Why a Negative Number Times a Negative Number Equals a Positive Number

bernard beecher


One of the most mysterious mathematical topics taught in any elementary mathematics classroom is the concept that a negative time a negative equal a positive. This fundamental mathematical idea is listed in most elementary algebra text books as a rule without any justification for the validity of the rule. In this paper, I will present numerous mathematical arguments that attempt to justify this concept.


Negative and Positive Numbers;

Full Text:



Bogomolny, A. (2015, March 3). Remarks on the history of complex numbers from interactive mathematics miscellany and puzzles. Retrieved from http://www.cut-the-knot.org/arithmetic/algebra/HistoricalRemarks.shtml.

Eves, H. (1983). Great moments in mathematics after 1650. MAA.

Frey, A. K. (2009 ). The negative. Retrieved from http://webspace.ship.edu/msrenault/.../Presentation%205%20Negatives.pdf

Kaufmann, J. (1992). Algebra with trigonometry for college students (3rd ed., p.6). Publisher: Brooks/Cole Publishing Company.

Kline, M. (1972). Mathematical thought from ancient to modern times (Vol.1). Oxford University Press.

Kline, M. (1972). Mathematical thought from ancient to modern times (Vol.2). Oxford University Press.

La Nave, F. (2012). Deductive narrative and epistemological function of belief in mathematics: On bombelli and imaginary numbers, in circles disturbed. In A. Doxiadis & B. Mazur (Eds.). Princeton University Press.

Lay, R. S. (2000). Analysis with an introduction to proof (3rd ed., p.95). Publisher: Prentice Hal.

Rajapakse, R. (2008 ). ISBN No: 0-9728657-2-1. Life and mathematics of brahamagupta; man who found zero, addition, subtraction, multiplication and division. Contact: rar321@gmail.com; fathersofmathematics.com/Brahamagupta.doc

Rogers, L. (2002 ). The history of Negative numbers; Stage: 3, 4 and 5. NRICH Headquarters: Centre for Mathematical Sciences; University of Cambridge
Wilberforce Road; Cambridge; CB3 0WA; nrich.maths.org/5961

Smith, D. E. (1968). History of mathematics. Dover

Smith, D. E. (1959). A source book in mathematics. Dover

Swetz, F. J. (1996). From five fingers to infinity, open court (3rd printing).

DOI: http://dx.doi.org/10.3968/6557

DOI (PDF): http://dx.doi.org/10.3968/pdf_13


  • There are currently no refbacks.

Copyright (c)

Share us to:   


If you have already registered in Journal A and plan to submit article(s) to Journal B, please click the "CATEGORIES", or "JOURNALS A-Z" on the right side of the "HOME".

We only use the follwoing mailboxes to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:

 Articles published in Progress in Applied Mathematics are licensed under Creative Commons Attribution 4.0 (CC-BY).


Address: 1020 Bouvier Street, Suite 400, Quebec City, Quebec, G2K 0K9, Canada.

Telephone: 1-514-558 6138
E-mail:office@cscanada.net office@cscanada.org caooc@hotmail.com

Copyright © 2010 Canadian Research & Development Center of Sciences and Cultures