= new reply since forum marked as read
How are you putting a stick in it?
Also ... Booooooo Chiefs!
...Google seems to agree with me. What am I missing?
See post #136.
Using your rule, proceed to complete the denominator from left to right, then the final division.
KY......
Division is defined as multiplication by reciprocals... cheers! 
Thank you 
Sid
https://en.wikipedia.org/wiki/HP-35
The computer programming language Forth also works that way.
You had to have a pretty clear idea of what you were actually trying to do before embarking on any calculation.
With practice each little chunk of the calculation often corresponded to something tangible in the system you were exploring so you didn't have to wait for the ending, pushing that "equals" button, to know you'd gone astray.
It's a long and bizarre story how he ended up teaching me, but what I learned from him stood me well in college. I came up with 1.
I thought I just didn't get it. Turned out a lot of her students didn't get it.
My senior year of high school, the final quarter in math was calculus. The teacher handed us a slender black book and said, "Here. This is all self-explanatory." Like hell it was!
Some years ago, my husband gave me a book entitled Math Without Tears. I gave up by page 6 after reading it 10 times.
Nonetheless, I must have learned something. I came up with 16 - 
A reason to be pissed off at Kimbutgar
I take issue with his/her general notion that there's any sort of implicit grouping on either side of a division sign, the talk of what 'immediately before' and 'immediately after' being understood to be 'grouped' and meant to happen earlier in the OOO. I've never heard of this and cannot imagine this was ever commonly understood to be the case. Could be wrong though 
It was definitely a more interesting argument than I anticipated. Now I have to leave this thread that I'm sure is boring the pants off 98% of DU because I have the next 9 months to experience the frustration of teaching mathematics and less than a week to get a zillion tomatoes picked... would any math debaters happen to know if I should blanch them before or after coring them for the freezer?!?
Edit: Wife finally responded to text... "core first then blanch, too hot and mushy after"... almost got me excited...
I think presenting it as a grouping around the slash sign was confusing on my part, and it's all because I was focusing on the typesetting angle because (a) I was thinking there was a symmetry here between the coalescence of the conventions first around the same time as the rise of movable type and now those conventions shifting as a result of a new dominant technology with the computer; and (b) I used to be a typesetter, and specifically for calculus and physics texts, so I find it a lot more interesting than most people do. But also because (c) it was like 1:30 in the morning and I wasn't thinking clearly .
Had I been thinking more clearly, I might still have mentioned typesetting offhand, but I would have focused on the simple fact that mathematicians and physicists (maybe engineers, i don't know, depending on the field, I suppose) often tend to view juxtaposed variables as single units. They're more prone to see ab as " (a * b)" rather than simply "a * b," while programmers and programs would be more likely to see ab as "a * b." Since students are more likely to be programmers (or to deal with computer programs) then to be mathematicians or physicists, though, it makes sense that in the last few decades the latter convention has overtaken academic instruction.
Nothing wrong with that. Nothing at all. But it's probably silly to assume that folks who write, read, or follow something like the style manual for the American Institute of Physics, which says you should "never write 1/3x unless you mean 1/(3x)," or the style guide for reviewers for the American Mathematical Society (http://web.archive.org/web/20011201061315/http://www.ams.org/authors/guide-reviewers.html), which says "We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division," simply don't understand basic seventh grade math.
Anyway, this comes up every couple of years when some similarly designed expression creates this sort of controversy, and I always find it entertaining. Fun to talk math, even though it's not my dominant language
"You can't really put the equation, as written, in most of the calculators or computers that kids would use for calculation, because doing so would require you to insert the operation symbol between two juxtaposed values after the slash. "
I realize this doesn't really address all your points but the fact is you can type it into any calculator that does order of operations correctly (ie "scientific" in exactly the way it is written and it will give you the answer of 16.
You can try it here:
https://www.meta-calculator.com/scientific-calculator.php?panel-201-calculator
I do not know how they wrote the language more than about 40 years ago when they wrote the textbooks I used in HS but I do know that there is a single right answer to the equation now the way it is written. If a student used the improper order in the midst of any of my classes from Algebra through calculus that I've taught I would have no problems subtracting points nor would I would guess (without evidence) 95% of HS mathematics teachers. Understanding rules of order of operations is rather basic to number sense and it is not arbitrary. I believe that you were agreeing with that and just arguing that symbols and how they are arranged to convey meaning is what you are calling arbitrary. That it is based in convention. I agree but I would also argue that we have to have some basic agreement over those principals or it would lead to serious problems in all sorts of applications.
Some here have said it would be clearer to add another set of parentheses around the first 2 terms. I agree with that as well and its a small joke I have told my students for years (which very few get) that "a LIBERAL use of parentheses in computation is almost always a good thing and wholly uncontroversial unlike in politics." When in doubt, add them. That being said, the extra parentheses would be redundant and do not change the meaning of the equation from what is written.
I don't really have a problem with you (or any other instructor) taking points off for a student getting the wrong answer, assuming they've been taught the convention. Mastering the convention is part of the point of the class. So they should be expected to execute whatever conventions have been adopted and conveyed. That's the point. Randos on the internet, though, not so much. Some of them might have simply been trained before java and google became the default. Or, they could be physicists or engineers, fields where the convention about grouping juxtaposed variables together remains very much in play.
Understanding rules of order of operations is rather basic to number sense and it is not arbitrary. I believe that you were agreeing with that and just arguing that symbols and how they are arranged to convey meaning is what you are calling arbitrary.
I think I agree with you here, but we may disagree on where the border between the two is. I mean, I think we could technically change the rules to the order of operations however we wanted and it wouldn't change the mathematical facts that the language of math describes -- but I agree as it relates to number sense and higher orders of operations. The levels of the order make perfect sense: if we didn't all agree to do exponents first than there wouldn't be much need for exponential notation, and the efficiency of exponential notation would be lost. Similarly, We don't *need* a multiplication operator, since any x * y can also be represented by x + x + x ... y number of times. But the multiplication symbol makes things easier, and so giving it precedence in the order of operations makes perfect sense.
The specific point as it relates to the order of operations in this equation, I believe, is whether ab = a * b or (a * b), and that's arbitrary. The "a * b" side has gained prominence in the past couple of decades because, well, that's what google says and what java says and what python says, and so that's the easier convention to follow. But that's just a programmed choice--there's nothing about it that is inherently right. It's just become the dominant convention, at least for simple calculations. When it comes to, say, engineers and scientists working with variables, I think one would still find a lot of people and texts treating ab as (a * b).
Anyway, this has been a fun conversation, and I'm all in for the liberal use of parentheses!
There's only one answer. And the fact that there is so much disagreement a day after the rules have been explained gives one an idea of why a topic like politics which is full of gray areas could be so hard to reach consensus!
I say we take it to the streets!!!
Imagine the protest signage. We would look EXACTLY like what we are... the educated elites (many who live on the coasts).
Last edited Sat Aug 10, 2019, 08:07 AM - Edit history (1)
Any hypothetical compiler that stumbled upon the programmer's intended meaning would reduce this text to a small integer constant, and then, if it was smart enough, would issue a 
Kevin compiler warning.
8 divided by 8 equals 1
The 2 + 2 operation is done first because it's in parentheses - and 2 times 4 is 8.
times 4
equals 16
Mommy math - did it intuitively because when I was in school we didn't have calculators.
Something must have been drilled into my head though.
The math in the denominator must be completed before proceeding with the rest. Because there's no space between 2 and (2+2) in the denominator, that operation is done first so 2(4)=8, making the answer 1.
Rather than looking at it from left to right, see it as up and down like so:
8
--------- = 1
2(2+2)
KY......
since the 60s when I had basic math, algebra and calculus. I solved the equation instinctively just as I would have in 1965, LOL.
In those days, we had no computers, calculators (that we could afford), smart devices or internet.
Some might see the OP format as potentially causing errors and prefer it be written (2+2)8/2 = 16, or we might have written it as 8/2 x (2+2) = 16 or for the other instance, 8/2 x 1/(2+2) = 1.
That points out the various profession's use of the multiply operand, whether to use "x" or "*" or "." (dot or asterisk vertically centered). In engineering we used the dot most times when everything was hand-written.
I didn't get to participate much in the "new math" my kids had because I was out traveling to pay the bills. I missed out on a lot in those days.......
Thanks for the interesting OP......
