Multiplication
Pronunciation: /ˌmʌl.tɪ.plɪˈkeɪ.ʃən/ Explain
Multiplication is a shortcut for repeated
addition.^{[2][3]} For example,
2 · 3 means add 2 to itself
3 times (2 · 3 = 6 = 2 + 2 + 2).
Multiplication of integers is often
represented
by rows of dots. For example, we can represent 2 · 3
with 3 rows of 2 dots.

Figure 1: Representation of 2·3 
Properties of Multiplication
Commutative Property of Multiplication
The commutative property of multiplication
states that a · b = b
· a for any
real numbers
a and b.
Associative Property of Multiplication
The associative property of multiplication
states that if multiple numbers are multiplied together, it doesn't matter in which
order they are multiplied. Stated algebraically:
(a · b) · c =
a · (b · c).
Property of Multiplying by 1
The property of multiplying by 1
states that any number multiplied by 1 remains the same. Stated
algebraically: 1 · a = a.
Property of Multiplying by 0
The property of multiplying by 0
states that any number multiplied by 0 is
0. Stated algebraically:
0 · a = 0.
References
 McAdams, David E.. All Math Words Dictionary, multiplication. 2nd Classroom edition 201501084799968. pg 120. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Fine, Henry B., Ph. D.. NumberSystem of Algebra Treated Theoretically and Historically. 2nd edition. pg 5. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 9/2/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920pdf#page/n14/mode/1up/search/multiplication. Buy the book
 Keigwin, H. W.. Principles of Elementary Algebra. pp 911. www.archive.org. Ginn & Company. 1886. Last Accessed 9/2/2018. http://www.archive.org/stream/principlesofelem00dupurich#page/9/mode/1up/search/multiplication. Buy the book
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 2. www.archive.org. International Textbook Company. January 1963. Last Accessed 9/2/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 5859. Thomson, Brooks/Cole. 2005. Last Accessed 9/2/2018. Buy the book
More Information
 McAdams, David E.. Multiplicative Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/m/multiplicativeinverse.html.
Educator Resources
 Math Chase. mathchase.com. 4/5/2019. https://www.mathschase.com/.
Cite this article as:
McAdams, David E. Multiplication. 4/25/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/multiplication.html.
Image Credits
Revision History
4/25/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
9/4/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
12/19/2009: Added "References". (
McAdams, David E.)
12/18/2009: Added revision. (
McAdams, David E.)
3/22/2008: Changed More Information to current standard. Added more properties of multiplication (
McAdams, David E.)
1/17/2008: Initial version. (
McAdams, David E.)