Pick a side! Try to explain why YOUR interpretation of mathematical order of operation is correct!
Facebook Math Debate: 6÷2(1+2)=?
- Thread starter Chaos Descending
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PEMDAS
Parentheses,
Exponents
Multiplication & Division
Addition & Subtration
Left to right.
Ergo:
6÷2(2+1) is the same as 6÷2*(2+1) (numbers against parentheses imply a "*" operator)
6÷2*3 (now we go left to right)
6÷2 = 3 and 3*3 = 9
Correct answer is 9.
Parentheses,
Exponents
Multiplication & Division
Addition & Subtration
Left to right.
Ergo:
6÷2(2+1) is the same as 6÷2*(2+1) (numbers against parentheses imply a "*" operator)
6÷2*3 (now we go left to right)
6÷2 = 3 and 3*3 = 9
Correct answer is 9.
Yeah, 9.
6÷2(1+2)
3(3)
3 * 3
It's 9.
6÷2(1+2)
3(3)
3 * 3
It's 9.
I am astonished at how many people REALLY THINK that the "2(1+2)" is all one "clause", if you will, that must be evaluated before the "6÷" part comes into play.
That's why so many people out in the Greater InterWebs Land say that it's "1".
That's why so many people out in the Greater InterWebs Land say that it's "1".
This is why you use LaTeX (or another suitable tool) to write formulae, instead of typing it on a keyboard like a cheap whore.
The formatting is not optimal, it would be clearer to write it like
(6÷2)(1+2)
or if it were intended the other way
6 ÷ (2 (1+2) )
(6÷2)(1+2)
or if it were intended the other way
6 ÷ (2 (1+2) )
I was having a debate with a guy today about this, he was in the "it's equal to one" camp.
He actually told me, "It's obvious you've only ever learned math by using a calculator" or something like that. I was most amused!
He actually told me, "It's obvious you've only ever learned math by using a calculator" or something like that. I was most amused!
I can see it both ways.
It's common in mathematics to omit the multiplication sign, but do use division signs. And things like AB÷CD, are frequently written on blackboards or in papers, to mean (A*B)÷(C*D), even though that goes against PIDMAS/BODMAS or whatever you call it.
Where a multiplication sign is omitted, I tend to read that part as if it is bracketed.
ie CD reads as (C*D) not just C*D
A related example: 6a ÷ 2a = ??
It's common in mathematics to omit the multiplication sign, but do use division signs. And things like AB÷CD, are frequently written on blackboards or in papers, to mean (A*B)÷(C*D), even though that goes against PIDMAS/BODMAS or whatever you call it.
Where a multiplication sign is omitted, I tend to read that part as if it is bracketed.
ie CD reads as (C*D) not just C*D
A related example: 6a ÷ 2a = ??
It's true that adding variables makes everything much more complex, but there are none in this example. It's very straightforward to me.
Variables obey the same algebraic rules as numbers. My example is equivalent to your example.
What both our questions boil down to is how do we interpret expressions with omitted multiplication signs.
I would say that 6a ÷ 2a = 3, because 2a means (2*a) and not just 2*a.
I agree with your interpretation, but then I have always been explicitly taught, "variable expressions always have implied parentheses".
The programmer in me knows that 6a/2a is probably an incorrect attempt to write 6*a/(2*a), but the optimist in me hopes that by pointing out the error, it might not be repeated. So it's best to follow the strict rules rather than assuming what is meant.
I know that the answer is 9, but I've always felt like multiplication should come before division. I don't know why, it just seems nicer. So I wish the answer were 1, but it is not.
Well...sorry.
I was certain it was 1 myself. And then I read everyone's explanations and felt pretty stupid.
Now, in my own defense, I've been out of school for over 30 years and haven't worked with equations at all in that time. But I have to say that I find it extremely weird that I was so sure that I remembered it correctly as taught (when obviously I didn't) and that so many people apparently have the same problem. It's just odd, and I wonder why. *shrug*
I was taught to do the stuff in parentheses first.
6 (divided by) 2(1+2)=
6 (divided by) 2(3)=
Now we get tricky since this can be interpreted two ways as multiplication and division are both in the same order of operations and the problem above can be interpreted two different ways. But I was also always taught the fraction/division bar is different than the division symbol. The fraction bar would suggest a different problem.
6/2(3) is completely different than 6 (divided by) 2(3).
The former suggests a fraction. 6 over 2(3). Which would give us an answer of "1."
But since the symbol is used we treat that as a separate problem and it's next in the order of operations.
6/2 is 3.
Now we have 3(3) and we have the two problems (the stand-alone one and the one that was in parentheses) done and can now do the inferred operation of the parenthetical "problem" interacting with the former division problem. Giving us a result of 9.
The divisor means something completely different than the slash.
The slash implies a fraction the divisor infers a mathematical computation.
The answer is 9.
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