General Discussion
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(15,124 posts)mr_lebowski
(33,643 posts)Maxheader
(4,366 posts)Watch me show how to put a stick in it..
Preform the operation in parens..= 4...
Multply numerator and denomerator
4 times 8 = 32
divided by 2 = 16
mr_lebowski
(33,643 posts)How are you putting a stick in it?
Also ... Booooooo Chiefs!
TeamPooka
(24,155 posts)when I signed up here
OneGrassRoot
(22,917 posts)KentuckyWoman
(6,666 posts)Anon-C
(3,430 posts)...Google seems to agree with me. What am I missing?
mr_lebowski
(33,643 posts)The other possible answer is 1, but that's wrong ... operations happen left to right, beginning with multiplication/division, then addition/subtraction. Although parentheses override that.
So 8/(2(2+2)) would be 1. But not 8/2(2+2).
Dr. Strange
(25,898 posts)kimbutgar
(20,871 posts)This is how they come up with 1.
8/2 = 8 as a decimal of 2 hence 1/16
1/16x2 = 1/8
1/8 x 2 = 1/4
1/4 (4 ) = 1
I lost my mind as a 63 year old that I had learned this new math
Drahthaardogs
(6,843 posts)You do the parentheses first, the orders of operation left to right.
kimbutgar
(20,871 posts)Ms. Toad
(33,915 posts)GulfCoast66
(11,949 posts)Division and multiplication left to right after you add inside parenthesis... its 16.
The way you would get 1 is by writing it like this... 8/(2(2+2)) placing the multiplication in the denominator.
missingthebigdog
(1,233 posts)In no universe does 8/2=1/16. 8 as a decimal of 2 makes no sense to me....
FiveGoodMen
(20,018 posts)Ms. Toad
(33,915 posts)Your first line makes no sense.
I also generally think that common core - like the "new math" you likely learned as a child - is mathematically sound. Unfortunately, like new math, it is largely taught by people who don't understand the logical basis for it. That makes it a frustrating, meaningless exercise. I didn't understand the power of "new math" until I was working on my Master's degree in applied math, because it was taught as rote exercises, completely disconnected from its mathematical power.
Common core doesn't have the mathematical power of "new math," but it is draws on things people of our age did because they made math without calculators easier. Some of the crazy addition and subtraction rely on the same principles we used to use to count out change by counting up to the nearest coin, then to the nearest bill.
That said - I don't have a clue what you mean by your first line.
honest.abe
(8,556 posts)What you wrote is complete non-sense from a mathematical point of view.
LeftInTX
(24,540 posts)Without locating fancy keys, I can't find the appropriate math symbols.
jcgoldie
(11,582 posts)16.
customerserviceguy
(25,183 posts)And I haven't heard that expression in years, thanks for the reminder!
SlogginThroughIt
(1,977 posts)PEMDAS
SlogginThroughIt
(1,977 posts)Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
First you have to do what is in the parentheses 2+2 = 4
We have no exponents
Next we have to do the multiplication 2x4= 8
Now we do the division which is 8/8=1
jcgoldie
(11,582 posts)Multiplication is not a higher operation than division. It is done from left to right, the acronym doesn't really capture that point.
SlogginThroughIt
(1,977 posts)interesting
jcgoldie
(11,582 posts)And I teach HS math... just drop that little formula in any scientific calculator which I assure you is programmed to compute with the correct order of operations and it will tell you the same.
Dr. Strange
(25,898 posts)Division is really just multiplication. So 8/2(2+2) can be viewed as
8 x (1/2) x (2 + 2)
since dividing by 2 is the same as multiplying as 1/2.
Ms. Toad
(33,915 posts)That acronym drives me crazy.
mr_lebowski
(33,643 posts)Multiplication and Division are equal in terms of order of operations, so whichever is first left to right is done first. Same with Addition and Subtraction.
KY_EnviroGuy
(14,483 posts)See post #136.
Using your rule, proceed to complete the denominator from left to right, then the final division.
KY......
tinrobot
(10,848 posts)Ms. Toad
(33,915 posts)P - E - MD - AS
As a former math teacher, I hate it that sloppy acronym, since it leads people to incorrect results.
Multiplication and division are equal priority - so you do whichever you encounter first, from left to right.
Same for addition and subtraction.
You can see this by recognizing that division is just multiplication by the reciprocol - so you have to get the same answer whether you divide by 2 or multiply by 1/2.
swapping *1/2 for /2, the problem becomes: 8 * 1/2 * (2+2)
8*1/2*4, doing the multiplicaiton from left to right = 4*4 = 16.
The fact that you get a different answer merely by changing it to a pure multiplication should tell you that you don't do all multiplication before doing division.
(Same for addition and subtraction. All subtraction is really just adding a negative, so they have to be the same priority)
jcgoldie
(11,582 posts)Division is defined as multiplication by reciprocals... cheers!
Ms. Toad
(33,915 posts)Not much use these days since I'm now teaching law.
But I did have to explain basic rules for percentages to a colleague.
Polly Hennessey
(6,745 posts)Hoyt
(54,770 posts)know too many people, or even some computer formulas, are going to get that right. Thats how things get really screwed up.
wryter2000
(46,016 posts)Thank you
Sid
hunter
(38,263 posts)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.
kimbutgar
(20,871 posts)But I figured out why someone would say 1 the way they teach math nowadays.
Brother Buzz
(36,212 posts)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.
missingthebigdog
(1,233 posts)8/2(2+2)=
8/2(4)=
8/2*4=
8/8=
1
The error is in using the PEMDAS (or Please Excuse my dear Aunt Sallly- parenthesis exponents multiplication division addition subtraction) mnemonic too stringently. If you follow the mnemonic, the multiplication comes before the division, so you resolve that equation after elimination of the parentheses.
However, multiplication and division are actually treated equally in order of operations (as are addition and subtraction), so the correct method is to solve from left to right once the parentheses are eliminated:
8/2(2+2)=
8/2(4)=
8/2*4=
4*4=
16
applegrove
(118,006 posts)Turbineguy
(37,206 posts)brackets first
Multiplication second
Division third
jcgoldie
(11,582 posts)Division and Multiplication have the same weight. For the best explanation please read post #19 by Ms Toad.
GulfCoast66
(11,949 posts)Do the equation left to right but parentheses are done before factoring into the rest of the equation. Hence the parentheses!
16.
I used to be able to tell you the law that drove this. Some dude from 500 years ago Im sure! But I was a fair math student at best. Did just good enough to get a plant science degree.
Ok. Never made lower than a B but only went up to calc 2 in college. Cant remember any of that shit!
BootinUp
(46,924 posts)mr_lebowski
(33,643 posts)Abundant explanations above, esp. replies 19 and 21.
:cheers:
BootinUp
(46,924 posts)mr_lebowski
(33,643 posts)jcgoldie
(11,582 posts)hunter
(38,263 posts)Anyone writing this out by hand, or as a computer program, wouldn't write it this way.
The purpose of this convention was to make life easier for typesetters.
This typesetting convention was then beaten into a dead joyless math "fact" that was force fed to middle school students.
dem4decades
(11,241 posts)Mossfern
(2,375 posts)Clash City Rocker
(3,377 posts)3catwoman3
(23,812 posts)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 -
sarisataka
(18,197 posts)6.693x10^25
Oh wait, I forgot to carry the 3...
It's 16, as well explained above
rufus dog
(8,419 posts)A reason to be pissed off at Kimbutgar
fishwax
(29,146 posts)The dispute here is basically one involving different mathematical grammars. It's a result of an evolution in the grammar of mathematical notation that stems from the rise of computer-programmed calculations, the fact that typesetting vertical fractions is difficult, and the fact that basic keyboards have no simple key for the traditional division symbol.
In the beginning there was a horizontal fraction bar, and it functioned as a grouping symbol. Everything above the line (the numerator) was grouped as though with an implied parenthesis and everything below the line (denominator) was grouped. But vertical fractions (with a horizontal fraction bar) are difficult to typeset, and so the diagonal fraction was introduced in the 18th century.
The fraction slash, unlike the horizontal fraction bar, is not a grouping symbol--however, traditionally typesetting for algebraic functions held that the diagonal slash grouped together everything immediately before it (that is to say, everything not separated by a space or a function symbol was the numerator) and everything immediately after it (everything connected to the slash bar and not separated by a space or an explicit function symbol was the denominator). So, for example, b/cd would group the quantity of c times d as the denominator, and therefore that would take place first in the order of operations. In my experience (as a student and then later as a typesetter and editor for educational publishers) that is the convention that textbooks and instructional manuals followed.
That convention, though, doesn't translate to computer programming, where the parenthesis becomes essential because generally (I'm not an expert here on coding, but this is my understanding) programming languages are going to require an explicit function. You can't put cd in a computer code and have the program understand that you are multiplying c times d. You have to include the operator.
The equation in the OP basically follows the pattern of a/bc, where a = 8, b = 2, and c = (2+2) = 4. The ambiguity arises because it isn't specifically clear whether a/bc is meant to be read as (a/b)c or a/(bc). It just depends on which grammar convention one uses.
My instinct (because of my background in typesetting and editorial) is to treat "bc" as the denominator of a fraction. It seems odd to me to say that a/bc = ac/b. Or that 4a/a(a+a) = 8a rather than the (to me) more intuitive 4/(a+a). But, again, that's because my training is rooted heavily in the latter. I don't know how widespread that convention is in educational textbooks today--my guess is that, with the increasing prominence of programming languages, texts would be more inclined to use parentheses to eliminate any potential ambiguity. I believe that there are some fields (for example, academic journals in physics) which still treat implicit multiplication immediately before or after a fractional slash as the numerator or denominator.
jcgoldie
(11,582 posts)Thereby implicitly adding a second set of parenthesis and pushing the multiplication into the denominator. The reason I believe that is a mistake, however, in any application and not just computer programming language as you cited is that the "/" is really the only way on a standard keyboard to express division. There's no "÷" on the keyboard. Therefore its how we write division without grouping and if we want to show that everything after the / should be divided by we have to introduce parenthesis. This isn't really obscure, kids have been required to know this to correctly use any scientific or graphing calculator in HS math class for 20 years.
fishwax
(29,146 posts)The use of the "/" on keyboards (as I noted in my first paragraph before) is one of the factors that has led to this shift in conventions, but even without considering it as a fraction bar the principle of implicit multiplication (or multiplication by juxtaposition) taking precedence in the order of operations has a longstanding tradition behind it. This doesn't come up until you start introducing variables (at which point the "÷" symbol tends to be phased out).
When variables are juxtaposed, we tend to group those as a single unit: ab is equal to a times b, but we generally read it as simply "ab" ... and so if someone were to write "3 ÷ ab" this would bring a tendency to read that as 3 divided by ab (3/(ab)) rather than 3 divided by a times b. Simiilarly, when we see 2x we see that as a discrete unit (two times the value of x) rather than as two separate units (2 X x). This convention also isn't obscure, and is still used in some contexts.
Neither approach is obscure, exactly, which is why, unless one could expect everyone reading to understand the convention in play, it would be best to write 3/(ab) or (3/a)b, depending on which is intended. The fact is that, unlike, say 2+2=4, the order of operations is an entirely arbitrary convention. As such, it is subject to shifting across time and contexts.
jcgoldie
(11,582 posts)No I disagree. I do not know anything about "implicit multiplication" except to know that in this case it is wrong. I understand that its an assumption that people are making which you are explaining... but it is still an incorrect assumption. There is no way to prioritize multiplication without undermining the very definition of division as multiplication by reciprocals (ie 8/2 = 8*(1/2)) If you take the ACT test there's only one right answer to this simple problem. If you punch it into any scientific calculator, it will compute it in the same way. If you pick up any elementary algebra textbook which has been modernized to the point that kids use calculators or computers for basic computation... you will see it written in this way and not with the added parenthesis around 8/2... in fact it is often written in this way for just the purpose of teasing out this misunderstanding of the rule.
mr_lebowski
(33,643 posts)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
jcgoldie
(11,582 posts)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...
fishwax
(29,146 posts)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
fishwax
(29,146 posts)As I said, these conventions have shifted over the years. That's because they're arbitrary, and the assumptions underscoring the conventions have shifted. Nothing about math has shifted--the computation itself isn't arbitrary. But how we organize and present it as a language is/has. In this case these conventions have shifted, as I noted in my original post (and as you reinforce here) because of the increasing prominence of programmed calculations, among other things. 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. (Or, the program might be written to enter it automatically.) Again, that's not because this is the one and only correct way to do it (as, for instance, the non-arbitrary and universally true fact adding 2 to 2 gives you 4) ... rather, it's because that is now the governing convention in that context. (Indeed, it is the far more common convention now, precisely because of the prominence of computers as computational tools.)
This fact that this equation uses all numerals and no variables makes it particularly useful for revealing (and sowing, lol) this sort of distinction/argument. I think the ambiguity would be quite a bit clearer if the equation were written in variables. Now, everybody can agree that bc = b * c, right? But it is also absolutely true that bc = (b * c). So if you're given the expression a/bc, you've got an ambiguity problem, because it could be a/b * c or it could be a/(b * c).
jcgoldie
(11,582 posts)"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.
fishwax
(29,146 posts)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!
muriel_volestrangler
(101,144 posts)(since it doesn't have the / sign), I actually get '2' on the screen. This is because on scientific calculators you should be putting in the multiplication symbol explicitly; without it, what it does is reject the first '2', and so works out 8÷(2+2) ; similarly, 8÷2(3+3) comes out as 1.33 recurring. And that brings us back to fishwax's point about juxtaposed quantities.
See https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html (George Bergman, Dept of Mathematics, Berkeley)
Nay
(12,051 posts)operations on the top or bottom of the bar would be done separately. Only then would you reduce the fraction to get your final answer.
LeftInTX
(24,540 posts)Hard for a novice to format for use in MS Word!
8
2(2 + 2)
8
______
2(2 + 2)
hunter
(38,263 posts)struggle4progress
(118,032 posts)2+2=4
2*4=8
8/8=1
Hotler
(11,353 posts)Last edited Thu Aug 8, 2019, 10:36 AM - Edit history (1)
16
5 out 3 people struggle with math.
blugbox
(951 posts)You are correct about the answer being 16 lol
Afromania
(2,767 posts)I'm still trying to figure out how some folks are getting 16.
edit: I see it. my aging math mind refuses to believe it. Of course I was have math dyslexia... probably.
Joe941
(2,848 posts)8/2(2+2) = 8/2(4) = 4(4) = 16
LeftInTX
(24,540 posts)I have a degree in math from 1978 and I get 1 because we were taught that / was a horizontal bar over 2(2+2).
Also back then calculators couldn't do parenthesis etc.
FBaggins
(26,693 posts)Because (2+2) is 22.
USALiberal
(10,877 posts)Trumpocalypse
(6,143 posts)The answer is 16.
Hotler
(11,353 posts)MD = Evaluate all multiplications and divisions as they occur in order from left to right.
AS = Evaluate all additions and subtractions as they occur in order from left to right.
It is easy to forget this tid bit of info.
kimbutgar
(20,871 posts)I think the answer is 16 also.
But I also can see how one could come up with one if you look at 2 divided by 8. And not 8 divided by 2.
jcgoldie
(11,582 posts)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!
Ms. Toad
(33,915 posts)There is no ambiguity: 8/2 can never mean 2/8. (two divided by 8).
Claritie Pixie
(2,199 posts)8/2*(2+2)
4*(2+2)
4*(4)
16
honest.abe
(8,556 posts)Its should be written like this:
(8/2) * (2+2)
So there is absolutely no confusion or debate about the stupid order of math operators.
not_the_one
(2,227 posts)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).
Ms. Toad
(33,915 posts)Multiplication and division have the same priority. Parentheses say: Do this first. Division preceding multiplication says: Do this first.
honest.abe
(8,556 posts)I am a programmer and parens are always used in cases like this to ensure clarity and reliability.
Ms. Toad
(33,915 posts)and building in that redundancy (absent a linguistic requirement) does not match my experience.
honest.abe
(8,556 posts)but I would never trust any code that was not clearly defined with parens that contained equations like this. A minor inconvenience to ensure clarity and accuracy.
Remember what is clear and obvious to you may not be to the next person editing your code.
Ms. Toad
(33,915 posts)should understand 7th grade math**, not to mention that any programmer worth their salt also documents their code.
**I do come from the generation in which computer science degrees did not yet exist so most programmers majored in mathematics or physics.
From my perspective, adding unnecessary parenthesis is far more likely to make the code harder to read and to lead to coding errors - especially with a complex functions where one misplaced parenthesis out of the dozen or so in the funciton would be a beast to soft through for the error. Omitting redundant parentheses simplifies the error checking when the run produces an unanticipated result.
honest.abe
(8,556 posts)My preference is to use both parens and comments to ensure clarity and understanding. If the equation is complex I would also use indenting and line spacing to help with readability.
Ms. Toad
(33,915 posts)Indenting and line spacing don't helpwith locating the misplaced parenthesis that is messing with your results. So when the meaning is clear (i.e. 7th grade math rules), I want to remove extraneous characters that make it harder to debug.
honest.abe
(8,556 posts)Thats quite a broad and unfair insult.
Ms. Toad
(33,915 posts)with a judgment about whether people have, or have not, mastered a particuar skill.
When math skills are taught (X-grade math skills) is objective. It is not an insult to state the facts. (Although a quick google search suggests that the skill is now a 4th grade math skill - not surprising since math skills have progressively moved to lower grade levels to create enough room for 3 years of what used to be college level math in high school.)
I did say that I expected programmers to have mastered 7th grade math skills. I expect programmers to have better than average math skills given the nature of the reasoning required to program. It is also essential to their jobs to understand how a particular string of mathematical operations will be carried out by a computer - i.e. to understand that when told to calculate x/y*z the computer will divide first and then multiply.
FWIW, I expressly demanded that level of mathematical mastery from the 9th-12th grade students to whom I taught programming - and very few of them expected to earn a living as a programmer.
honest.abe
(8,556 posts)Ms. Toad
(33,915 posts)And Google visibly demonstating the order in which it understands operations will be performed is significantly different from a programmer inserting parentheses whihc are operationally redundant - and which make it more likely that parentheses will be mismatched or misplaced causing computational errors that would not exist but for the insertion of redundant parentheses.
Aside from which - the fact that Google inserted them demonstrates there is no ambiguity as to the meaning of the phrase, confirming the fact that they are redundant.
I've spent way too much time debugging mismatched or misplaced parentheses to insert parentheses when they are redundant.
honest.abe
(8,556 posts)Last edited Sat Aug 10, 2019, 08:07 AM - Edit history (1)
LeftInTX
(24,540 posts)We had to write the programs to fit the notation of the day
So we would have written something like:
A = 2 + 2
B = 2 * A
C = 8/B
Ms. Toad
(33,915 posts)That was 1-2 years past the era when there was a single computer serving campus (the entire basement of the library) and I hoped I didn't trip on the way to the computer center with my massive box of punch cards - because if I put one of them back in out of order I had to wait 24 hours before I got my results to be able to fix the out-of-order run. About 4 years after a 4-function calculator cost ~ $100. 3-4 years before I was teaching programming still using dumb terminals and a punch tape - with one live phone link to a remote computer. Those were the days. Not.
But construction, particularly of longer functions, was particularly challenging because of limitations on both character count and computing power.
And - you really had to understand the order of operations to write it out that way!
hunter
(38,263 posts)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.
Ms. Toad
(33,915 posts)DanTex
(20,709 posts)Proud Liberal Dem
(24,353 posts)per order of operations
jcgoldie
(11,582 posts)8/2*4
No distinction in order between multiplication and division - work left to right.
Punch into any AB CLX or PLC and they will confirm.
FakeNoose
(32,328 posts)8 divided by 8 equals 1
The 2 + 2 operation is done first because it's in parentheses - and 2 times 4 is 8.
Rstrstx
(1,393 posts)8
-- (2 + 2)
2
Perhaps DU can provide an "insert formula" button right after the "smilies"
After you add the 2+2 you go the beginning from left to right.
jimmy the one
(2,708 posts)Our grandparents or ggparents would have been correct with '1', while today not so... well, listen & see:
I thought 1 myself; my integral & differential calculus & non euclid-geom helped me not a whit.
LeftInTX
(24,540 posts)Back in the day, my calculators didn't have parenthesis and could only do one step at a time... The were great for exponents...and difficult numbers, but a calculator for algebra!
Cicada
(4,533 posts)C_U_L8R
(44,889 posts)At least that's what Donald Trump says.
Midnightwalk
(3,131 posts)I would never trust a line of code that was so dependent on ordering rules. Another pair of parentheses would save me from figuring out if you meant what you wrote.
wryter2000
(46,016 posts)If everything to the right of the slash is the denominator, the answer is 1. If there's an asterisk like so--2*(2+2)-the answer is 16. Written out by hand, there would be no confusion about what is meant.
Never mind. My way is also ambiguous. Better explanations of why this is misleading can be found upthread.
JustABozoOnThisBus
(23,282 posts)Or, 16.
Tommy_Carcetti
(43,079 posts)Simply because I immediately go for what is in parenthesis first.
For some reason I think that's how I was taught. But maybe it was wrong. We're talking decades now since I've had a refresher (although with my kids working their way up school, that will naturally work to help me reboot.)
SidDithers
(44,228 posts)Math is a language, like any other. And the goal of any language is to communicate clearly and concisely.
A statement that isn't clear and concise, in math, is meaningless.
Is it (8/2)(2+2) = 16?
Is it 8/(2(2+2)? = 1?
Meaningless.
Sid
Mossfern
(2,375 posts)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.
pwb
(11,204 posts)0
Buns_of_Fire
(17,118 posts)Actually, I saw it as "1". As an ex-programmer, I would politely hand it back and ask for clarification before I committed it to running code.
ismnotwasm
(41,916 posts)Then 8/2 which 4, then 4*4=16
DanTex
(20,709 posts)Not invalid, just poorly written. (8/2)(2+2) is much better. Technically, both are equal to 16, but really this is a sort of math version of "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo."
2020Junker
(99 posts)The entire poem is written with the shi sound, but because of how tonal the language is, it looks like a garbled mess even though you could totally parse it out according to grammatical rules.
https://chinesepod.com/blog/2014/10/25/how-to-read-a-chinese-poem-with-only-one-sound/
(Scroll down to the Pinyin version. It's hilarious)
Takket
(21,421 posts)any decent scientist/mathematician/engineer wouldn't be caught dead using the "divide" symbol, we use a slash / and we sure as hell also wouldn't be caught dead writing an expression with division in it on a single line. you always clearly build your numerator and denominator with everything "on top", horizontal bar, and everything "on the bottom".
they have a word for people who write ambiguous equations: Fired.
Recursion
(56,582 posts)I find this question unbelievably uninteresting, but it keeps clogging my facebook feed.
lpbk2713
(42,696 posts)My Ninth Grade Algebra I teacher.
I knew the answer before I opened up the OP.
DangerousRhythm
(2,916 posts)2+2=4
8/2=4
4x4=16
I am long out of math class so I could be wrong.
NutmegYankee
(16,177 posts)But because we evaluate the equation from left to right, we get 16. In reality, it's a bullshit question because no mathematician would write an equation like this.
mfcorey1
(10,997 posts)LuckyCharms
(17,278 posts)MadLinguist
(781 posts)Let's call the whole thing off
GeorgeGist
(25,294 posts)Silver Swan
(1,110 posts)That has little to do with the holy study of mathematics.
kimbutgar
(20,871 posts)wendyb-NC
(3,250 posts)aikoaiko
(34,127 posts)KentuckyWoman
(6,666 posts)God only knows now.....
muriel_volestrangler
(101,144 posts)6 x 10^9 / 3 x 10^5
(taken from http://mathforum.org/library/drmath/view/57021.html)
KY_EnviroGuy
(14,483 posts)from 2 x 10^4.
I found out that our blog software will not allow the ^ symbol in the title line.
KY_EnviroGuy
(14,483 posts)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......
Trumpocalypse
(6,143 posts)8/(2(2+2))
muriel_volestrangler
(101,144 posts)For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash, and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.
https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication
See http://www.feynmanlectures.caltech.edu/I_06.html - it is written in one line as "within the deviation 1/2√N", and the full formula right after that is clear that it is
1
____
2√N
Trumpocalypse
(6,143 posts)and see what you get.
muriel_volestrangler
(101,144 posts)Ooh, that's tricky, isn't it?
The point is that, as others such as fishwax above have said, the way it's written is ambiguous. Many mathematicians, and there are references in that Wikipedia article, and this thread, do say that implied multiplication (ie from 2 expressions placed next to each other, with no symbol - in this case '2' and '(2+2)' - does take precedence over division.
Trumpocalypse
(6,143 posts)muriel_volestrangler
(101,144 posts)One of the best teachers of physics there's ever been.
And, as I said, the point is that it can be interpreted in both ways. If your thought process is "if Excel interprets it this way, I must too", then you need to rethink your approach to life.
Trumpocalypse
(6,143 posts)Mathematics in physics is very different that ordinary mathematics. It is incorrect to apply those rules to a standard problem.
muriel_volestrangler
(101,144 posts)jcgoldie
(11,582 posts)...makes it a completely different expression. The (2+2) as written in the expression in the OP does not belong in the denominator at all.
There's a lot of debate here, but the rules for order of operations are very simple and straightforward. The ambiguity comes with either a too literal reading of the PEMDAS acronym causing people to prioritize multiplication over division which is incorrect or by making an assumption that you did that "/" should mean a fraction bar and everything after should be grouped. If we agree that is the case thats fine, but that is not the convention. Nor is the "implicit multiplication" that has been referenced here conventional in any modern arithmetic sense.
muriel_volestrangler
(101,144 posts)That's the point. That's why it can be interpreted either way.
KY_EnviroGuy
(14,483 posts)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......
LeftInTX
(24,540 posts)Last edited Sat Aug 10, 2019, 02:55 PM - Edit history (1)
20 ÷ 5x if x is 40?
is 20 ÷ 5x the same as
20/5x?
or
20/5*40?
honest.abe
(8,556 posts)If written with a variable like 5x you have to do that first regardless of the order of operators rules. If no variable then the standard rules apply which would give you a much different answer.
Yes confusing which is why equations like this should always use parens to clearly define what should be done.
Last edited Sat Aug 10, 2019, 01:52 PM - Edit history (1)
Update: Just got schooled by a math teacher. 16 or 1 could be correct. She says it's a bastard equation with an undefined operator. The equation is solved like an array, hence two answers. I have been humbled.........again.
Throck
(2,520 posts)zipplewrath
(16,646 posts)For any other purpose that trying to test a students ability to correctly deconstruct an equation, this is a horribly written equation.
Having spent a career expressing ideas and conveying instructions in equations, one would NEVER write it this way. Even in a piece of software, one would write it more clearly to reflect intent.
But furthermore, most equations are combinations of various "quantities" that represent something "physical" or an individual effect. So 8/2 might be a radius calculation. Or (2+2) might be a+b where both just happen to be 2. Or it could be that 8*(2+2) represents a whole quantity and we are looking for half of it. But whatever the case, I would write the equation to clearly show these relationships.