Times

Times

Multiplication (often denoted by the cross 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".

Educators differ as to which number should normally be considered as the number of copies, and whether multiplication should even be introduced as repeated addition. For example 3 multiplied by 4 can also be calculated by adding 3 copies of 4 together:

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 you measure first, which illustrates that the order numbers are multiplied together in doesn't matter.

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

The inverse operation of multiplication is division. For example, 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.

Multiplication is also defined for other types of numbers (such as complex numbers), and for more abstract constructs such as matrices. For these more abstract constructs, the order that the operands are multiplied in sometimes does matter.

Famous quotes containing the word times:

“In former times and in less complex societies, children could find their way into the adult world by watching workers and perhaps giving them a hand; by lingering at the general store long enough to chat with, and overhear conversations of, adults...; by sharing and participating in the tasks of family and community that were necessary to survival. They were in, and of, the adult world while yet sensing themselves apart as children.”
—Dorothy H. Cohen (20th century)

“History by apprising them [students] of the past will enable them to judge of the future; it will avail them of the experience of other times and other nations; it will qualify them as judges of the actions and designs of men; it will enable them to know ambition under every disguise it may assume; and knowing it, to defeat its views.”
—Thomas Jefferson (1743–1826)

“There is no difference between the client and the prostitute. If a man goes to a prostitute, he is also a prostitute.”
—Sister Michele, Indian nun. As quoted in the New York Times Magazine, p. 35 (January 16, 1994)