Associative Property of Multiplication

Pronunciation: /əˈsoʊ siˌeɪ tɪv ˈprɒp ər ti ʌv ˌmʌl tə plɪˈkeɪ ʃən/ ?

The associative property of multiplication states that, when multiplying three numbers, it does not matter in which order they are multiplied.[1] This is expressed by the equation: a·(b·c) = (a·b)·c.

One way to remember the associative property of multiplication is to use the root word, 'associate'. So in the associative property of multiplication, the variables 'b' and 'c' associate closely on one side of the equals, while 'a' and 'b' associate closely on the other side.

A representation of the associative property of multiplication using dots is:

Associative property of multiplication - two sets of ( three dots by four dots ) equals 24, which is the same as ( two dots by three dots ) by four dots which also equals 24.
Figure 1: 3·(2·4) = (3·2)·4 = 24.

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/associative.
  2. 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.

More Information

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

Cite this article as:
Associative Property of Multiplication. 2009-12-19. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/a/associativemultiplication.html.

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2009-12-19: Added "References" (McAdams, David.)
2008-06-24: Added caption to figure 1 (McAdams, David.)
2008-06-16: Initial version (McAdams, David.)

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