Multiplication
Pronunciation: /ˌmʌl tə plɪˈkeɪ ʃən/ ?
Multiplication is a shortcut for repeated addition.^{[1][2]} For example,
2·3 means add 2 to itself
3 times (2·3 = 6 = 2+2+2).
Multiplication of integers is often
represented
by rows of dots. For example, we can represent 2·3
with 3 rows of 2 dots.

Figure 1: Representation of 2·3 
Properties of Multiplication
Commutative Property of Multiplication
The commutative property of multiplication
states that a·b = b·a for any
real numbers
a and b.
Associative Property of Multiplication
The associative property of multiplication
states that if multiple
numbers are multiplied together, it doesn't matter in which order they are multiplied. Stated
algebraically: (a·b)·c = a·(b·c).
Property of Multiplying by 1
The property of multiplying by 1 states that
any number multiplied by 1 remains the same. Stated
algebraically: 1·a = a.
Property of Multiplying by 0
The property of multiplying by 0 states that
any number multiplied by 0 is 0.
Stated algebraically: 0·a = 0.
References
 Fine, Henry B., Ph. D.. NumberSystem of Algebra Treated Theoretically and Historically, 2nd edition, pg 5. D. C. Heath & Co., Boston, U.S.A., 1907. (Accessed: 20091219). http://www.archive.org/stream/thenumbersystemo17920gut/17920pdf#page/n14/mode/1up/search/multiplication.
 Keigwin, H. W.. Principles of Elementary Algebra, pp 911. Ginn & Company, 1886. (Accessed: 20100112). http://www.archive.org/stream/principlesofelem00dupurich#page/9/mode/1up/search/multiplication.
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pg 2. International Textbook Company, January 1963. (Accessed: 20100112). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 5859. Thomson, Brooks/Cole, 2005.
More Information
 McAdams, David. Multiplicative Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 20090312. http://www.allmathwords.org/article.aspx?lang=en&id=Multiplicative%20Inverse.
 McAdams, David. Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 20090312. http://www.allmathwords.org/article.aspx?lang=en&id=Inverse%20of%20an%20Operation.
 McAdams, David. Identity. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 20090312. http://www.allmathwords.org/article.aspx?lang=en&id=Identity.
Cite this article as:
Multiplication. 20091219. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/multiplication.html.
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Revision History
20091219: Added "References" (
McAdams, David.)
20091218: Added revision (
McAdams, David.)
20080322: Changed More Information to current standard. Added more properties of multiplication (
McAdams, David.)
20080117: Initial version (
McAdams, David.)