# PEMDAS

Discussion in 'Secondary Education' started by Michelle, Aug 2, 2019.

1. ### MichelleRookie

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People are saying it’s 1 because you have to distribute and not divide first

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3. ### futuremathsprofPhenom

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It is 1, for goodness sakes!

4. ### MichelleRookie

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As I have asked you, go back and solve the problem I posted and do not add your additional ( ). They are not in the problem. If done correctly your first do what is inside the ( ). Then you multiply / divide in the order they appear from left to right. That gives you 16.

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5. ### futuremathsprofPhenom

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I think further study of math is ideal for math credential programs going forward.

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6. ### futuremathsprofPhenom

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Don’t tell me what math is. When you take an advanced math course, then we’ll talk.

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8. ### Ima TeacherVirtuoso

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We are talking about a basic math problem that follows the standard order of operations (PEMDAS).

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9. ### MichelleRookie

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I have thank you very much - no need to be rude.
This is a basic order of operations math problem -

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10. ### MichelleRookie

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Yes thank you. I agree. Others are taking it way too far.

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11. ### futuremathsprofPhenom

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No.

And to be fair, you just said that math is math and that there is no such thing as an expected computer answer, which I clearly demonstrated is, in fact, false.

Last edited: Aug 2, 2019
12. ### futuremathsprofPhenom

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The rules of math apply the same regardless of the forum or situation. There is no opinion when it comes to math. You can agree or disagree all you like, but math just is. It exists independently of anyone’s thoughts or feelings.

13. ### MichelleRookie

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The problem is you will not solve the original problem exactly as written. If you correctly follow PEMDAS you will not get 1.

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14. ### MichelleRookie

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Ok so this went WAY beyond what I expected from this forum.
I’m still on summer vacation. No need for all this ...

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15. ### futuremathsprofPhenom

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I even showed how calculators don’t know what the order of operations is and get completely different answers. The grouping symbols are very important!

Last edited: Aug 2, 2019
16. ### a2zVirtuoso

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Here is an explanation of the problem.

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17. ### futuremathsprofPhenom

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His explanation completely glosses over the historical interpretation and usage of mathematics operators and grouping symbols. My goodness, multiple calculators have been shown to yield both answers. Only in the presence of the grouping symbols, as I’ve said multiple times now, will the correct mathematical output be obtained.

With that said, UC Berkeley and Harvard reason that both answers are accepted:

http://www.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html

However, computer programmers agree with my interpretation, which is the correct accepted usage in the mathematics community. And since calculators were used to show the answer is “16,” I clearly demonstrated that is not the case.

Last edited: Aug 2, 2019
18. ### a2zVirtuoso

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Not sure what bee is in your bonnet, future. You certainly are ornery tonight and downright abusive.

Goodnight.

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19. ### Ima TeacherVirtuoso

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20. ### futuremathsprofPhenom

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If you are wondering why I am so worked up is because people are commonly spreading disinformation about math and having debates that have no basis in fact. Like the “famous” proof that 0 = 1. People think that the proof makes “sense” even though it requires that you divide by zero in it. Every implication thereafter is false.

I’m not upset with you or any other forum member, I’m aggravated that math teachers are confused by this.

I really don’t get why people are willing to trust what their calculator says when several other models can produce an entirely different result with the same inputs. That’s why I said what I said about expected computer answers... For example, if we go by conditions for engineering standards (ISO standard), we get 1. Here is the link for that: https://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv021.cgi?read=246984

Notice that many makes and models of calculators show 1 or 16 with no added brackets or parentheses.

21. ### futuremathsprofPhenom

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I apologize for being terse and combative. There was a better way of debating and I should have been more cordial.

22. ### futuremathsprofPhenom

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I apologize for my rudeness. I realize that I should have been more polite and you did not deserve that. Please forgive me for that.

23. ### AcesDevotee

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Aug 3, 2019

So while I realize that I think this got decided, I did want to add another perspective perhaps to explain why there's a discrepancy.

As it is written, future, I'm afraid that I would say your original grouping of the problem was incorrect. There is a division symbol, not a fraction line/slash. So correct grouping if we're adding grouping would be:
(8÷2)(2+2)
If it were a slash, then yes, I would agree it would be 8 over 2(2+2), which again I agree would be 8/2(4) --> 8/8 = 1.

But moreover, I wanted to add a chemistry perspective, because, well, that's what I thought of first. Say you are conducting an experiment in which you are combining chemicals A, B, C, & D in a particular order. According to your instructions, you are to mix A and B, then C and D. Only then would combine the AB mixture with the CD mixture. To get the correct chemical reaction.

However, it could be said that because you are simply combining A+B+C+D, you could rearrange the combinations. So you could potentially combine A+C, then B+D, then combine the two mixtures. But this produces the incorrect chemical response. As would combining A+B, then adding C to the AB mixture, then adding D to the ABC mixture.

In this case, why is the resulting reaction from the first part correct, and the others incorrect? Because the first result is the intended result according to the instructions provided. If one follows the instructions as provided, then they get the intended results. Failure to do so could produce potentially harmful results, depending on what's being mixed. In a controlled science classroom, only one of these answers would be correct: the by the instructions intended result. But in the field, where you don't know what the chemicals actually do, we would record the results of all the experiments where there is no right or wrong answer — assuming we don't die from the chemical mixtures.

Sorry for the long winded response, and not trying to restart the dispute. But as written, following the instructions provided, the answer is 16.

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24. ### Tired TeacherConnoisseur

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OMGoodness! Some of you are sure passionate about math!
I was on here earlier this afternoon.
Then I left to spend the evening w/ my dear friend who happens to be a 4th grade teacher. ( A level above me.)
I was concerned I'd been showing the kids similar math problems wrong for many years. Plus, I am super curious about somethings. She is a math major and explains things in simple terms to me.
Automatically, she popped off with 16 like I had, but I told her some people say, "It = 1." In less than 2 minutes, she showed me how it could =1. Then she was sure it was 1. I came home, popped on here, and was amazed by all of the comments and loved the video posted. Thanks a2z Maven for your explanation and video.

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25. ### Tired TeacherConnoisseur

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This is a great example too! , Aces.

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26. ### rpanCohort

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If any of our students got presented with this problem and came up with either I don’t think we should be too upset, because it means they do know how to apply PEMDAS.
I read that the head of a Mathematical Society got 16 as the correct answer. Personally I got 1 as I was always taught to do what’s in brackets first and then everything associated with brackets next. So I don’t see
8 ➗ 2(4) as equal to 8 ➗ 2 X 4.
But I can see both arguments.

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I’m essence, math problems can be poorly written and this is intentionally written poorly to cause this controversy.

Based on how we teach BEDMAS in Canada I would say as written it is 16 but I see other ways of writing it in the article where it is 1.

In essence, I would love to use this with kids to highlight why communication, showing your work, etc is so important in math (because this really isn’t a controversy - it’s a problem that is written badly on purpose to cause controversy.

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28. ### a2zVirtuoso

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That is interesting that you were taught everything associated with brackets next.

Do you happen to have a resource that says this or was it just what was taught? No snark here, just wondering.

I was taught that this was ambiguous as written. In CS courses there would be a huge red x over the code because of the ambiguity. It wouldn't fly. Additional brackets would need to be used to further clarify the equation. The good thing was that writing code, you know what your equation is supposed to mean.

Last edited: Aug 3, 2019
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29. ### futuremathsprofPhenom

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Adding brackets is a very common practice for the many reasons that I outlined previously.

Engineers, computer programmers, and mathematicians have basically stopped using the non-slash division symbol because of the ambiguity it causes.

As many institutions have chimed in on this (UC Berkeley and Harvard, etc.) and they definitely did not say the answer Is definitively 16. They concluded that the problem is ambiguous, but they did say the modern standard is to add brackets. If you read through the links I provided, many mathematicians, engineers, and the like have responded and stated this.

30. ### futuremathsprofPhenom

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Exactly this!

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32. ### a2zVirtuoso

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Berkley did not say that the modern standard is to add brackets. What you linked specifically said it is ambiguous.

It did offer that ambiguous equations should not be written and brackets should be used in order that your expression is unambiguous. Nowhere did it even suggest to add brackets to an ambiguous equation to solve it. Just use them when you write your own.

33. ### a2zVirtuoso

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Yet you try to claim over and over that the only correct answer is 1. Then you demean others and offer sources that say both answers are acceptable.

They also did not say the answer is definitely 1 as you keep trying to claim.

34. ### a2zVirtuoso

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Any quality programmer ensures that their equations are written unambiguously unlike the equation we were presented. It has nothing to do with the non-slash division symbol or not.

Sloppy programmers will let an ambiguous equation slide when they know how the language processes the equation because they know the chances of the language changing how it processes equations is so slim they just don't bother.

35. ### futuremathsprofPhenom

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They may let it slide, but employers and industry professionals would not. If you did something like that at my college, or at Google, for example, Then you would quickly find yourself in trouble.

36. ### futuremathsprofPhenom

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I based my answers off of actual professionals who work in both the mathematical and scientific communities. I now concede that the original problem was intentionally written ambiguously, though.

Do you also see how the other posters were saying that the answer is 16? I countered that modern standards would not yield such an answer and that brackets would, in fact, be used so the answer produced would be 1. I don’t see the value or practically of using an example that wouldn’t be used in the real world. Does that hopefully make sense?

37. ### futuremathsprofPhenom

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So if it is saying that you should use brackets when you (us, anyone) “write our own,” then why wouldn’t we? Do you see? It is now standard practice.

38. ### a2zVirtuoso

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Yes, employers and industry professionals let this type of stuff slide all of the time. It usually goes unnoticed because the programs function properly. It isn't until the system is re-written into a different language (which does happen way too often) when this error comes to light because the new language happens to process differently. In fact, if the new language processes the same, it will go unnoticed again unless the coder knows to check for ambiguity. Many don't. Some do. Some are just under such a crunch that if it works they just don't care.

39. ### rpanCohort

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I was taught this when I was a kid in school and it has stuck with me. The brackets B or parentheses P meant I solved whatever was in the brackets first and then whatever was associated with brackets. The goal was to “get rid of the brackets” before moving on to the MD and AS. I went on to complete a pure mathematics degree and I’ve taught Maths from primary to high school level and I taught this concept the way that I was taught when I was a kid. I’ve never questioned it until I read the article.

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40. ### futuremathsprofPhenom

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Actually, no. I actually do programming projects on the side for extra cash and every program that I have submitted for review, by various employers, has to be properly formatted and no ambiguity is permitted.

If I were to submit unformatted or improperly formatted code, then it would either be rejected or heavily edited.

Did you read my article posted earlier? I showed several examples how code would NOT function properly without brackets. It does not run properly.