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 Recipricals and Division
Name: stephanie
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: N/A 

Why do we have to use reciprocals in dividing fractions?

At first glance this question, "Why do we use reciprocals in division?" seems rather trivial. However, after some reflection, the question really raises two very fundamental concepts: "What are 'numbers'?" and "What are 'mathematical operations'?" Consequently, to answer the question properly, the definition of these terms must be laid out precisely.

To do this it was necessary to append my answer in a "msworks" document because e-mail does not give the necessary flexibility of choices of letters and characters needed.

It's a little spooky, I had a very similar question asked of me on a take-home exam in freshman calculus many years ago!

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 (, or at Argonne's Educational Programs

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

Argonne National Laboratory