I'll try to identify all the causes of giving the wrong 2 answer.
1. Assuming that the division sign and the fractional bar are the same:
A division sign requires parentheses to tell you where it ends.
(a+b/c)/(a+d)
A fractional bar works like a vinculum - it shows you what is grouped above and below it, so you don't have to put parentheses there.
If you tried to omit the parentheses in the inline format with a division sign, you would write something completely different.
They are not the same. Period.
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2. Inability to convert from inline format to vertical format:
a+b/c+d
Is not
It will always be just
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3. The unfortunate mnemonics of PEMDAS wich are understood by some, as Parentheses, then Exponents, then Multiplication, then Division, then Addition, then Substraction:
It should be PEMaDAaS or Parentheses, then Exponents, then Multiplication and Division, then Addition and Substraction.
Multiplication and Division are equal, because
2*2=2*(2/1)=2/(1/2)
And Addition and Substraction are equal, because
2+2=2-(-2)
So if we have Multiplication and Division signs, we go from left to right.
And if we have Addition and Substraction signs, we go from left to right too.
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4. Breaking the basic, holy, unbreakable rule of PEMaDAaS with the distributive property "oneness":
We can't break PEMaDAaS with anything, or we would arrive at the whole new twisted and wrong universe of wrong mathematics.
2(9+3)=(2*9)+(2*3)=24
We can use the distributive property here.
2+2(9+3)=2+(2*9)+(2*3)=26
And here too.
2/2(9+3)=2/2*12=1*12=12
But not here, because the division which is higher than multiplication in PEMaDAaS ripped the 2 and the inside of the bracket apart.
2^2(9+3)=2^2*12=4*12=48
And again not here, because the exponent sign, or as we say in Europe "to the power of" sign, powerfully stole the 2 from the (9+3).
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5. Trying to imagine what the author of the equation had in mind, when he was writing it, instead of just solving the problem exactly as it is written:
E=mc^2 is not E=(mc)^2
People could die if some construction engineer assumed these parentheses around m and c just "because they are written together".
a+b/c+d is not (a+b)/(c+b)
I saw some "scientist" on another forum, trying to tell us that it could be justified to imagine parentheses there.
Interpreting a formula to "really" mean that addition without parentheses around it comes before division ??? No words... Just a big, loud LOL !!!
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6. Trolling.
Well... hehehe.
