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A way of combining two numbers to obtain a third; symbolized by ×, ., or merely the juxtaposition of the numbers (where suitable). Where x (the multiplicand) and y are natural numbers, x × y is commutative and defined by x + x + ... + x, the number x appearing y times (see addition).

For multiplication of negative integers, such as (-x) and (-y), (-x).y = x.(-y) = -(x.y); and (-x).(y) = x.y. Multiplication of any number by 0 (see zero) is defined to give the product 0. Fractions may be multiplied by simple extension of the system. The inverse operation of multiplication is division, since x/y = x.(1/y). In cases other than with real numbers, multiplication must be independently defined (see complex number).

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