Regarding the PEMDAS order of operations for math expressions, I’ve seen some sites claim that using ÷ has a precise meaning differing from the slash operator. True, or pulled out of someone’s burrow?
Anal nonsense.
OTOH, there is no international government stadards agency enforcing consistency either
This symbol is only used by elementary school students who haven’t tackled anything more advanced than basic arithmetic yet. It’s strictly for use in teaching division as its own standalone operation. Otherwise its main use is on calculators for clarity.
/ is available on every computer. ÷ is not without going deeper into character sets. Similar with * and ×, though that has the added difficulty of being confused with x.
Well, ÷ does have the difference that it means only one thing, while / is used for more than one purpose. If somebody types either/or, they aren’t trying to divide either by or. Of course usually context is enough to make the intended purpose obvious, but the difference does exist.
But the question has nothing to do with computers.
I agree, ÷ is just a pedagogical symbol used for teaching elementary school arithmetic. It’s essentially unused in algebra and beyond, but to the extent that it’s meaningful, it’s a synonym for /.
What is their argument?
What I find amusing is that many calculators have a key marked ÷ , but if you press it, what appears on the screen is / .
I’m having trouble finding a cite now but iirc it’s the claim that it mandates the division of the two terms on either side of it first regardless of other operations.
You’d still need to specify left- or right-associativity. Otherwise, what would be the value of 8÷4÷2? And then one of those two divisions wouldn’t be “first”.
I think the point is that people are more likely to write 1/(1+x) ambiguously as 1/1+x than as 1÷1+x (since nobody really uses the ÷ sign after grade school).
Out of curiousity, I checked my calculator, as well as the calculator function on my phone. Both have the ÷ on the keypad. On the calculator, none of the operation signs (+, ×,÷,-) are displayed when pressed. The arithmetric operation is performed, but no operators are shown! But on the phone, when I press ÷, indeed it is ÷ that shows up on the screen.
It’s easier to draw a ‘/’ on simple segmented and lo-res dot matrix displays commonly used on calculators.
Okay, some informative links I’ve turned up since starting this thread:
Order of operations - Wikipedia and Obelus - Wikipedia. In particular, the former gets into how there was a lack of standardization in how early electronic calculators handled order of operations; this might have given rise to the idea that the Obelus division sign signified one particular standard.
Doesn’t ÷ represent a blank fraction? I’m not sure if that is ever explained, but if it was it would make later High School maths a little bit easier, in my opinion.
My ancient Hewlett-Packard HP-25 has a ÷ symbol on the division key. I suspect they all do.
Of course it is an RPN calculator so there is no ambiguity whatsoever about order of operations.
I don’t recall ever seeing “the slash operator” (i.e. the symbol / placed between two numbers on the same line to indicate division) until its use on computers in the 1980s. But I was a child then, and I might not have been aware of how things were done in “grown-up math.”
Still, my understanding is that the / came to be used a lot more widely as a division symbol with the advent of computers that already had that symbol on their keyboards (much as the asterisk came to be used as a multiplication symbol).
Before it’s use on computers the slash was commonly used on typewriters to express fractions, IOW as a division symbol.
The problem mostly shows up on click-bait posts. “9 out of 10 people can’t get this right”.
The show something like 10 ÷ 2(3+2)
The logic is with PEMDAS you should be doing the division before the 2 x (3+2).
But anyone who’s paid attention in math and science classes will automatically think the term without a symbol “2(5)” should be done first, since that’s usually how terms are dealt with.
The problem also arises from trying to shoehorn scientific math into a business character set from IBM punch cards. EBCDIC (and then ASCII) had no “÷” and no obvious multiplication and it was awkward to do complex multiline equations. Early lineprinters with the limited character set did not do small super- and subscripts. So, it’s easy to make up stuff that can be confusing when you try to shoehorn handwritten or specially typeset equations into linear text.
Short answer for the OP - it means what it should mean, depending on context. Meaningless made-up strings of operations can mean whatever the person composing them wants it to mean. Good expressions are written so as to be unambiguous, with liberal use of parentheses.
In some countries, notably in Scandinavia, there is an old practice of using ÷ for subtraction.