Aha, difficulty solved! I wasn’t aware that you thought the “O” in BODMAS stood for “Of” instead of “Orders” (which is the archaic form of “exponents”, although still used today when describing polynomials “of order n” where n is the highest power that occurs in the polynomial). If “Of” is to be read as a multiplication operator (as logic dictates it must) then it would be pointless to include it alongside “D” and “M” because all three are at the same precedence level.
'Luthon64
Indeed. Of course, after grade 8, we never, ever again saw problems with the “of” construct, so I cheerfully forgot about it, and order of operations was just never an issue again, until I got confronted by it once again in primary school materials! But it now seems I was quite simply fed completely false information by a high school teacher, way back in the early 14th century. Whatever else I teach my own students, I really must get this into their heads: never, ever, blindly believe a teacher. 
I wonder whether it was only my own high school though, or whether that crap was taught to an entire generation of students. I should ask around some teens of my acquaintance and find out whether they perhaps STILL teach it that way…
It looks like public opinion remains divided as to what the “O” in BODMAS stands for. What Does BODMAS stand for in Mathematics? | Yahoo Answers. So at some point the idea of “of” must have snuck in.
I recall my teacher applying the Brackets, Addition, Division, Angular Substitution and Simplification approach. 
r.
Hmm, yes, lots of people apparently think the O stands for “of”, so one must presume that at some point, this is what schools taught. One wonders how that happened. There may be a whole interesting book there. At least I got the right information eventually, even though my hair is graying, and despite my schooling.
At least I got the right information eventually, even though my hair is graying, and despite my schoolingYes sometimes I wonder that we actually survived. I had a German teacher who was quite adamant that the whole manned space satellites thing in the early 60's was a scam, but then again I had a brilliant Afrikaans and Math teacher (my math was abysmal)in Affies, Pretoria.