PEMDAS

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

  1. Michelle

    Michelle Rookie

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    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 ?
     
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  3. Tired Teacher

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

    Michelle Rookie

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

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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. TeacherGroupie

    TeacherGroupie Moderator

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

    futuremathsprof Aficionado

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    Insert grouping symbols; specifically, parentheses:

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

    Gotta the love the American educational system...
     
  8. futuremathsprof

    futuremathsprof Aficionado

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    ...
     
    Last edited: Aug 2, 2019
  9. futuremathsprof

    futuremathsprof Aficionado

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

    vickilyn Magnifico

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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 Teacher

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    Vickilyn, I wish that had been my problem, but that might be the problem for some.. :)
     
  12. a2z

    a2z Maven

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    .................................
     
  13. Tired Teacher

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

    futuremathsprof Aficionado

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    a2z clarified their original post and I retract my previous statement.
     
    Last edited: Aug 2, 2019
  15. futuremathsprof

    futuremathsprof Aficionado

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    Nope. It’s pretty obvious. You don’t need multiple math degrees like I have to see this.
     
  16. a2z

    a2z Maven

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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. a2z

    a2z Maven

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    Why are you being rude?
     
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  18. a2z

    a2z Maven

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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. vickilyn

    vickilyn Magnifico

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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. futuremathsprof

    futuremathsprof Aficionado

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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. futuremathsprof

    futuremathsprof Aficionado

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    Edit: You’re right. I need to tone it down.
     
    Last edited: Aug 2, 2019
  22. a2z

    a2z Maven

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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. futuremathsprof

    futuremathsprof Aficionado

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    You give me hope for America!
     
  24. vickilyn

    vickilyn Magnifico

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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.:eek:
     
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  25. futuremathsprof

    futuremathsprof Aficionado

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    You absolutely are! Take that back!
     
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  26. Ima Teacher

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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. a2z

    a2z Maven

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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. futuremathsprof

    futuremathsprof Aficionado

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    Well, you’re both wrong.
     
  29. futuremathsprof

    futuremathsprof Aficionado

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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. a2z

    a2z Maven

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    That doesn't answer the question.

    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 Teacher

    Ima Teacher Maven

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  32. futuremathsprof

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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. futuremathsprof

    futuremathsprof Aficionado

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    Explained above. Try again.
     
  34. a2z

    a2z Maven

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

    Ima Teacher Maven

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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. vickilyn

    vickilyn Magnifico

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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. Michelle

    Michelle Rookie

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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. :confused:
     
  38. Michelle

    Michelle Rookie

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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. futuremathsprof

    futuremathsprof Aficionado

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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:

    https://mobile.twitter.com/celestiallight_/status/1156296200586289153
     
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  40. Michelle

    Michelle Rookie

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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.
    Redo the original problem and don’t add your extra ( ).
     
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  41. futuremathsprof

    futuremathsprof Aficionado

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    Mathematics is not about feelings.
     
    Last edited: Aug 2, 2019

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