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/ Explain

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 the figure and drag them to change the figure.

What happens if c is zero?
Manipulative 1 - Distributive Property of Multiplication Over Addition and Subtraction Created with GeoGebra.


  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 8/6/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n14/mode/1up/search/distributive. Buy the book
  2. Jones, Burton. Elementary Concepts of Mathematics. pp 38-41. www.archive.org. MacMillan and Company. 1947. Last Accessed 8/6/2018. http://www.archive.org/stream/elementaryconcep029487mbp#page/n59/mode/1up/search/distributive. Buy the book
  3. Keigwin, H. W.. Principles of Elementary Algebra. pg 7. www.archive.org. Ginn & Company. 1886. Last Accessed 8/6/2018. http://www.archive.org/stream/principlesofelem00dupurich#page/7/mode/1up. Buy the book
  4. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 3. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/6/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book

More Information

  • McAdams, David E.. Distributive Property. lifeisastoryproblem.com. Life is a Story Problem LLC. 3/12/2009. http://www.lifeisastoryproblem.com/algebra/distributive.html.

Cite this article as:

McAdams, David E. Distributive Property of Multiplication Over Addition and Subtraction. 7/4/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/distributiveprop.html.

Image Credits

Revision History

7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/24/2010: Added "References". (McAdams, David E.)
7/11/2008: Add manipulative 1. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License