Distributive Property of Multiplication Over Addition and Subtraction

Pronunciation: /dɪˈs trɪ byə tɪv ˈprɒp ər ti ʌv ˌmʌl tə plɪˈkeɪ ʃən ˈoʊ vər əˈdɪʃ ən ənd səbˈtræk ʃən/ ?

The distributive property of multiplication over addition and subtraction states that a(b + c) = ab + ac.[1] This property holds for real numbers and complex numbers. Click on the blue points in Manipulative 1 and drag them to change the figure.

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Manipulative 1: Distributive Property


  1. distributive property. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-24). http://www.merriam-webster.com/dictionary/distributive property.
  2. 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/distributive.
  3. Jones, Burton. Elementary Concepts of Mathematics, pp 38-41. MacMillan and Company, 1947. (Accessed: 2010-01-12). http://www.archive.org/stream/elementaryconcep029487mbp#page/n59/mode/1up/search/distributive.
  4. Keigwin, H. W.. Principles of Elementary Algebra, pg 7. Ginn & Company, 1886. (Accessed: 2010-01-12). http://www.archive.org/stream/principlesofelem00dupurich#page/7/mode/1up.
  5. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pg 3. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.

More Information

  • McAdams, David. Distributive Property. LifeIsAStoryProblem.org. Life is a Story Problem LLC. 2009-03-12. http://www.lifeisastoryproblem.org/algebra/distributive.html.
  • McAdams, David. Distribute. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-01-24. http://www.allmathwords.org/article.aspx?lang=en&id=Distribute.

Cite this article as:

Distributive Property of Multiplication Over Addition and Subtraction. 2010-01-24. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/distributiveprop.html.


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Revision History

2010-01-24: Added "References" (McAdams, David.)
2008-07-11: Add manipulative 1 (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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