In simple algebra, multiplication is the process of calculating the result when a number a is taken b times. The result of a multiplication is called the product of a and b, and each of the numbers a and b is called a factor of the product ab. Multiplication is denoted a×b, a·b, (a)(b), or simply ab. The symbol × is known as the multiplication sign. Normal multiplication is associative, commutative, and distributive.

More generally, multiplication can also be defined for other mathematical objects such as groups, matrices, sets, and tensors.

Karatsuba and Ofman (1962) discovered that multiplication of two n digit numbers can be done with a bit complexity of less than n^2 using an algorithm now known as Karatsuba multiplication.

Eddy Grant's pop song "Electric Avenue" (Electric Avenue, 2001) includes the commentary: "Who is to blame in one country; Never can get to the one; Dealin' in multiplication; And they still can't feed everyone, oh no."

See also

Addition, Bit Complexity, Complex Multiplication, Division, Factor, Karatsuba Multiplication, Long Multiplication, Matrix Multiplication, Multiplicand, Multiplier, Product, Russian Multiplication, Scalar Multiplication, Subtraction, Times

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Cundy, H. M. "What Is ×?" Math. Gaz. 43, 101, 1959.Karatsuba, A. and Ofman, Yu. "Multiplication of Many-Digital Numbers by Automatic Computers." Doklady Akad. Nauk SSSR 145, 293-294, 1962. Translation in Physics-Doklady 7, 595-596, 1963.

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Cite this as:

Weisstein, Eric W. "Multiplication." From MathWorld--A Wolfram Web Resource.

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