# Zero Sum

Pronunciation: /ˈzɪər.oʊ sʌm/ Explain
1. A zero sum is made by adding a value and its additive inverse. Zero sums are used in canceling while simplifying.

Canceling Using a Zero Sum
StepEquationDescription
1x + 3 = 5 This is the equation to simplify.
2x + 3 - 3 = 5 - 3 Subtract 3 from both sides. The 3 - 3 on the left side of the equation is a zero sum.
3x + 0 = 2 Simplify the constant terms
4x = 2 Apply the additive property of zero to transform x + 0 to x. This is the solution.

2. In game theory, a zero sum game is a game where the gains of one player must be offset by the losses of other players. See Zero sum game in Wikipedia Encyclopedia.

### References

1. McAdams, David E.. All Math Words Dictionary, zero sum. 2nd Classroom edition 20150108-4799968. pg 192. Life is a Story Problem LLC. January 8, 2015. Buy the book

McAdams, David E. Zero Sum. 5/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/z/zerosum.html.

### Revision History

5/13/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/28/2009: Changed example from paragraph to table. (McAdams, David E.)
12/24/2008: Initial version. (McAdams, David E.)

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