# PEMDAS

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

1. ### a2zVirtuoso

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Aug 3, 2019

Standard practice didn't dictate where to put those brackets. It just said to use them so a problem isn't ambiguous. You chose to start your bracket where the division symbol was. Others may have put it before and then after the first 2.

Don't you see? The standard did not say where to put the brackets, just to use them so your equation is clear.

Again, modern standards do not state what you are claiming. Brackets could (not would) yield 1. Brackets could (not would) also yield 16 depending on where they were placed. The standards do not make any claim as to where to put those brackets because it is ambiguous meaning we don't know for sure where they would go.

2. ### futuremathsprofPhenom

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See, now you have changed what you said and are arguing semantics. You said earlier, “Nowhere did it even suggest to add brackets to an ambiguous equation to solve it. Just use them when you write your own.”

They did, in fact, suggest the use of brackets to make an ambiguous equation unambiguous.

The modern standard is to remove ambiguity. That entails the use of brackets. That is why brackets should be used. They were not utilized at all and that is the problem here. One of the very first things I said was that they should be used. Why they weren’t, I have no idea.

3. ### a2zVirtuoso

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Thank you for your response.

As we know, most times the equations aren't ambiguous so we don't run into an issue. Good thing.

Is there a difference between 2 * (2 + 2) and 2(2 + 2) ?

4. ### rpanCohort

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To me, no. Because according to the way I was taught you end up with 2 X 4 in both scenarios.

I’m just saying what I was taught, not saying that my way is absolutely correct.

5. ### futuremathsprofPhenom

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There is no difference if you write it either way. However, if it were a much more complicated expression, then you would insert brackets because you could get multiple answers otherwise.

But, if you just wanted to compute either of the two ways written as a stand-alone statement, then they are both interpreted the same.

Last edited: Aug 3, 2019
6. ### rpanCohort

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I think brackets do take away the ambiguity because the rule of doing what’s in brackets first is never in question. In higher level maths, multiple layers of brackets are our bread and butter.

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7. ### futuremathsprofPhenom

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You make me smile!

8. ### a2zVirtuoso

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Aug 3, 2019

I understand.

My question is what is your understanding of 2(2 + 2) vs 2*(2 +2)? Are they the same?

I've heard both yes and no in the past. Some believe that there is an implied multiplication sign and others say no it is not the same even though when you distribute you multiply.

9. ### a2zVirtuoso

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It is not semantics.

There is a difference between:

Add bracket to an already written ambiguous equation in order to solve it. (This is what you did.)

and

When writing your own equation, use brackets to make sure it is not ambiguous.

They say two distinctly different things. The former starts with something you were given. The latter is something you are creating.

In the case of this thread we received the former. No where in anything you linked did they say to randomly insert brackets to solve it. They specifically said it is ambiguous. It can have either answer.

They do suggest going forward to ensure what you create is unambiguous as standard practice. What you did is to try to apply a standard method in an unacceptable way. You do not know the writer of the equation. You can't know what the writer meant. There is no other information as to what this equation is supposed to be solving to even determine what the writer may have meant. If this was a multiple choice test using that equation, the correct answer would have been C - not enough information given to solve.

Motivations as to why the original equation was ambiguous:
To spark discussion.
Error.
Taught something else so to them it was not ambiguous.

10. ### a2zVirtuoso

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I forgot. Your limited experience is truly representative of all. Your experience is that of millions of programmers across the globe. He he he. I will tell you. It is not.

While what you describe may be best practice, the reality is so very different.

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11. ### futuremathsprofPhenom

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And your experience is what, exactly?

12. ### a2zVirtuoso

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Aug 3, 2019

Different than yours.

13. ### futuremathsprofPhenom

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Ah, yes, the “benefits” of ambiguity. When asking for directions, I’d like them to be given so that I have to figure out the true meaning. When a surgeon is directing his PA’s, it is ideal for him or her to direct them so there is uncertainty. I’m sure the patient would appreciate that. I’m also sure people like it when search engines produce lackluster and ambiguous results after they enter a search string.

Best practices are standard practices. Businesses continually want their workers to operate at peak performance and to write efficient AND elegant code. Here is a mock interview from Google:

Notice that the interviewer keeps reiterating that speed is a very important factor when she says, “This is not fast enough for Google.” Here, conciseness and speed take precedence over code structure. However, all throughout the interviewee is adding bracket after bracket.

Your notion that code can be written ambiguously is just not true in the industry when applied. Sure, the programmer can write out an outline before it’s submitted to guide their thought process, but what they deliver to their employer is very different.

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

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What programming experience specifically do you have, is what I’m asking. What I’ve heard and experienced from engineering and computer colleagues and private workers is very different from what you are purporting here.

Who have you worked for? I’ve done consulting work for Facebook, Google, the CA state department (only a few of these, though), Sun Microsystems, Foxconn, and I just secured a project recently from a local technology company.

15. ### futuremathsprofPhenom

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Well, there are ISO standards and such that are applied in exactly the way I’ve described and engineers and the like have concluded the same. That is why I said what I said. When industry professionals are coming out and saying, “This is how we would actually do it,” then there is a reason for that. Real-world application is the most important, in my opinion.

16. ### a2zVirtuoso

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Future, whatever I give as an answer, you will then tell me how your experience is right and/or better, and I am wrong. So, what is the point in sharing? You are already setting up for that next, "I'm better than you", jab by putting out a pedigree of "top companies".

So, you win, future. You can be right. There are no sloppy programmers in the world that get away with sloppy programming.

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17. ### futuremathsprofPhenom

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I apologize if my previous answer was seen as rude. I am not mitigating your experience. I am merely stating that I’ve worked with major and mid-sized companies who expect what I’ve said. Maybe you’re right and I’m wrong. I was asking to see what the motivations for writing less formatted code is/was.

I am not better than you. Please excuse me if I came off that way before. Help me understand what I am missing.

18. ### rpanCohort

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To me, in this particular scenario, based on what I’ve been taught, they are the same. I do what’s in the brackets first, which gives me 4 in both scenarios. Then I multiply by 2.

19. ### TeacherGroupieModerator

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Aug 3, 2019

That's "obelus", not "obelisk": one example of an obelisk is the Washington Monument, which I prefer to believe is somewhat less divisive than this thread has been.

(I am amused to see that the Wikipedia article on "obelus" begins with this: "Not to be confused with Obelisk, Obelix, or Obolus." For those of you who don't know Asterix and Obelix, please remedy that. The puns are almost as hilarious in English as they are in the original French.)

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20. ### AcesDevotee

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Aug 3, 2019

The only French I know is not appropriate for this forum. However, my humble opinion, perhaps it might be prudent to uh silence the conversation?

21. ### gr3teacherPhenom

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1) This entire topic is an excellent example of why the division sign is seldom used after elementary school.

2) There is no "real" way to solve this. Plenty of people with gobs of knowledge and experience with mathematics have come up with perfectly valid arguments for 1 and 16.

2a) That's the whole [redacted] point to this question in the first place. This is in no way a valid math question in the first place. Nobody would ever seriously write a problem like this just because of the confusion of it.

3) No need to act unpleasant over it.

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22. ### futuremathsprofPhenom

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Whoops, texting from my iPhone. Gotta love autocorrect. I did know that it was obelus. It’s funny that my phone doesn’t recognize obelus, though. Hmm. It tried to change it to obelisk each time I typed it in this post. Weird.

23. ### Teacher234Cohort

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Currently a 2nd-4th grade Special Class teacher.
I arrived at 1. Sorry!

On a calculator, it comes up with 16.

Pre-Algebra

24. ### TeacherGroupieModerator

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That's one of the reasons I limit the text-intensive apps on my phone: teaching the darned things the words I use in texts takes too much time as it is. You can convince your phone to accept "obelus", at least temporarily, by typing it several times in succession. It may also work to type the word correctly once, without adding the space at the end, then touch and hold the word to add it to your personal dictionary.

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25. ### futuremathsprofPhenom

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Whoa! I did not know that you could add words to a personal dictionary on a phone. I thought you could only do that on a laptop or desktop computer. Thanks!

26. ### futuremathsprofPhenom

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Different calculators return different results. I have many different versions of calculators and can confirm that the answers returned are 1 or 16 and this is without adding any brackets.

27. ### Teacher234Cohort

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That makes sense. I used the online google calculator. I do see both sides. 1 is the answer, if you follow PEMDAS.

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28. ### TeacherNYMaven

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Yes, I guess you could do it on a phone! My sister told me that after a while her phone started to recognize the nickname she calls me LOL

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Hahahaha!

30. ### gr3teacherPhenom

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My phone has finally realized that it is very seldom that I actually mean to use the word duck, (and that I neeeeeeeever use the word ducking) so if I don't write duck, I probably don't need it corrected to that.

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31. ### mathmagicEnthusiast

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Aug 6, 2019

Just read through this thread...basically my decision making on whether to share thoughts...

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32. ### GenesiserRookie

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Sep 1, 2019

I see a lot of people saying what to do, but I don't see much of a reason why. So hopefully this will clear things up and it'll be easy for anyone to go forward with these types of problems.
The parenthesis is first because that literally means "Do this first before you move on".
I.E. (3 +4) + 5 means do 3 +4 first. 3 + (4 + 5) means do 4 + 5 first.
Now, we have everything else in the pemdas and to understand this we have to realize that they are grouped into the types of operations. Or in other words, their inverses.

Start with adding and subtracting - these are inverses and when you have a problem like
3 - 4 + 7 - 6 + 8
You will do it from left to right because they are inverses of each other.
So 3 - 4 = -1, -1 + 7 = 6, 6 - 6 = 0, 0 + 8 = 8.

With this idea, we can now look at multiplication and division
These are also inverses of each other, so once again we would go left to right
3x4/2/2x3
Means
3x4 = 12, 12/2 = 6, 6/2 = 3, 3x3 = 9

With this idea, we can now solve our problem of 8/2(2 + 2)
Parenthesis tells us to do 2 + 2 first so we now have
8/2x4
Now we go left to right
8/2 = 4, 4x4 = 16

So in other words, it's not the words themselves that tell us the order. What I mean is, just because in pemdas, multiplication comes first, it doesn't mean you do multiplication first. It's just telling you that multiplication and division are grouped together as inverses.

I hope that helps!

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