# Multiplication

Pronunciation: /ˌmʌl.tɪ.plɪˈkeɪ.ʃən/ Explain

Multiplication is a shortcut for repeated addition. 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.

1. McAdams, David E.. All Math Words Dictionary, multiplication. 2nd Classroom edition 20150108-4799968. pg 120. 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 9/2/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n14/mode/1up/search/multiplication. Buy the book
3. Keigwin, H. W.. Principles of Elementary Algebra. pp 9-11. 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
4. 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
5. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 58-59. Thomson, Brooks/Cole. 2005. Last Accessed 9/2/2018. Buy the book

• McAdams, David E.. Multiplicative Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. https://www.allmathwords.org/en/m/multiplicativeinverse.html.

### Educator Resources

• Math Chase. mathchase.com. 4/5/2019. https://www.mathschase.com/.

McAdams, David E. Multiplication. 4/25/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/m/multiplication.html.

### 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.)