Grar, stop arguing over which end to crack your eggs.
The standard is that multiplication/division have same precedence, and are done left to right. Similarly for addition and subtraction.
However, some people drop parentheses around the divisor as short-hand, and others simply get it wrong.
The practical effect is that you should never write an expression like 1/2x unless you are sure it won't generate any confusion -- e.g. if you can be certain your audience will infer from context whether you mean (1/2)x or 1/(2x).
Sometimes, you will face an author/teacher who uses the standard convention. If you prefer a different convention, then you're going to have to learn to read the wrong convention, and avoid writing anything that would be different amongst the two conventions.
The same advice applies to someone who prefers the standard convention, but is faced with a book/teacher that uses a different one.
There's a general style guideline here -- if there is a reasonable chance of ambiguity, use parentheses.
For the record, on more than one occasion, I've seen a student who doesn't put parenthesis around divisors make arithmetic mistakes because he wrote an expression intending some operation to happen in the divisor, but later read the expression differently (and others make mistakes in the other direction). So I pretty much always insist on parentheses, no matter what convention the student wants to use.
