# multiplication

**multiplication,**fundamental operation in arithmetic and algebra. Multiplication by a whole number can be interpreted as successive addition. For example, a number

*N*multiplied by 3 is

*N*+

*N*+

*N.*In general, multiplying positive numbers

*N*and

*M*gives the area of the rectangle with sides

*N*and

*M.*The result of a multiplication is known as the product. Numbers that give a product when multiplied together are called factors of that product. The symbol of the operation is × or · and, in algebra, simple juxtaposition (e.g.,

*xy*means

*x*×

*y*or

*x*·

*y*). Like addition, multiplication, in arithmetic and elementary algebra, obeys the associative law, the commutative law, and, in combination with addition, the distributive law. Multiplication in abstract algebra, as between vectors or other mathematical objects, does not always obey these rules. Quantities with unlike units may sometimes be multiplied, resulting in such units as foot-pounds, gram-centimeters, and kilowatt-hours. See also division.

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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