- 1: the act or process of multiplying : the state of being multiplied
- 2.a : a mathematical operation that at its simplest is an abbreviated process of adding an integer to itself a specified number of times and that is extended to other numbers in accordance with laws that are valid for integers
- b : any of various mathematical operations that are analogous in some way to multiplication of the real numbers but are defined for other or larger sets of elements (as complex numbers, vectors, matrices, or functions)
Multiplication (often denoted by the cross symbol "×", by a point "·" or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition[, [https://en.wikipedia.org/wiki/Subtraction subtraction and division.
For example, 3 multiplied by 4 (often said as "3 times 4") can be calculated by adding 3 copies of 4 together:
Here 3 and 4 are the "factors" and 12 is the "product".
One of the main properties of multiplication is the commutative property, adding 3 copies of 4 gives the same result as adding 4 copies of 3:
Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property.
The inverse operation of the multiplication is the division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since the division of a number other than 0 by itself equals 1).
Multiplication is also defined for other types of numbers, such as complex numbers, and more abstract constructs, like matrices. For these more abstract constructs, the order that the operands are multiplied sometimes does matter.