Comment on SBA #119 maths

AHemlocksLie@lemmy.zip ⁨2⁩ ⁨weeks⁩ ago

• mic_check_one_two@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

  This is actually a generational thing. Millennials were taught “PEMDAS”:

  1. Parenthesis
  2. Exponent
  3. Multiplication
  4. Division
  5. Addition
  6. Subtraction

  But younger generations have been taught “BEDMAS” instead:

  1. Brackets
  2. Exponent
  3. Division
  4. Multiplication
  5. Addition
  6. Subtraction

  Notably, Division and Multiplication are swapped on PEMDAS and BEDMAS, to make this “both happen at the same time” more straightforward. But that only applies if the entire operation can happen at the same time.

  For instance, let’s say 6/2(3) compared to 6÷2(3). At first glance, they both appear to be the same operation. But in the former, the 6 dividend would be over the entire 2(3) divisor. Which means you would need to simplify the divisor (by resolving the multiplication of 2•3) before you divide. So the former would simplify to 6/6=1, while the latter would divide first and become 3(3)=9.

  Technically, if you wanted to be completely clear, you would write it using multiple parenthesis as needed. For instance, you would write it as either:
  (6÷2)(3)=9 or 6÷(2(3))=1 to avoid the ambiguity. Then it wouldn’t matter if you’re using PEMDAS or BEDMAS.

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  • AHemlocksLie@lemmy.zip ⁨2⁩ ⁨weeks⁩ ago

    But in the former, the 6 dividend would be over the entire 2(3) divisor.

    I have never heard of or seen an example of anyone using / and ÷ in different ways. If you want multiple terms in your divisor, either write it as a large fraction with all relevant terms in the dividend or divisor, or use parentheses. This just seems like sloppy notation to me.

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    • mic_check_one_two@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

      It was just because MarkDown doesn’t really make mathematical notation easy. The point is that with a slash, the 6 is over the entire 2(3) divisor. It’s the difference between these:
      Image

      You can even see that the automatic solution (in yellow) parses the two differently. In the first example, it correctly resolves the 2(3) first. But in the second, it parses the 6÷2 first, because it is left ambiguous.

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• Mistic@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

  Usually, no sign before the bracket means juxtaposition.

  So 2(1+2) is really (2+4)

  Compare 2/2x and 2/2*x where x is (1+2)

  The first is 2/(2+4)=1/3, the second is (2/2)*(1+2)=3

  Also, there’s no real rule about solving left to right due to associative and commutative properties: 123 = 1*(23) = (12)3 = 312 = 21*3 = 6

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• rapchee@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

  wiuld you say the same thing if the division was written out like a line under 2(3) and under that 6
  idk how this’ll come out but something like this:
  2(1+2)

   6
  

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  • AHemlocksLie@lemmy.zip ⁨2⁩ ⁨weeks⁩ ago

    In that case, I’d say the answer is 1. Top and bottom are each resolved to the fullest extent possible before dividing top by bottom. It’s equivalent to (top)÷(bottom), but it’s clearer and preferable if you can easily format that way in my opinion, just harder on a computer.

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  • Reyali@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    I think that’s why people are complaining about the division sign.

    It’s been decades since I took a math class so I am definitely not the right person to explain things, but I am using technology to confirm my understanding of the various notations:

    Image

    So yeah, if you put 6 over a denominator of 2(1+2), the answer is different (1) because the equation is different. But if you write it out literally, it would be 6 over 2 times (1+2).

    What you wrote swapped the denominator to make it 2(1+2)÷6, which will always be 1.

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