Multiplication

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Multiplication (symbol "×") is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic (the others being addition, subtraction and division).

Because the result of scaling by whole numbers can be thought of as consisting of some number of copies of the original, whole-number products greater than 1 can be computed by repeated addition; for example, 3 multiplied by 4 (often said as "3 times 4") can be calculated by adding 4 copies of 3 together:

Here 3 and 4 are the "factors" and 12 is the "product".

There are differences amongst educationalists which number should normally be considered as the number of copies or whether multiplication should even be introduced as repeated addition.[1]

Multiplication of rational numbers (fractions) and real numbers is defined by systematic generalization of this basic idea.

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 (for numbers generally). The area of a rectangle does not depend on which side is measured first which illustrates that the order in which numbers are multiplied together does not matter.

In general the result of multiplying two measurements gives a result of a new type depending on the measurements. For instance:

The inverse of multiplication is division: as 3 times 4 is equal to 12, so 12 divided by 3 is equal to 4.

Multiplication is generalized further to other types of numbers (such as complex numbers) and to more abstract constructs such as matrices. For these more abstract constructs, the order in which the operands are multiplied sometimes does matter.

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