Well, "subtraction before addition" still doesn't solve the problem of
whether 1-1-1 equals -1 or 1. Coming at the question from an academic
maths background, I'd say something like
"Minus and divide are not associative. So (a-b)-c != a-(b-c) and
similarly for division. Most people use the convention that equal
precedence operations are performed from left to right, so
a-b-c means (- (- a b) c), not (- a (- b c))
However, this is always a bit confusing and can get muddled when you
start manipulating complicated expressions. As a result, in order to
make sure that everyone understands you, it's generally best to use
brackets for anything more complicated than minus signs in front of
terms of a polynomial."
Then I'd say
"And, frankly, once you've spent five minutes thinking about it
(probably some time in your early teens), you understand what's going
on and get on with your life."
Unless you have the pleasure of teaching recalcitrant school
children. In which case, you have my sympathy.
Rupert
PS: In Britain, the mnemonic seems to be "BODMAS", standing for
Brackets, Other, Division, Multiplication, Addition,
Subtraction. "Other" is exponents and anything else, apparently.
(Function application?). I suspect that addition comes before
subtraction in this scheme because it starts with a vowel.
Everyone I have asked learned the mnemonic some time after learning
to do basic arithmetic.