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Multiplication

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Revision as of 15:12, 29 November 2008 by Mirzhan Irkegulov (Talk | contribs) (New page: {{subpages}} '''Multiplication''' is the binary mathematical operation of scaling one number or quantity by another (multiplying). It is one of the four basic operations in elementary arit...)

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Multiplication is the binary mathematical operation of scaling one number or quantity by another (multiplying). It is one of the four basic operations in elementary arithmetic (with addition, subtraction and division). A result of this operation is called product and the multiplied numbers are called factors. Multiplication is defined in terms of repeated addition: for example, 2 multiplied by 3 (often said as "2 times 3") is the same as adding 3 copies of 2: 2 × 3 = 2 + 2 + 2.

Multiplication can be visualised as counting objects arranged in a rectangle (for natural numbers) or as finding the area of a rectangle whose sides have given lengths (for numbers generally). The inverse of multiplication is division: as 2 times 3 equals to 6, so 6 divided by 3 equals to 2.

Multiplication is generalized further to other types of numbers (such as complex numbers) and to more abstract constructs such as matrices, groups, sets and tensors.

Properties

Commutativity

Multiplication is commutative, meaning a × b = b × a.

Associativity

Multiplication is associativity, meaning a × (b × c) = (a × b) × c.

Distributivity

Multiplication is distributivity, meaning a × (x + y) = a × x + a × y.