# 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:

The people of coming days will know
About the casting out of my net,
And how you have leaped times out of mind
Over the little silver cords,
And think that you were hard and unkind....
William Butler Yeats (1865–1939)

Why is it that we have enough memory to recollect the most minute circumstances of something that has happened to us, but not enough to remember how many times we have recounted them to the same person?
François, Duc De La Rochefoucauld (1613–1680)

It ought to be illegal for an artist to marry.... If the artist must marry let him find someone more interested in art, or his art, or the artist part of him, than in him. After which let them take tea together three times a week.
Ezra Pound (1885–1972)