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Math Help - Reverse Order of Operations vs. Order of Operations???

  1. #1
    Newbie resource room's Avatar
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    Reverse Order of Operations vs. Order of Operations???

    How do I know which one to use with an equation..???

    Thanks...
    Aimee
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  2. #2
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    Quote Originally Posted by resource room
    How do I know which one to use with an equation..???

    Thanks...
    Aimee
    Could you give a specific example?
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  3. #3
    Newbie resource room's Avatar
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    Examples...

    X+4x2=18 and Xx2-1=5
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  4. #4
    Member jacs's Avatar
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    x + 4 x 2 = 18

    x + 8 = 18 (if you have something you can simplify on one side, then you shoudl do that first)

    to eliminate the + 8, you do the opposite (reverse) to it: opposite to plus is minus so you subtract 8 from both sides leaving you with

    x = 10



    X x 2 -1 = 5 always simplify first wherever possible

    2x - 1 = 5 add one to both sides
    2x = 6 divide both sides by 2
    x = 3

    normally you do mulitply before subtract
    but since we are trying to solve an equation, then everythign is back to front, so you deal with the subtract before the multiply
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  5. #5
    Newbie resource room's Avatar
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    There is a difference between "simplifying" and "Order of Operations"..???

    So, you are saying that when I simplify, I am not ready to follow the order of operations yet..??? Could you give me an example then of a problem where you use the order of operations and one that you don't... I have Googled "order of operations" and just found out that there is a "reverse order of operations"...

    I feel that I need to confess something at this point... I am actually a newly certified resource room teacher... I have a degree in English and am working on a master's in history... I have not had algebra since 1965 (Yes, I will be retiring from teaching after next year.. ), but in the meantime I find myself teaching resource math to high school kids...

    I have been using an old pre-algebra book that looked like something "we" could do, but when the book started adding and subtracting instead of multiplying and dividing (on Friday) they threw me off completely... One of the regular algebra teachers had me drill into the kids G-E-M-A to help them remember the order... Now, how do I explain that you only follow that order at certain times...

    I found my algebra teacher advisor and another one to boot, but I didn't understand their explanation... It was Friday and I did not want to hold them up by going into a more detailed explanation for me... I just want to be able to explain it to MY students....like, okay we were following the order of operations but now we are not BECAUSE... See my dilemma..??? I don't know the "why" yet...

    Thanks for all your help... And if you can help me to understand this and you see me again on this board, just remember that I am trying to understand something myself before I try to "teach" it... Also, not having an answer key for the book I am using can be a real bummer...

    Aimee

    Quote Originally Posted by jacs
    x + 4 x 2 = 18

    x + 8 = 18 (if you have something you can simplify on one side, then you shoudl do that first)

    to eliminate the + 8, you do the opposite (reverse) to it: opposite to plus is minus so you subtract 8 from both sides leaving you with

    x = 10



    X x 2 -1 = 5 always simplify first wherever possible

    2x - 1 = 5 add one to both sides
    2x = 6 divide both sides by 2
    x = 3

    normally you do mulitply before subtract
    but since we are trying to solve an equation, then everythign is back to front, so you deal with the subtract before the multiply
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  6. #6
    Member jacs's Avatar
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    Smile

    when dealing with simple algebra, (not an equation) you need to follow the oder of operations to simplify

    so something like 2 x a + 3 x b = 2a + 3b doing the mulitply then the addition

    in an equation however we are looking to 'undo' what has been done so we need to do everything back to front.

    3a + 7 = 16

    the a has been mulitplied by 3 and then added by 7

    so we work it backwards. opposite to add 7 is subtract 7

    3a = 9

    then the opposite to times 3 is divide 3

    a = 3

    so if we are trying to solve for an unknown, that is the time when reverse order is necessary


    i hope that helps a little
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