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Math Help - What if Order of Operations was reverse?

  1. #1
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    What if Order of Operations was reverse?

    What if you reversed the order of operations? Instead of PEMDAS it was SADMEP.

    At first glance you would think the order of operations is arbitrary. A convention we agree upon for no reason other than that having a convention ensures (or at least tries to ensure) that expressions will evaluate the same way for one evaluator as they do for another.

    I got to thinking about this tonight and came across a consequence of the idea that I couldn't wrap my head around.

    Simple example:

    3*4+5 regularly = 17.
    3*4+5 inversely = 27.

    But here's my question. Let's say you're faced with a real life situation.

    You have a rectangular arrangement of stones 3 wide and 4 deep. In addition you have 5 more stones. The obvious arithmetic expression for how many stones there are is 3*4 + 5.

    This is intuitive and obvious. Partly because we are used to PEMDAS.

    But if the order of operations were SADMEP and we were faced with the same arrangement of stones, what would be the arithmetic expression for the amount of stones?

    Since I can't think of an arithmetic expression for this situation, does it mean that PEMDAS is the logical (not so arbitrary after all) order of operations?

    Or are there stone arrangements that would be equally hard to represent with PEMDAS but trivial to represent with SADMEP?
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  2. #2
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    Quote Originally Posted by onepostppete View Post
    What if you reversed the order of operations? Instead of PEMDAS it was SADMEP.
    ...
    I got to thinking about this tonight and came across a consequence of the idea that I couldn't wrap my head around.

    Simple example:

    3*4+5 regularly = 17.
    3*4+5 inversely = 27.

    ...
    I'm pretty sure that I didn't understand your question correctly. The only part of your example where I can (maybe) help a little bit is:
    3*4+5 inversely = 27
    In algebra this is written as: 3\cdot (4+5)=27

    So it is definitely no reverse operation but the distributive law.
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  3. #3
    Junior Member lanierms's Avatar
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    Yeah, but he's saying that we should do the order of operation backwards. For example, in the second equation, even without the parentheses, we should add first and then multiply.
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  4. #4
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    Quote Originally Posted by onepostppete View Post
    What if you reversed the order of operations? Instead of PEMDAS it was SADMEP.

    At first glance you would think the order of operations is arbitrary. A convention we agree upon for no reason other than that having a convention ensures (or at least tries to ensure) that expressions will evaluate the same way for one evaluator as they do for another.

    I got to thinking about this tonight and came across a consequence of the idea that I couldn't wrap my head around.

    Simple example:

    3*4+5 regularly = 17.
    3*4+5 inversely = 27.

    But here's my question. Let's say you're faced with a real life situation.

    You have a rectangular arrangement of stones 3 wide and 4 deep. In addition you have 5 more stones. The obvious arithmetic expression for how many stones there are is 3*4 + 5.

    This is intuitive and obvious. Partly because we are used to PEMDAS.

    But if the order of operations were SADMEP and we were faced with the same arrangement of stones, what would be the arithmetic expression for the amount of stones?
    (3*4)+ 5

    Since I can't think of an arithmetic expression for this situation, does it mean that PEMDAS is the logical (not so arbitrary after all) order of operations?
    It looks to me like you set up a situation that would fit that order of operations. Suppose you had a 4 rocks in one row, 5 rocks in another and then put two additional rows next to each? Wouldnt (4+ 5)*3, which would be 4+5*3 with "SADMEP", be reasonable?

    Or are there stone arrangements that would be equally hard to represent with PEMDAS but trivial to represent with SADMEP?
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  5. #5
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    I like SADMEP (not the order of operations - just the word).
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