often with its own case, windchest, and keyboard
- Division (album), is the name of the 2008 album by 10 Years.
- Division (music) a specific type of ornamentation, most common in 17th century English music
- Division viol, an English Renaissance instrument
- Joy Division, an English rock band
- "÷" (often named "Division") is a song from Aly & AJ's third album Insomniatic

Miscellaneous:

- In nautical navigation the compass is called dividers.

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Last updated on Wednesday October 08, 2008 at 17:13:41 PDT (GMT -0700)

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Last updated on Wednesday October 08, 2008 at 17:13:41 PDT (GMT -0700)

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