# 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

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

McAdams, David E. Distributive Property of Multiplication Over Addition and Subtraction. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/distributiveprop.html.

### 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.)