Date: May 17, 1995 10:46 PM
Author: Karen Dee Michalowicz
Subject: Re: order of operations, history
I have been looking at the history of orders of operations.
One source, Florian Cajori's A History of Mathematical
Notations, talks about the discussion in America at the turn of
the century about expressions where there is both a division
and multiplication. In fact, his book, first printed in l929,
says "If an arithemetical or algebraical term contains division
and multiplication, there is at present no agreement as to
which sign shall be used first...Other textbook writers direct
that multiplications in any order be performed first, the
divisions as they occur from left to right (ref.Slaught and
Lennes, High School Algebra, E.ementary Course, Boston l907).
The term a/bxb is interpreted (in Fisher's Text-Book of
Albegra, l898) as (a/b)xb. An English committee (The Report of
the Comittee on the Teaching of Arithmetic in Public Schools,
l917) recommends the use of brackets to avoid ambuiguity in
So, I find that a general consensus on the order of operations
on numbers was still developing 65 years ago.
Cajori's book has a wealth of information about mathematical
notation which I find very interesting. I got it and many
other of my math history books "for a song" from Dover
Math History Lives!
Karen Dee Michalowicz VQUEST Math Lead Teacher/Trainer
Upper School Mathematics Chair Virginia Quality Education
The Langley School in Sciences and Technology
1411 Balls Hill Rd, McLean, VA
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Fax: (703) 790-9712 --or-- KarenDM@aol.com