# PEMDAS

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

1. ### MichelleRookie

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Aug 2, 2019

8 ➗ 2 ( 2 ➕ 2 )

If solved correctly following the order of operations the answer should be 16. Correct?
Or are the math teachers I work with doing it wrong ?

3. ### Tired TeacherConnoisseur

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It looks like 16 to me too, but I only teach 3rd grade. lol

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4. ### MichelleRookie

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Yes I agree. But there are people arguing that 2(4) is not the same as 2x4 lol

5. ### Tired TeacherConnoisseur

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Hmmm... I should probably not be going down this road. lol After taking our state math test, I saw a group of coach- looking male teachers standing around chatting about how difficult 1 math problem had been. I remembered the problem and thought, "Wow! That was a simple 1 for them to have had such a hard time." On my ride home, feeling a bit smug, I realized it had been a really tricky problem I had missed a few steps of it.

6. ### TeacherGroupieModerator

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My goodness. What answer(s) are you being given?

7. ### futuremathsprofPhenom

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Insert grouping symbols; specifically, parentheses:

8/[2(2+2)] = 1

Gotta the love the American educational system...

8. ### futuremathsprofPhenom

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...

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

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The math teachers you are working with don’t know their subject matter well enough...

10. ### vickilynMultitudinous

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I think that some of the confusion is that the (divided by) sign very much resembles the + sign in the first post. Clean up those two images and it will give you the correct answer.

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11. ### Tired TeacherConnoisseur

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Vickilyn, I wish that had been my problem, but that might be the problem for some..

12. ### a2zVirtuoso

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.................................

13. ### Tired TeacherConnoisseur

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a2z, I am still trying to figure that out....lol

14. ### futuremathsprofPhenom

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a2z clarified their original post and I retract my previous statement.

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

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Nope. It’s pretty obvious. You don’t need multiple math degrees like I have to see this.

16. ### a2zVirtuoso

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Would you elaborate why you add additional groupings for those who don't know? Since the American educational system doesn't teach it correctly, please explain.

8 ➗ 2 ( 2 ➕ 2 )

Students are typically taught to do what is in the parenthesis first.
8 ➗ 2 ( 4 )
Then to do multiplication or division from left to right.
4(4)
16

Please explain to those who do not know why the additional grouping rather than treating the 2(4) like it is written 2 x 4. PEMDAS does not explain that. The American math curriculum does not teach that.

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17. ### a2zVirtuoso

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Why are you being rude?

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18. ### a2zVirtuoso

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Sorry, I deleted my post, Tired. I didn't mean to get you into this mess. I posted a different post.

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19. ### vickilynMultitudinous

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Am I missing something? P - 2+2=4, no Exponents, M - 2(4)=8, D - 8 divided by 8=1. I couldn't get 16 out of that equation no matter how hard I tried. Math isn't one of my certifications, but I thought I understood the basics

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20. ### futuremathsprofPhenom

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It does actually, and I learned it using grouping symbols followed by PEMDAS in an American School in CA. Nice try.

You insert the grouping symbols because the initial problem is asking us to find the quotient of 8 and some quantity 2*(2+2). 8 is the dividend and 2*(2+2) is the divisor. Sort of like when we simplify a complex fraction or some other rational expression, we simplify the numerator and/or denominator first. In this case, simplifying 2*(2+2) we get 2*(4) or 8. The problem then becomes 8/8, which is equivalent to 1.

21. ### futuremathsprofPhenom

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Edit: You’re right. I need to tone it down.

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

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Many teach PEMDAS that you don't do multiplication first and then division. Multiplication and division are seen equal (as are addition and subtraction). So, when equating you do either M or D from left to right.

In my example above I treated division and multiplication as equals which is how it is usually taught.

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23. ### futuremathsprofPhenom

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You give me hope for America!

24. ### vickilynMultitudinous

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And now you know why I choose not to work towards any math certification. I am dismayed, however, that I am no longer proficient to teach elementary math. That is a shame.

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25. ### futuremathsprofPhenom

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You absolutely are! Take that back!

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26. ### Ima TeacherVirtuoso

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I have two English degrees, but I always made A’s in math, which was actually my favorite subject. The answer is 16.

My husband, who has a math degree, also says 16.

27. ### a2zVirtuoso

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Why is all of that the divisor? Is it because parenthesis were used rather than the x for multiplication even though the x is implied by being next to the parenthesis?

If it was written
8 ➗ 2 x ( 2 ➕ 2 )
8 ➗ 2 x (4)
would you equate it differently?

28. ### futuremathsprofPhenom

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Well, you’re both wrong.

29. ### futuremathsprofPhenom

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It would not equate differently. The end result is still the same.

Think of it as if I wrote it like this: 8/stuff. Here, I am replacing the division symbol with the forward slash.

30. ### a2zVirtuoso

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M and D are equal in PEMDAS. There is no mathematical rule that say anything after a division sign is the divisor. Why are you treating everything right of it as the divisor?

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31. ### Ima TeacherVirtuoso

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32. ### futuremathsprofPhenom

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Let me try it this way: The order of operations for a programming language isn't always what you would expect. For the most part, PE(DM)(AS) where division and multiplication are on the same level left to right and addition and subtraction are on the same level left to right, is how most programming languages work. Whether or not that is mathematically correct is actually almost irrelevant because this is how the mathematical tools that we use normally work. Programmers regularly automatically add parenthesis to make the math work as expected.

The computer in C/C++/C#, Quick BASIC, Excel and others, including my old TI-60 calculator calculates (8/2)*(2+2) = 16. Note that this is quite often the wrong answer even when it is written yet another way. Those who grew up using calculators will likely get this answer because they were taught by their calculators that this is the answer. This is how the majority of compilers and interpreters are designed to work so it is unlikely to change.

In math, the formula should be calculated as 8/(2*(2+2)) because without the multiplication symbol the 2(2+2) evaluates to 8. If this was found in a book as a math problem, it would have been written 8 over 2(2+2) making it clear that 8 was being divided by the stuff on the bottom. The 2 is attached to the parenthesis so it reduces to 8/8 = 1.

So 1 is the correct mathematical answer and 16 is the expected computer answer.

33. ### futuremathsprofPhenom

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Explained above. Try again.

34. ### a2zVirtuoso

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Attached? No it is 2 x the value in the parenthesis.

35. ### Ima TeacherVirtuoso

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Math is math.

There is no such thing as “mathematical answer” and “expected computer answer”.

You’re not working the problem as it is written.

Sample Problem

36. ### vickilynMultitudinous

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Best news I've had all year - can I send out huge thanks to my truly excellent math teachers? They were so good that I passed out of college math. I was given the credits necessary, and I never went on to more classes. I revisited math when raising our son, however, since it was not his strong suit. I was his at home tutor through Pre-calc, which did refresh my skill sets. I can't, however, use his high functioning calculator. Haven't decided if that is a liability or an asset.

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37. ### MichelleRookie

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There are no additional grouping symbols in the problem in question.
I feel that the correct answer is 16. I’m not sure why people are saying that it’s 1 and that a ( ) next to a number doesn’t mean multiply but you distribute.

38. ### MichelleRookie

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If you solve the problem as it is first you do what is in the ( ) and then divide then multiply.

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39. ### futuremathsprofPhenom

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Here is a picture showing how calculators can arrive at different answers for the exact same reason I outlined above. I’ve actually have extensive programming language knowledge and have written quite a few lines of code:

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40. ### MichelleRookie

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I work with highly qualified math teachers. I was questioning this because lots of people on another site were saying you have to distribute.

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