Associative Property of Addition

Pronunciation: /əˈsoʊ siˌeɪ tɪv ˈprɒp ər ti ʌv əˈdɪ ʃən/ ?

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

One way to remember the associative property of addition is to use the root word, 'associate'. So in the associative property of addition, 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 addition using dots is:

Associative property of addition - two dots plus
    ( three dots plus four dots ) add up to
    9, which is the same as ( two dots plus three dots ) plus four dots which also add up to nine.
Figure 1: 3+(2+4) = (3+2)+4 = 9.

Manipulative 1 contains a representation of the associative property of addition that uses the length of a line segment to represent each number. Notice that when the three segments are placed end to end, it doesn't matter which comes first, the total size is the same. Click on the end points and drag them to change the manipulative.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
Manipulative 1: Associative property of addition. Created with GeoGebra.

The associative property of addition holds for real numbers, complex numbers, matrices of real and complex numbers, and vectors. Click on the points in manipulative 1 and drag them to change the figure.

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 LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Associative.

Cite this article as:


Associative Property of Addition. 2009-12-19. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/associativeaddition.html.

Translations

Image Credits

Revision History


2009-12-19: Added "References" (McAdams, David.)
2008-10-27: Change manipulative from sketchpad to geogebra (McAdams, David.)
2008-06-16: Added 'Associative' to More Info (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License