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[–] 100 points 1 year ago* (66 children)

I'm sure we're all geniuses here, but just in case...

Please excuse my dear aunt Sally.

Parenthesis, exponents, multiplication, division, addition, subtraction.

Why? Because a bunch of dead Greeks say so!

3x3-3÷3+3

(3x3)-(3÷3)+3

9-1+3

8+3

11

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  • [–] 95 points 1 year ago (9 children)

    I guess remembering grade school order of operation means you're a guinus now? Bar has gotten pretty low...

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  • [+] 26 points 1 year ago* (last edited 1 month ago) (4 children)
  • [–] 8 points 1 year ago (2 children)

    I like the version where these problems are made purposefully ambiguous so people will fight over it and raise the level of interaction

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  • [–] 10 points 1 year ago (2 children)

    G U I N U S.

    I know it's probably a typo, but I'm enjoying it.

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  • [–] 13 points 1 year ago (19 children)

    Not a genius. But if subtraction is last, why isn't it 9-4?

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  • [–] 30 points 1 year ago (15 children)

    Parenthesis, exponents, multiplication, division, addition, subtraction.

    should actually be

    Parenthesis, exponents, (multiplication and division), (addition and subtraction).

    Addition and subtraction are given the same priority, and are done in the same step, from left to right.

    It's not a great system of notation, it could be made far clearer (and parenthesis allow you to make it as clear as you like), but it's essentially the universal standard now and it's what we're stuck with.

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  • [–] 3 points 1 year ago* (14 children)

    No, it should simply be "Parenthesis, exponents, multiplication, addition."

    A division is defined as a multiplication, and a substraction is defined as an addition.

    I am so confused everytime I see people arguing about this, as this is basic real number arithmetics that every kid in my country learns at 12 yo, when moving on from the simplified version you learn in elementary school.

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  • [–] 4 points 1 year ago (8 children)

    You want PEMA with knowledge of what is defined, when people can't even understand PEMDAS. You wish for too much.

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  • [–] 3 points 1 year ago (6 children)

    I hate most math eduction because it's all about memorizing formulas and rules, and then memorizing exceptions. The user above's system is easier to learn, because there's no exceptions or weirdness. You just learn the rule that division is multiplication and subtraction is addition. They're just written in a different notation. It's simpler, not more difficult. It just requires being educated on it. Yes, it's harder if you weren't obviously, as is everything you weren't educated on.

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  • [–] 0 points 1 year ago* (last edited 1 year ago) (5 children)

    That's because (strictly speaking) they aren't teaching math. They're teaching "tricks" to solve equations easier, which can lead to more confusion.

    Like the PEMDAS thing that's being discussed here. There's no such thing as "order of operations" in math, but it's easier to teach by assuming that there is.

    Edit: To the people downvoting: I want to hear your opinions. Do you think I'm wrong? If so, why?

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  • [–] 17 points 1 year ago*

    Addition/subtraction work out the same regardless of how you order the operations. If you do subtraction last you start with the original:

    9-1+3

    and you are adding 3 to the result of (9-1). Since you are trying to perform it before the (9-1) operation is carried out, you can add 3 to the 9:

    12-1 = 11

    or you can add three to the -1 and get:

    9+2 = 11

    You only end up with 9-4 if you were subtracting 3 rather than adding three. It all becomes more obvious if you read the original as:

    9 + (-1) + 3

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  • [–] 9 points 1 year ago* (last edited 1 year ago)

    The "why" goes a little further than that.

    In actuality, it's because of fundamental properties of operations

    • Commutation

    a + b = b + a

    a×b = b×a

    • Association

    (a + b) + c = a + (b + c)

    (a×b)×c = a×(b×c)

    • Identity

    a + 0 = a

    a×1 = a

    If you know that, then PEMDAS and such are useless because they're derived from those properties but do not fully encompass them.

    Eg.

    3×2×(2+2) = 3×(4+4) = 12+12 = 24

    This is a correct solution that is improper if you're strictly adhering to PEMDAS rule as I've done multiplication before parenthesis from right to left.

    I could even go completely out of order by doing 3×2×(2+2) = 2×(6+6) and it will still be correct

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