Can you solve 8÷2(2+2)

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  • Snapdragon

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    Can someone please link to an authoritative source that says "implied" multiplication is different than explicit multiplication, and therefore an exception to PEMDAS?

    Is there a PE {do whatever you want} MDAS rule we don't know about?

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    BugI02

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    Can someone please link to an authoritative source that says "implied" multiplication is different than explicit multiplication, and therefore an exception to PEMDAS?

    Is there a PE {do whatever you want} MDAS rule we don't know about?


    So, if there is no difference between explicit and implicit multiplication, division and multiplication are of equal level and comparable operations are performed left to right...

    When you see 3x ÷ 3y, do you get xy? I should think not
     

    Snapdragon

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    So, if there is no difference between explicit and implicit multiplication, division and multiplication are of equal level and comparable operations are performed left to right...

    When you see 3x ÷ 3y, do you get xy? I should think not
    There were no variables in the original problem, so introducing them is a moot point. The original expression contained only integers, so the order of operations still applies.
     

    DoggyDaddy

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    So, if there is no difference between explicit and implicit multiplication, division and multiplication are of equal level and comparable operations are performed left to right...

    When you see 3x ÷ 3y, do you get xy? I should think not

    Why would you get xy? It would simplify to x/y. (I can't seem to find a "divided by" symbol on my keyboard other than the slash.)
     

    jagee

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    Why would you get xy? It would simplify to x/y. (I can't seem to find a "divided by" symbol on my keyboard other than the slash.)

    His argument:
    3x ÷ 3y = 3*x÷3*y

    Going left to right, 3*×÷3 would leave x. Then its just xy.

    Its wrong, but I could see his point.
     

    danimal

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    Distributive property comes to mind

    • = 8 / 2(2+2)
    • = 8 / (4+4)
    • = 8 / 8
    • = 1

    The distributive property is really a simplification, and while I'm not sure it takes precedence over parenthesis or exponents, it certainly takes precedence over multiplication and division. Else we'd be saying the equation was (8/2)(2+2), but it is only the 2 that distinctly belongs to the grouping in the original statement.
     

    danimal

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    Why are you simplifying from right to left?
    Well, we have parenthesis, and a number or variable preceding the parenthesis. So the distributive property has been used we're dealing with a simplified statement. First order of business is to expand and un-simplify it. What number precedes the parenthesis? A 2, or is it 8/2? Is 8/2 is parenthesis also? If not, then you are dealing with with another operator, and the value to distribute is everything after the operator and before the opening parenthesis. Therefore only the 2 is distributed into the parenthesis, making it (4+4).
     
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