Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Multiplication and Addition
Name: John W.
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: N/A 


Question:
I once asked my Calculus teacher if multiplication was just an advanced form of addition and he didn't seem to understand my meaning. What I mean couldn't you say multiplication is a simplification of addition? You either say two times three or add 3 twice or add 2 three times.



Replies:
Yes, multiplication is defined as sequential addition, and division is defined as sequential subtraction.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois


Perhaps a better way to word it is: Multiplication is a short-hand way to do multiple additions. If you want to add 8 to something, but you want to add it seven times, it is quicker to add 8x7 to that something. This becomes less easy to see when decimals, fractions, and algebra are considered. However, it is still there.

I complement you on realizing an attribute of multiplication missed by many students. It indicates a desire to understand rather than to simply repeat.

Kenneth Mellendorf


You are quite correct n*m is just (m+m+m+...m) n-times or \ (n+n+...+n) m-times. However, you have to be careful when the definition of multiplication is generalized to decimals and fractions. For example, what does 3*(2.71) mean?

Vince Calder



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory