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 such cases."
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 Publications. --
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 22012 USA 703-356-1920(w) E-Mail: firstname.lastname@example.org Fax: (703) 790-9712 --or-- KarenDM@aol.com