Multiplicative Inverse

Pronunciation: /ˈmʌl tə plɪˌkeɪ tɪv ˈɪn vɜrs/ ?

The multiplicative inverse of r is a number r-1 such that r · r-1 = 1.[1] 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
  • a3b-2 · a-3b2 = 1

References

  1. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 4-6 (see reciprocal). International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.

More Information

  • McAdams, David. Exponent. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Exponent.
  • McAdams, David. Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Inverse%20of%20an%20Operation.
  • McAdams, David. Identity. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Identity.

Cite this article as:


Multiplicative Inverse. 2008-03-22. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/multiplicativeinverse.html.

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2008-03-22: Changed More Information section to current standards (McAdams, David.)
2007-08-10: Initial version (McAdams, David.)

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