Inversely Proportional

Pronunciation: /ɪnˈvɜr sli prə-ˈpȯr-sh nə1/ ?

Two variables are inversely proportional if the multiplicative inverse of one has a common ratio with the other. A general equation for variables that are inversely proportional is
y=a/x.
In this equation x and y are the variables that are inversely proportional. a is the constant of variation.

An example of variables that are inversely proportional is the time it takes to make a trip as a function of speed. The faster you go, the quicker (less time) you get there. This can be expressed with the function
t(s)=100/s
where t(s) is the time it takes to make the trip, 100 is the distance, and s is the speed of travel.

References

  1. inversely proportional. merriam-webster.com. Merriam-Webster Online Dictionary. Merriam-Webster Online, 2010. (Accessed: 2010-03-02). http://www.merriam-webster.com/dictionary/inversely%20proportional.
  2. Davies, Charles. New Elementary Algebra : Embracing the First Principles of the Science, pp 274-275. Barnes & Burr, Publishers, 1864. (Accessed: 2010-03-02). http://www.archive.org/stream/newelementaryalg00daviiala#page/274/mode/1up/search/inversely.
  3. Underwood,Ralph S.; Nelson,Thomas R.; Selby,Samuel.. Intermediate Algebra, pp 218-219. The Macmillan Company, 1947. (Accessed: 2010-03-02). http://www.archive.org/stream/intermediatealge033585mbp#page/n219/mode/1up/search/inversely.
  4. Rong Yang. A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra 1, revised edition, pg 269. A-Plus Notes Learning Center, January 1, 2006.

More Information

  • McAdams, David. Proportional. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Proportional.

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Inversely Proportional. 2010-03-02. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/inverselyproportional.html.

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Revision History


2010-03-02: Added "References" (McAdams, David.)
2008-08-13: Added general equation for inverse proportion. Changed equation t(s)=100/s to hot_eqn. Added vocabulary link for 'multiplicative inverse' (McAdams, David.)
2008-07-07: Corrected link errors. Corrected spelling (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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