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
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... Ondieki received All-America accolades six times at Iowa State ... occasions, earning NCAA runner-up honors three times and third-place status three times ... His time broke the mark set by Richard Chelimo only five days earlier in Stockholm by over 9 seconds ...
... Reviewing the book for The Times, John Nicholson wrote it was "endearingly dotty", but doubted its commercial potential ... Austin MacCurtain of the Sunday Times reviewed the paperback edition in 1988, saying that it was "more of the same" as Hitchhiker's, and that the "cosmic romp is stretched thin ... finished it, I turned back to page one and read it straight through again – the only time I have ever done that, and I wrote to tell him so ...
Famous quotes containing the word times:
“Were not all her life but storm,
Would not painters paint a form
Of such noble times ...”
—William Butler Yeats (18651939)
“There are three times in a mans life when he has the right to yell at the moonwhen he marries; when his children come; and when he finishes a job he had to be crazy to start.”
—Borden Chase [Frank Fowler] (19001971)
“I will soon be going out to shape all the singing tomorrows.”
—Gabriel Péri, French Communist leader. Letter, July 1942, written shortly before his execution by the Germans. Quoted in New York Times (April 11, 1943)