when a negative sign follows a division sign, what is on the right hand side of the division sign? This is a bit of a dumb question (and not a very useful one either), but nonetheless:
I've been taught that grammatically, the negative sign is actually just negative one being multiplied with the number on its right. Thats why $-x^2$ is practically $(-1)\cdot(x^2)$ and not ($-1\cdot x)^{(2)}$.
But, by that logic, shouldn't $x/-y$ be $(x/-1)\cdot y$?
It's similar to the confusion of this question in that you'd normally see it written as a fraction. Does this kind of stuff really not get on anyone else's nerves?
 A: All you need to know is:


*

*$/$, ^ and $-$ are operators; the first two binary, the third unary.

*^ has the highest precedence, then comes $/$ and then $-$


Now the two expressions are unambiguous:


*

*$-x \text{^} 2 = - (x\text{^}2)$ because ^ has higher precedence

*$x\,/{-y} = x / (- y)$ because $-$ is an operator


You can then replace $-a$ by $(-1) * a$ if you want, once it has been made clear what the minus sign is applied to: $-x\text{^}2=(-1)*(x\text{^}2)$ and $x/{-y}=x/((-1)*y)$
A: Negative sign versus minus sign could be part of it. Also, a double division, is the equivalent to a multiplication under a fractions line ( can't remember the special name it has). so in your example we get ${x\over{-1\cdot y}}= {\big({x\over-1}\big )\over y}$
A: This is why computer programming languages (and scripting, too) have carefully designed lists of not just operator precedence but also operator associativity.
But we are human beings, or at least I am, and I assume you are, too. As human beings, we often make assumptions about what other human beings mean. If I write $$\frac{7}{-4},$$ would you think I actually meant $$\frac{7}{-1} \times 4?$$ That boils down to $-7 \times 4 = -28$, so if that's what I actually mean, it would make more sense for me to just go ahead and write the $-7$, not bother with the the $-1$, and go to the multiplication by 4.
So what I mean by the first expression is $$\frac{7}{-4} = \frac{-7}{4} = -\frac{7}{4} = -1.75.$$
Now I want you to try three things. First, open your browser's Javascript console (F12 on Firefox for Windows, then look for the Console button). Type in 7/-4, press Enter. It should respond -1.75. Then try the same thing on Wolfram Alpha. And think of a third way to have a computer do this calculation for you. In each case, the answer should be -1.75 or something like that.
If you look on the Mozilla Developer Network's page on Javascript operator precedence, you will see that "unary negation" is level 16 precedence with right-to-left associativity, while division is only level 14 precedence (the higher the number, the higher the priority).
Also notice that exponentiation is by itself on level 15 precedence. However, I got an error when I tried to put -2**3 on the Javascript console. I haven't checked this in the context of an actual script on an HTML document.
On Wolfram Alpha, -2^2 should give $-4$ for the result, and (-2)^2 should give 4. That's how it ought to be.
But we humans are frequently confused by that one. By comparison, $x/-y$ is a straightforward expression with no implied division by $-1$ to pull out of who knows where.
A: When one uses the horizontal fraction bar instead of the in-line diagonal one, the denominator is effectively in parentheses.
$$\frac{a}{bc}=a/(bc)\neq\frac{a}{b}\cdot c$$
Notice that if $\color{red}{\frac{a}{bc}=\frac ab\cdot c}$, then it would hold that $\color{red}{\frac{a}{bc}=\frac{ac}{b}}$.
Try this with $b=-1$ and $a$ and $c$ equal to numbers of your choice.
Also, it’s just universally understood that you cannot divide a number by the negative sign (but we usually parenthesize the denominator anyways).
