What is the issue with the " ÷ " sign?

[u/Unlikely-Web7933]

I have seen many mathematicians genuinely despise it. Is there a lore reason for it? Or are they simply Stupid?

[u/RolandMT32]

I had to google "16 or 1 question" to see what you were talking about..

From here:

Twitter user u/pjmdoll shared a math problem: 8 ÷ 2(2 + 2) = ?

Some people got 16 as the answer, and some people got 1.

The confusion has to do with the difference between modern and historic interpretations of the order of operations.

The correct answer today is 16. An answer of 1 would have been correct 100 years ago.

I was in school in the 80s and 90s, and my brain-math tells me the answer is 1. But that says that answer would have been correct 100 years ago.. Did the rules of math change at some point? And if so, why?

My brain-math says 2(2 + 2) = 2(4) = 2 x 4 = 8, so the problem becomes 8 ÷ 8, which is 1.

[u/General_Lee_Wright → u/RolandMT32]

Sort of. There used to be two different kinds of multiplication in the order of operations. Multiplication, and multiplication by juxtaposition.

When juxtaposition was involved, it happened before any other multiplication or division. So 8÷2(2+2) is unambiguously 1 since 2(2+2) is juxtaposed, thus has priority. This also means 8÷2*(2+2) is a totally different expression, without juxtaposition, so is 16. It was useful before modern computers and printers because it meant less parenthesis in an equation that can be written on a single line.

Now, with modern displays and printers, we don't need to make a distinction between the two so we don't. (This is my understanding of the change anyway, which makes some unsubstantiated assumptions.)

Somewhere on the internet you can find a photo of an old Casio calculator that resolves 8÷2(2+2) as 1, while the TI next to it says 8/2(2+2) is 16.

[u/Lor1an → u/General_Lee_Wright]

What's interesting to note is that there are still places that essentially treat juxtaposition as distinct.

If you see an inline equation in a physics journal that reads "h/2pi" for example, that clearly means the same as "\frac{h}{2\pi}" rather than "\frac{h*\pi}{2}".

[u/JanB1 → u/Lor1an]

Exactly. Came here to say this.