Not quite, the Multiplication/Division and Addition/Subtraction come in the order they appear. The only reason division comes first in this particular scenario is because it actually appears to the left of the multiplication.
FWIW, as a PhD student in math, I agree entirely. Realistically you'll confuse people with the sort of expression above so you should just use extra brackets, but the common convention does cover this case and gives 9, not 1.
The time you enjoy wasting is not wasted time. Bertrand Russell