Distributive Property of Multiplication Over Addition and Subtraction

Pronunciation: /dɪsˈtrɪ.bjə.tɪv ˈprɒp.ər.ti ʌv ˌmʌl.tə.plɪˈkeɪ.ʃən ˈoʊ.vər əˈdɪ.ʃən ənd səbˈtræk.ʃən/ Explain

The distributive property of multiplication over addition and subtraction states that a(b + c) = ab + ac.^[2] 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.

References

1. McAdams, David E.. All Math Words Dictionary, distributive property of multiplication over addition and subtraction. 2nd Classroom edition 20150108-4799968. pg 64. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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 7/3/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n14/mode/1up/search/distributive. Buy the book
3. Jones, Burton. Elementary Concepts of Mathematics. pp 38-41. www.archive.org. MacMillan and Company. 1947. Last Accessed 7/3/2018. http://www.archive.org/stream/elementaryconcep029487mbp#page/n59/mode/1up/search/distributive. Buy the book
4. Keigwin, H. W.. Principles of Elementary Algebra. pg 7. www.archive.org. Ginn & Company. 1886. Last Accessed 7/3/2018. http://www.archive.org/stream/principlesofelem00dupurich#page/7/mode/1up. Buy the book
5. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 3. www.archive.org. International Textbook Company. January 1963. Last Accessed 7/3/2018. 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. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/d/distributiveprop.html.

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 LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/20/2019: Updated equations and expressions to the new format (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
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.)