Multiplicative Inverse

Pronunciation: /ˈmʌl.tɪ.plɪˌkeɪ.tɪv ˈɪn.vɜrs/ Explain

The multiplicative inverse of r is a number r-1 such that r · r-1 = 1.[2] The number 1 is used here because it is the multiplicative identity.


The negative exponent is used to indicate division. So r-1 = 1/r, which indicates that r-1 is the multiplicative inverse of r. The reciprocal of a number is the same as the multiplicative inverse of a number.

Examples of multiplicative inverses:
5*(1/5)=1, 8*0.125=1, (3/5)*(5/3)=1, (1/10)*10=1, (a/b)*(b/a)=1, a^2b^(-2)*a^(-2)b^3=1


  1. McAdams, David E.. All Math Words Dictionary, multiplicative inverse. 2nd Classroom edition 20150108-4799968. pg 121. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 4-6. Last Accessed 9/2/2018. Buy the book

More Information

  • McAdams, David E.. Exponent. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009.

Cite this article as:

McAdams, David E. Multiplicative Inverse. 4/25/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

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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.)
3/22/2008: Changed More Information section to current standards. (McAdams, David E.)
8/10/2007: Initial version. (McAdams, David E.)

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