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Math Help - Order of operations clarification

  1. #1
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    Order of operations clarification

    Hello all!

    I am a new member of this forum, and am eager to partake in many wonderful math discussions and offer as much help as I can!

    My first post, however, is a bit of an embarrassing confession (especially considering I enjoy math so much that I teach it at the high school level)! I have an order of operations misunderstanding, it would seem, and am looking for some clarification.

    The problem as given is:

    3st^2 / st + 6
    where s = 4 and t =8.

    My understanding of the problem, then, is:

    3*4*8^2 / 4 * 8 + 6

    Order of operations state that parentheses ought to go first, then exponents, then multiplication or division, then addition or subtraction.

    My order of solving the problem:

    3*4*64 / 4 * 8 + 6 (exponents first)
    12 * 64 / 4 * 8 + 6 (left to right multiplication or division)
    768 / 4 * 8 + 6
    192 * 8 + 6
    1536 + 6 (addition)
    1542

    Wolfram alpha did corroborate my answer: 3*4*8^2/4*8+6 - Wolfram|Alpha (although I'm not sure I used the proper division symbol)

    However, this is not the answer that the book gives! The book gives an answer of 30. I can reproduce this answer IF I choose to multiply all my numbers first, then divide, then finish by adding.

    Who is right? Is my understanding of Order of Operations flawed? Do I really need to complete all of my multiplication, then jump to division? I thought I merely went left to right on order of operations when I arrived at related operations (ie multiplication and division, or addition and subtraction).

    Please help!

    Thanks!
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  2. #2
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    Re: Order of operations clarification

    3st^2 / st + 6
    where s = 4 and t =8.
    I think your expression is

    \frac{3st^2}{st}+6 = 3t + 6 = 24 + 6 = 30
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  3. #3
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    Re: Order of operations clarification

    Your notation is extremely ambiguous it could be either of
    \frac{(3)(4)(8^2)}{4(8)+ 6} or
    \frac{(3)(4)(8^2)}{4(8)}+ 6 or

    Apparently you mean the second. For the fraction, the order of multiplications or divisions is irrelevant- though it would be a good idea to do as much cancelling as possible.
    Last edited by HallsofIvy; September 6th 2012 at 05:25 PM.
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  4. #4
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    Re: Order of operations clarification

    Thanks for the replies, guys.

    I completely see where simplifying the expression first, then substituting, then evaluating would be the ideal way to solve the problem. I'm teaching order of operations to brand new Algebra 1 students, however. I want to make sure I teach them the correct and accepted method for using order of operations.

    I should have mentioned this: The division symbol that the book used was not the forward slash (and therefore it wasn't really a fraction) but the line with the two dots (one on the top and one on the bottom; the symbol that, for whatever reason, we are all first taught division with).
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