This.
Miss Chicken said what I was going to type, almost word for word, so I'll just quote her.
Facebook Math Debate: 6÷2(1+2)=?
- Thread starter Chaos Descending
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You guys are missing the point, it's not a simple "do you understand symbolic logic" question. It's a demonstration of the inadequacy and oversimplicity of the 400 year old order of operations rules. Want proof?
What about factorials, unary operators, non analytical functions (trigonometric, statistical, summations, error functions, the signum function, infinite products), limits, matrix operators, vector operators, differential operators, the list goes ON because the old BEDMAS thing is insufficient.
What about factorials, unary operators, non analytical functions (trigonometric, statistical, summations, error functions, the signum function, infinite products), limits, matrix operators, vector operators, differential operators, the list goes ON because the old BEDMAS thing is insufficient.
Isn't BODMAS sufficient for a simple equation as simple as 6÷2(1+2)?
JohnO, I'd like to hear your opinion about what I said above.
To summarise, I think that with 6÷2×(1+2), it's clear what is meant, but when we omit the multiplication sign as with ab÷cd, I'm inclined to read that as if the factors are bracketed expressions (ab)÷(cd).
ie, ab means (a×b) rather than just a×b
This equation could have been written more clearly. Just looking at it my instinctive answer is "1". However, when we bring PEMDAS into it I can see that the actual answer is "9".
Although, it still seems that the equation is written incorrectly. It should be: (6%2)(1+2) or (6%2) * (1+2)
The way it seems written is: 6/2(1+2) or 6/(2(1+2))
I guess my main hang-up is the division symbol. Whenever I see one used and its not in parentheses or stand alone my mind automatically turns the problem into a fraction.
Although, it still seems that the equation is written incorrectly. It should be: (6%2)(1+2) or (6%2) * (1+2)
The way it seems written is: 6/2(1+2) or 6/(2(1+2))
I guess my main hang-up is the division symbol. Whenever I see one used and its not in parentheses or stand alone my mind automatically turns the problem into a fraction.
Bah! I got 9 the first time, then changed my answer to 1. It was a trick question! 
Seriously, I went from "right to left" thinking multiplication preceded division. So the PEMDAS model is actually misleading. Aunt Sally my ass. It should be written differently: P, E, [M/D], [A/S].
Seriously, I went from "right to left" thinking multiplication preceded division. So the PEMDAS model is actually misleading. Aunt Sally my ass. It should be written differently: P, E, [M/D], [A/S].
That is exactly the problem I had. Aside from the button on a calculator, I have never seen the division symbol used in practice. Hell, even calculators don't use the division symbol anymore. They use a slash.
The actual answer is 0, because % is modulo, not divide. 
I think the problem is clearly written to confuse and confound. A "real problem" wold, and should be written as clearly as possible for the best understanding of the intended answer. But most tell of all was that it took me a moment of reading it to figure out how to even get and answer of one.
As to my earlier comment re: the slash and the division symbol, it's just what I remember either being taught in high school or at some point.
That while the "/" and "÷" mean the same thing they can imply two different things, especially when typing.
2/3+4 either answers 4.66 or 0.286 depending on how you view the "/" symbol as typed. Is it "Two Thirds" plus 4 or is it 2 divided by 3+4? Using the "÷" in typing (or even writing depending on how you write fractions) makes it a bit clearer you're saying 2÷3+4, getting an answer of 4.66. But, again, I see it as a case of an intentionally confounding problem that'd be better solved by using parentheses. (2/3)+4
As to my earlier comment re: the slash and the division symbol, it's just what I remember either being taught in high school or at some point.
That while the "/" and "÷" mean the same thing they can imply two different things, especially when typing.
2/3+4 either answers 4.66 or 0.286 depending on how you view the "/" symbol as typed. Is it "Two Thirds" plus 4 or is it 2 divided by 3+4? Using the "÷" in typing (or even writing depending on how you write fractions) makes it a bit clearer you're saying 2÷3+4, getting an answer of 4.66. But, again, I see it as a case of an intentionally confounding problem that'd be better solved by using parentheses. (2/3)+4
Dammit, I forgot you evaluate multiplication and division before addition and subtraction.
So it's really 6÷2 (= 3)
3 x 2 x (2+1) = 3 x 2 x 3 = 18. Uhh, wait, what?
My initial take was as Litmus Dragon said, which can be written as 6 ÷ (2(2+1)).
Hmm, glad maths is not part of my life.
So it's really 6÷2 (= 3)
3 x 2 x (2+1) = 3 x 2 x 3 = 18. Uhh, wait, what?
My initial take was as Litmus Dragon said, which can be written as 6 ÷ (2(2+1)).
Hmm, glad maths is not part of my life.
The 2 that I bolded and underlined in your quote shouldn't be there anymore.
Once you turn 6÷2 into 3, the 2 is gone. You used it up.
So it becomes just 3 * (2+1) = 3 * 3 = 9.
But even then, you still did it out of order. You're supposed to do the PARENTHESES first.
6÷2(2+1) = 6÷2*(2+1) = 6÷2*3 = 3*3 = 9
Which brings is back to how do you know it's (6/2)*3 and not 6/(2*3)?
In the order of operations multiplication and division fall in the same place and aren't separate (near as I can remember) so, as I said, it either depends on if you treat the division-symbol is different than the slash in how you're supposed to divide or the problem is not formatted in a way to allow for a clear answer to be made.
If I were writing this problem out I'd make it as clear as possible for the person doing it "(6/2)*(2+1)" which clearly shows that there are to separate problems there that are interacted with one another once solved.
Otherwise it's possible to get "1" out of "6÷2(1+2)." As "2(1+2)" can be seen it's own little problem that's being divided into 6.
That said, however, I gave this problem to my mother, who has no memory/knowledge of the "order of operations" and I even had to explain to her how a number next to a parenthesis implies multiplication and the answer she got was "9."
Well, it's really the computer that's making the problem confusing. If you were to write it out by hand, you would put 2(1+2) underneath 6/ if you intended it to be together.
Yes, multiplication and division have the same value in the order of operations, so you would read them from left to right.
Bump.
Actually, I was doing some research on Einstein, and realised I had misinterpreted the famous equation.
E=MC2
isn't E= Mx(CxC), it's (MxC)x(MxC), yes?
And if E=MC2
then C = ?
In other words, how would the formula be rendered for C?
Or am I misunderstanding this?
Actually, I was doing some research on Einstein, and realised I had misinterpreted the famous equation.
E=MC2
isn't E= Mx(CxC), it's (MxC)x(MxC), yes?
And if E=MC2
then C = ?
In other words, how would the formula be rendered for C?
Or am I misunderstanding this?
It's the first one.
E = M x C^2
It would only be the second one if it was written E=(MC)^2
E equals mass times the speed-of-light squared.
Since doing an exponent isn't easy to do when typing, if possible at all considering there may not be an ASCII code for it, people just simply say "C2."
Some will go the extra mile and say "E=MC^2" but it is supposed to be E=M(C*C).
"C" is letter used to represent the constant of the speed of light through a given material, in this case a vacuum. E is energy, M is mass.
Since doing an exponent isn't easy to do when typing, if possible at all considering there may not be an ASCII code for it, people just simply say "C2."
Some will go the extra mile and say "E=MC^2" but it is supposed to be E=M(C*C).
"C" is letter used to represent the constant of the speed of light through a given material, in this case a vacuum. E is energy, M is mass.
Exactly.
Actually, now that I'm thinking about it, these equations are saying the exact same thing. The only difference is that in the second version you've used the distributive property to re-write the problem.
C is the speed of light. It's just easier to write "C."
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