[kstrauser]

The disconnect is that a lot of people mentally treat implicit multiplication with a higher priority than explicit, which is pretty understandable. For instance:

  1/3x

is likely to be understood as 1/(3*x), because otherwise it would’ve been written like x/3. If that’s true, then so surely

  1/3(x) 

should be the same, right?

Smarter people than I have argued both sides of this, and I don’t have a strong opinion except to use parentheses if there’s any possible ambiguity. Just saying, I totally understand why you’d come to that conclusion, and I probably would too.

[spsful]

The part that confuses me is why someone would think the SpeedCrunch implementation is correct:

Say again that you have 1/3x. This is implicitly stating 1/3x. However, no parenthesis are used, and multiplication & division are on the same level in the order of operations, so the expression gets evaluated sequentially from left to right.

If you have 1/3(9.8), evaluating the parenthesis gives you 9.8. So you now have 1/39.8. The expression inside the parenthesis gets evaluated first, then the final result is just multiplied by whatever precedes or succeeds the parenthetical if no other term is given. So 1/3+(9.8) would obviously evaluate to be 1/3+9.8.

Again, if the parenthesis aren't enclosing operations within themselves, then they shouldn't modify the way you'd evaluate the expression. I've had this problem with SpeedCrunch many times over and wish they would update it. Still the best desktop calculator IMO.

edit: a word

[zestyping]

Implied multiplication (with no operator) has a higher precedence than explicit multiplication (with an operator). Most mathematicians see it this way.

[bee_rider]

Really though, order of operations is just a convention. Practically, I'd think of PEMDAS as descriptive rather than proscriptive (nobody is going to revoke your math license if you and your friends violate PEMDAS together). Frequent topics of debate or confusion seem to indicate a edge case in the living convention. Therefore, I think you are smarter than either of the debaters if you stick with the parentheses.

[danbruc]

I would be confused if 1/2gt^2 would mean anything but 1/2 g t^2 and 0.5 g t^2. 1/3x in isolation may look a bit unusual, but with context the choice between 1/3 x and x / 3 may actually convey additional information, information about the structure of the calculation. Manipulating an equation into some kind of normal form may lose information.