**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.

Read more about Times: Notation and Terminology, Computation, Products of Measurements, Properties, Axioms, Multiplication With Set Theory, Multiplication in Group Theory, Multiplication of Different Kinds of Numbers, Exponentiation, See Also

### Famous quotes containing the word times:

“Today we all speak, if not the same tongue, the same universal language. There is no one center, and time has lost its former coherence: East and West, yesterday and tomorrow exist as a confused jumble in each one of us. Different *times* and different spaces are combined in a here and now that is everywhere at once.”

—Octavio Paz (b. 1914)

“When General Motors has to go to the bathroom ten *times* a day, the whole country’s ready to let go. You heard of that market crash in ‘29? I predicted that.... I was nursing a director of General Motors. Kidney ailment, they said; nerves, I said. Then I asked myself, “What’s General Motors got to be nervous about?” “Overproduction,” I says. “Collapse.””

—John Michael Hayes (b. 1919)

“It is the mark of a mean, vulgar and ignoble spirit to dwell on the thought of food before meal *times* or worse to dwell on it afterwards, to discuss it and wallow in the remembered pleasures of every mouthful. Those whose minds dwell before dinner on the spit, and after on the dishes, are fit only to be scullions.”

—Francis De Sales, Saint (1567–1622)