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

1. Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically, 2nd edition, pg 5. D. C. Heath & Co., Boston, U.S.A., 1907. (Accessed: 2009-12-19). http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n14/mode/1up/search/multiplication.
2. Keigwin, H. W.. Principles of Elementary Algebra, pp 9-11. Ginn & Company, 1886. (Accessed: 2010-01-12). http://www.archive.org/stream/principlesofelem00dupurich#page/9/mode/1up/search/multiplication.
3. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pg 2. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.
4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 58-59. Thomson, Brooks/Cole, 2005.

More Information

• McAdams, David. Multiplicative Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem.org. 2009-03-12. 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.org. 2009-03-12. 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.org. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Identity.

Cite this article as:

Multiplication. 2009-12-19. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/m/multiplication.html.

Translations

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Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem.org and are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Revision History

2009-12-19: Added "References" (McAdams, David.)
2009-12-18: Added revision (McAdams, David.)
2008-03-22: Changed More Information to current standard. Added more properties of multiplication (McAdams, David.)
2008-01-17: Initial version (McAdams, David.)