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Comment on A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

vithigar@lemmy.ca ⁨10⁩ ⁨months⁩ ago

The same priority operations can be done in any order without affecting the result, that’s why they can be same priority and don’t need an explicit order.

6 × 4 ÷ 2 × 3 ÷ 9 evaluates the same regardless of order. Can you provide a counter example?

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Robust_Mirror@aussie.zone ⁨10⁩ ⁨months⁩ ago
Another person already replied using your equation, but I felt the need to reply with a simpler one as well that shows it:

9-1+3=?

Subtraction first:
8+3=11

Addition first:
9-4=5

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- SmartmanApps@programming.dev ⁨9⁩ ⁨months⁩ ago
  
  Addition first: 9-4=5
  
  Nope. Addition first is 9+3-1=12-1=11. You did 9-(1+3), incorrectly adding brackets and changing the answer (thus a wrong answer)
  
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HereIAm@lemmy.world ⁨10⁩ ⁨months⁩ ago
So let’s try out some different prioritization systems.

Left to right:
(((6 * 4) / 2) * 3) / 9
((24 / 2) * 3) / 9
(12 * 3) / 9
36 / 9 = 4

Right to left:
6 * (4 / (2 * (3 / 9)))
6 * (4 / (2 * 0.333…))
6 * (4 / 0.666…)
6 * 6 = 36

Multiplication first:
(6 * 4) / (2 * 3) / 9
24 / 6 / 9
Here the path divides again, we can do the left division or right division first.
Left first:
(24 / 6) / 9
4 / 9 = 0.444… Right side first:
24 / (6 / 9)
24 / 0.666… = 36

And finally division first:
6 * (4 / 2) * (3 / 9)
6 * 2 * 0.333…
12 * 0.333… = 4

It’s ambiguous which one of these is correct. Hence the best method we have for “correct” is left to right.

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- SmartmanApps@programming.dev ⁨9⁩ ⁨months⁩ ago
  
  Right to left:
  
  6 * (4 / (2 * (3 / 9)))
  
  Nope! 6 × 4 ÷ 2 × 3 ÷ 9 =4 right to left is 6 ÷ 9 x 3 ÷ 2 × 4 =4. You disobeyed the rule of Left Associativity, and your answer is wrong
  
  Multiplication first: (6 * 4) / (2 * 3) / 9
  
  Also nope. Multiplication first is 6 x 4 x 3 ÷ 2 ÷ 9 =4
  
  Left first: (24 / 6) / 9
  
  Still nope. 6 × 4 x 3 ÷ 2 ÷ 9 =4
  
  Right side first: 24 / (6 / 9)
  
  Still nope. 6 × 4 x 3 ÷ 9 ÷ 2 =4
  
  And finally division first: 6 * (4 / 2) * (3 / 9)
  
  And finally still nope. 6 ÷ 9 ÷ 2 x 4 x 3 =4
  
  Hint: note that I never once added any brackets. You did, hence your multiple wrong answers.
  
  It’s ambiguous which one of these is correct
  
  No it isn’t. Only 4 is correct, as I have just shown repeatedly.
  
  Hence the best method we have for “correct” is left to right
  
  It’s because students don’t make mistakes with signs if you don’t change the order. I just showed you can still get the correct answer with different orders, but you have to make sure you obey Left Associativity at every step.
  
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- vithigar@lemmy.ca ⁨10⁩ ⁨months⁩ ago
  I stand corrected
  
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  - SmartmanApps@programming.dev ⁨9⁩ ⁨months⁩ ago
    
    I stand corrected
    
    No, you weren’t. Most of their answers were wrong. You were right. See my reply. 4 is the only correct answer, and if you don’t get 4 then you did something wrong, as they did repeatedly (kept adding brackets and thus changing the Associativity).
    
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- Melvin_Ferd@lemmy.world ⁨10⁩ ⁨months⁩ ago
  Maybe I’m wrong but the way I explain it is until the ambiguity is removed by adding in extra information to make it more specific then all those answers are correct.
  
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  - SmartmanApps@programming.dev ⁨9⁩ ⁨months⁩ ago
    
    until the ambiguity is removed
    
    There isn’t any ambiguity.
    
    all those answers are correct
    
    No, only 1 answer is correct, and all the others are wrong.
    
    Until the author gives me clarity then that sentence has multiple meanings. With math
    
    Maths isn’t English and doesn’t have multiple meanings. It has rules. Obey the rules and you always get the right answer.
    
    it doesn’t click for people that the equation is incomplete.
    
    It isn’t incomplete.
    
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    Melvin_Ferd@lemmy.world ⁨9⁩ ⁨months⁩ ago
    Can you explain how that is? Like with an example?
    
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  - HereIAm@lemmy.world ⁨10⁩ ⁨months⁩ ago
    100% with you. “Left to right” as far as I can tell only exists to make otherwise “unsolvable” problems a kind of official solution. I personally feel like it is a bodge, and I would rather the correct solution for such a problem to be undefined.
    
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    SmartmanApps@programming.dev ⁨9⁩ ⁨months⁩ ago
    
    100% with you. “Left to right” as far as I can tell only exists to make otherwise “unsolvable” problems a kind of official solution
    
    It’s not a rule, it’s a convention, and it exists so as to avoid making mistakes with signs, mistakes you made in almost every example you gave where you disobeyed left to right.
    
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    Robust_Mirror@aussie.zone ⁨10⁩ ⁨months⁩ ago
    It’s so we don’t have to spam brackets everywhere
    
    9+2-1+6-4+7-3+5=
    
    Becomes
    
    ((((((9+2)-1)+6)-4)+7)-3)+5=
    
    That’s just clutter for no good reason when we can just say if it doesn’t have parentheses it’s left to right. Having a default evaluation order makes sense and means we only need parentheses when we want to deviate from the norm.
    
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- barsoap@lemm.ee ⁨10⁩ ⁨months⁩ ago
  
  It’s ambiguous which one of these is correct. Hence the best method we have for “correct” is left to right.
  
  The solution accepted anywhere but in the US school system is “Bloody use parenthesis, then”, as well as “Why is there more than one division in this formula why didn’t you re-arrange everything to be less confusing” up to “50 Hertz, in base units, are 50s^-1^”.
  
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  - SmartmanApps@programming.dev ⁨9⁩ ⁨months⁩ ago
    
    The solution accepted anywhere but in the US school system range from “Bloody use parenthesis, then” over “Why is there more than one division in this formula why didn’t you re-arrange everything to be less confusing” to “50 Hertz, in base units, are 50s-1”.
    
    No, the solution is learn the rules of Maths. You can find them in Maths textbooks.
    
    so no actual mathematician, or other people using maths in earnest, use that kind of notation.
    
    Yes we do, and it’s what we teach students to do.
    
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  - HereIAm@lemmy.world ⁨10⁩ ⁨months⁩ ago
    I fully agree that if it comes down to “left to right” the problem really needs to be rewritten to be more clear. But I’ve just shown why that “rule” is a common part of these meme problems because it is so weird and quite esoteric.
    
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    SmartmanApps@programming.dev ⁨8⁩ ⁨months⁩ ago
    
    I fully agree that if it comes down to “left to right”
    
    It never does
    
    But I’ve just shown why that “rule” is a common part
    
    No you didn’t. You showed you didn’t understand the rules. Doing addition first for 10-1+1 is 10+1-1, not 10-(1+1). It literally means add all positive numbers together first, which are +10 and +1, as per Maths textbooks…
    
    Image
    
    Note in the above simplification of the coefficients we have 6-11+5-7+2=6+5+2-11-7=13-18=-5, and not, as you claim 6-(11+5)-(7+2)=6-16-9=-19
    
    because it is so weird and quite esoteric
    
    It’s a convention, not a rule, and as such can be completely ignored by those who understand the rules. See literal textbook example
    
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troistigrestristes@lemmy.eco.br ⁨10⁩ ⁨months⁩ ago
Oh my god now this is going to be Lemmy’s top thread for 6 months, isn’t it?

Btw, yeah I’m with you on this, you just need to know the priorities and you’re good, because the order doesn’t matter for operations with the same priority

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- HereIAm@lemmy.world ⁨10⁩ ⁨months⁩ ago
  Except it does matter. I left some examples for another post with multiplication and division, I’ll give you some addition and subtraction to see order matter with those operations as well.
  
  Let’s take:
  1 + 2 - 3 + 4
  
  Addition first:
  (1 + 2) - (3 + 4)
  3 - 7 = -4
  
  Subtraction first:
  1 + (2 - 3) + 4
  1 + (-1) + 4 = 4
  
  Right to left:
  1 + (2 - (3 + 4))
  1 + (2 - 7)
  1 + (-5) = -4
  
  Left to right:
  ((1 + 2) - 3) + 4 (3 - 3) + 4 = 4
  
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  - SmartmanApps@programming.dev ⁨9⁩ ⁨months⁩ ago
    
    Except it does matter
    
    No it doesn’t. You disobeying the rules and getting lots of wrong answers in your examples doesn’t change that.
    
    I left some examples for another post with multiplication and division
    
    Which you did wrong.
    
    I’ll give you some addition and subtraction to see order matter with those operations as well
    
    And I’ll show you it doesn’t matter when you do it correctly
    
    Subtraction first: 1 + (2 - 3) + 4 1 + (-1) + 4 = 4
    
    Nope. Right answer for wrong reason - you only co-incidentally got the answer right. -3+1+2+4=-3+7=4
    
    Right to left: 1 + (2 - (3 + 4)) 1 + (2 - 7) 1 + (-5) = -4
    
    Nope. 4-3+2+1=1+2+1=3+1=4
    
    Edit: You can argue that, for example, the addition first could be (1 + 2) + (-3 + 4)
    
    Or you could just do it correctly in the first place, always obeying Left Associativity and never adding Brackets
    
    in my opinion that’s another ambiguous case
    
    There aren’t ANY ambiguous cases. In every case it’s equal to 4. If you didn’t get 4, then you made a mistake and got a wrong answer.
    
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  - troistigrestristes@lemmy.eco.br ⁨10⁩ ⁨months⁩ ago
    Oh, but of course the statement changes if you add parentheses. Basically, you’re changing the effective numbers that are being used, because the parentheses act as containers with a given value (you even showed the effective numbers in your examples).
    
    Get this : + 1 - 1 + 1 - 1 + 1 - 1 + 1
    
    You can change the result several times by choosing where you want to put the parentheses. However, the order of operations of same priority inside a container (parentheses) does not change the resulting value of the container.
    
    In the example, there were no parentheses, so no ambiguity (there wouldn’t be any ambiguity with parentheses either, the correct way of calculating would just change), and I don’t think you can add “ambiguity” by adding parentheses — you’re just changing the effective expression to be evaluated.
    
    By the way, this is the reason why I absolutely overuse parentheses in my engineering code. It can be redundant, but at least I am SURE that it is going to follow the order that I wanted.
    
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    SmartmanApps@programming.dev ⁨9⁩ ⁨months⁩ ago
    
    Oh, but of course the statement changes if you add parentheses
    
    It sure does, but they don’t seem to understand that.
    
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