Multiplication

Pronunciation: /ˌmʌl tə plɪˈkeɪ ʃən/ Explain

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.

Three rows and two columns of 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

  1. Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically. 2nd edition. pg 5. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 12/19/2009. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n14/mode/1up/search/multiplication. Buy the book
  2. Keigwin, H. W.. Principles of Elementary Algebra. pp 9-11. www.archive.org. Ginn & Company. 1886. Last Accessed 1/12/2010. http://www.archive.org/stream/principlesofelem00dupurich#page/9/mode/1up/search/multiplication. Buy the book
  3. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 2. www.archive.org. International Textbook Company. January 1963. Last Accessed 1/12/2010. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
  4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 58-59. Thomson, Brooks/Cole. 2005. Buy the book

More Information

  • McAdams, David E.. Multiplicative Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/m/multiplicativeinverse.html.

Cite this article as:

McAdams, David E. Multiplication. 9/4/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/multiplication.html.

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Revision History

9/4/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
12/19/2009: Added "References". (McAdams, David E.)
12/18/2009: Added revision. (McAdams, David E.)
3/22/2008: Changed More Information to current standard. Added more properties of multiplication (McAdams, David E.)
1/17/2008: Initial version. (McAdams, David E.)

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