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#1
Old 09-02-2012, 01:06 PM
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Math question (order of operations)

This popped up in my Facebook today.
6-1X0+2/2=?
Half of the answers say the correct answer is 7 as you do the order of operations with multiplication and division first giving you:
6-(1X0)+(2/2)
6-0+1=7

The other half of the people say that sans brackets or parentheses you go left to right.
(6-1)X0+2/2=1
My algebra classes were a loooong time ago, and I'm flat not sure of the correct answer. My first thought was the the latter of the two methods was correct working left to right, but I am not sure.
So mathematical dopers, what is the correct answer?
#2
Old 09-02-2012, 01:09 PM
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The correct answer depends on which order of operations you adopt.
#3
Old 09-02-2012, 01:12 PM
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The usual order of operations is BODMAS (in the UK) or PEDMAS (in the US):
Brackets, Orders, Division, Multiplication, Addition, Subtraction
Parantheses, Exponents, as above.

So 6 - (1 x 0) + (2 / 2) is right, which gives you 7.
#4
Old 09-02-2012, 01:16 PM
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Yep, 7. Not having parentheses doesn't mean you throw out all the other order of operations, just that you start with exponents. Not having exponents doesn't mean you throw out all the other order of operations, just that you start with multiplication.

(We learned it PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

Last edited by WhyNot; 09-02-2012 at 01:17 PM.
#5
Old 09-02-2012, 01:23 PM
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The first half is right. In the expression in the OP, you do the multiplication and division first.
#6
Old 09-02-2012, 01:52 PM
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Quote:
Originally Posted by Dervorin View Post
The usual order of operations is BODMAS (in the UK) or PEDMAS (in the US):
Brackets, Orders, Division, Multiplication, Addition, Subtraction
Parantheses, Exponents, as above.

So 6 - (1 x 0) + (2 / 2) is right, which gives you 7.
To further confuse people, it's BEDMAS in Canada...
#7
Old 09-02-2012, 02:08 PM
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I've always wondered this about these threads: Are you guys just abbreviating for the Internet, or do you actually pronounce the word "Pedmas" in your head when you do math? I mean, was there actually a teacher somewhere in your lives that was like "Remember, kids, always follow pedmas when you work out arithmetic."?

Because I of course learned O.o.O. in grade school, but until last years I'd never once heard of "PEDMAS" or "BODMAS" or any of these words.
#8
Old 09-02-2012, 02:14 PM
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I say "pedmas". I learned that mnemonic trick only recently on this forum. I don't remember learning such a trick in school. I say "pedmas" because I can easily remember it by thinking of a pedophile Christmas. The absurdity and offensiveness makes it stick in my head.

What is "0.o.0."?
#9
Old 09-02-2012, 02:15 PM
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Should be PERMDAS, with the "R" representing radicals, on the same level with exponents.
#10
Old 09-02-2012, 02:18 PM
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Or PERMA since multiplying and dividing is really the same operation as is adding and subtracting.

Last edited by John Mace; 09-02-2012 at 02:18 PM.
#11
Old 09-02-2012, 02:21 PM
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Quote:
Originally Posted by MichaelEmouse View Post
What is "0.o.0."?
O.o.O presumably means Order of Operations.

And John, radicals are just the opposite of exponents, so PEMA will probably do the trick.
#12
Old 09-02-2012, 05:21 PM
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I've heard PEMDAS, not PEDMAS. You know, "Please excuse my dear aunt Sally" or similar.

But really, it doesn't matter, as some have hinted. The order is P E (MD) (AS). Meaning you don't distinguish between * and / or + and -, they are treated the same, left to right. In what system would the answer be 1? I understand some calculators do some funky things.

Yeah sqrt(4) = 4^0.5, so radicals aren't very necessary to note.

Quote:
Originally Posted by MichaelEmouse View Post
What is "0.o.0."?
o.O or O.o is Internet speak for a sort of befuddled or surprised expression. Therefore, 0.o.0 is obviously a triclops.
#13
Old 09-02-2012, 05:26 PM
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Quote:
Originally Posted by John DiFool View Post
Should be PERMDAS, with the "R" representing radicals, on the same level with exponents.
Radicals written with the usual notation don't need any special indication for order of operations, any more than fractions written vertically or cosines or binomial coefficients or the power (though not the base) in exponentiation or other such things... They explicitly indicate where their arguments start and stop (for radicals, the one argument is under the top line of the radical sign, the other is slightly raised and to the left of it); there's nothing left for "order of operations" to do.

For what it's worth, even though it is of course manifestly reasonable to call this a "math question", it still (unreasonably) irks me to do so... It's not really about mathematics, per se. Order of operations is a purely notational ambiguity, and it's only because we happen to have chosen this infix notation for + and * and so on that we have to bother with it. Had we chosen different ways of putting marks on paper to express our ideas, none of this would have come up in the first place. It has nothing to do with the mathematical content it is introduced in connection with; it is just syntactic parsing.

Last edited by Indistinguishable; 09-02-2012 at 05:30 PM.
#14
Old 09-02-2012, 05:56 PM
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Quote:
Originally Posted by thelurkinghorror View Post
In what system would the answer be 1?
In the system of idiots:

6-1X0+2/2=?

6-1=5
5X0=0
0+2=2
2/2=1

Just working straight across. Which is incorrect.
#15
Old 09-02-2012, 06:15 PM
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It may be incorrect parsing relative to the orthographic standard, but I hardly see need to call it idiotic...

Last edited by Indistinguishable; 09-02-2012 at 06:16 PM.
#16
Old 09-02-2012, 06:27 PM
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Originally Posted by Indistinguishable View Post
It may be incorrect parsing relative to the orthographic standard, but I hardly see need to call it idiotic...
That's because you haven't had the kind of day I've had.

Okay...in the system of people who didn't pay attention in pre-algebra class when they were 11. Better?
#17
Old 09-02-2012, 07:46 PM
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I've never heard of any of these acronyms (PEDMAS, etc.), but they do accurately represent what I was always taught many moons ago.

As for the alternate approach, just going left to right: there is nothing inherently wrong with that, other than the fact that it is different than the accepted standard. If left-to-right had been the standard all along, everything would work out just fine. As long as the person writing the equation and the person reading the equation had used the same standard.
#18
Old 09-02-2012, 08:16 PM
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Quote:
Originally Posted by Rick View Post
This popped up in my Facebook today.
Oh, geez—when you mentioned the order of operations and Facebook, I thought you were going to be asking about the problem that spawned this multipage thread!
Quote:
6-1X0+2/2=
If you enter this into a basic, "four-function" calculator (i.e. the simplest and cheapest kind), it'll simply do all the operations from left to right, giving an answer of 1. If you enter it into a scientific calculator (or a graphing calculator), it'll know about the rule for the order of operations and will do the multiplcation and division before the subtraction and addition, giving you an answer of 7.
#19
Old 09-02-2012, 09:17 PM
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They never taught me PEDMAS, and it would've save me a lot of trouble had ever since first grade.

Of course, using the initial letters should have occurred to me by second grade.

My very educated mother just served us nine pickles.
#20
Old 09-02-2012, 09:30 PM
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Originally Posted by Leo Bloom View Post
My very educated mother just served us nine pickles.
Pluto isn't a planet anymore. My very extroverted maid just served us naked.
#21
Old 09-02-2012, 11:10 PM
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Quote:
Originally Posted by Terr View Post
The correct answer depends on which order of operations you adopt.
I could adopt any arbitrary order of operations I want but it would be useless for communication if nobody else used it. What order of operations that is actually used by anybody would yield an answer of 1?
#22
Old 09-02-2012, 11:11 PM
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Originally Posted by CookingWithGas View Post
I could adopt any arbitrary order of operations I want but it would be useless for communication if nobody else used it. What order of operations that is actually used by anybody would yield an answer of 1?
Left-to-right order.
#23
Old 09-03-2012, 02:19 AM
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...which is the mode used by Calculator in Windows 7 in "Standard Mode".
#24
Old 09-03-2012, 08:48 AM
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KCalc (Linux/KDE calculator) gives the answer 7 even in "simple mode".
#25
Old 09-03-2012, 09:52 AM
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Quote:
Originally Posted by Terr View Post
Left-to-right order.
Who uses that?
#26
Old 09-03-2012, 10:29 AM
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Quote:
Originally Posted by Chessic Sense View Post
I've always wondered this about these threads: Are you guys just abbreviating for the Internet, or do you actually pronounce the word "Pedmas" in your head when you do math? I mean, was there actually a teacher somewhere in your lives that was like "Remember, kids, always follow pedmas when you work out arithmetic."?

Because I of course learned O.o.O. in grade school, but until last years I'd never once heard of "PEDMAS" or "BODMAS" or any of these words.
It was actually taught to me as "BODMAS" as an acronym to remember, which was useful until it just became second nature. This was in the late 80s in India, so it's possible that it's just another colonial artefact that isn't used anywhere else, but I'm pretty sure I've seen the word in some contemporary maths textbooks here in the UK. I will investigate if possible.

On Google, "BODMAS" returns about 220,000 results, against 17,000 for "BOMDAS" and 6,000 for "BIDMAS" so I suspect "BODMAS" is fairly common. For example: http://mathsisfun.com/operation-order-bodmas.html
#27
Old 09-03-2012, 12:02 PM
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Quote:
Originally Posted by DarrenS View Post
...which is the mode used by Calculator in Windows 7 in "Standard Mode".
At least as far back as Windows 3.1, Windows calculator has had a "Standard Mode," in which it behaves like a basic calculator and uses left-to-right order, and a "Scientific Mode," in which it behaves like a scientific calculator and follows the rules for the algebraic order of operations.
#28
Old 09-03-2012, 12:53 PM
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Somewhat related thread from last year.
#29
Old 09-03-2012, 12:54 PM
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Originally Posted by Tim R. Mortiss View Post
As for the alternate approach, just going left to right: there is nothing inherently wrong with that, other than the fact that it is different than the accepted standard. If left-to-right had been the standard all along, everything would work out just fine. As long as the person writing the equation and the person reading the equation had used the same standard.
Left-to-Right actually makes the actually process of doing math more complicated. With standard order of operations, something like 3*2+5=5+2*3, which isn't true for left-to-right. And part of the power of standard order of operations is the concept of a term, which I'm not sure has an equivalent in left-to-right order. In many case, such as multiplying polynomials or integrating, you can treat terms separately, and you would lose that with left-to-right order of operations.
#30
Old 09-03-2012, 02:36 PM
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Originally Posted by Enginerd View Post
Who uses that?
Some calculators and programming languages. There is a picture going around the tubes showing four calculators giving four different answers to the same problem. When in doubt, use parentheses.
#31
Old 09-03-2012, 03:07 PM
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This discussion reminds me of my first math class in college, which was the first class I ever had where we were allowed to use calculators (calculators were forbidden in math classes when I was a lad). On the first day of class the teacher was telling us how to choose a calculator. He said to punch in something like 1 + 2 * 3, and if the answer it gives is 9, don't buy it.

On a side note, he said the reason we were allowed to use them in college was that by the time we graduated high school we should already know how to do basic math by "brute force".
#32
Old 09-03-2012, 03:23 PM
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The OP is not, strictly speaking, a "math question". There is nothing inherently, objectively, "right" about the widely adopted order of mathematical operations, it is a convention, nothing else. It's not "math", it can't be proven. In any case, relying on this, both casually and in stuff like programming, is not a good idea. When I code, I always disambiguate with parentheses.
#33
Old 09-03-2012, 03:38 PM
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Quote:
Originally Posted by Doug K. View Post
This discussion reminds me of my first math class in college, which was the first class I ever had where we were allowed to use calculators (calculators were forbidden in math classes when I was a lad). On the first day of class the teacher was telling us how to choose a calculator. He said to punch in something like 1 + 2 * 3, and if the answer it gives is 9, don't buy it.

On a side note, he said the reason we were allowed to use them in college was that by the time we graduated high school we should already know how to do basic math by "brute force".
Yeah, for graphing or other calculators that let you punch the whole line in. If it's a simple calculator that only does one calculation at a time, and you get 7, well I'm not even sure if that's possible.
#34
Old 09-03-2012, 03:38 PM
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Quote:
Originally Posted by Terr View Post
Pluto isn't a planet anymore. My very extroverted maid just served us naked.
I thought it was re-instated...
Would you mind cross-posting your comment to the current thread on mnemonic sentences?

Last edited by Leo Bloom; 09-03-2012 at 03:39 PM.
#35
Old 09-03-2012, 04:05 PM
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Originally Posted by thelurkinghorror View Post
Yeah, for graphing or other calculators that let you punch the whole line in. If it's a simple calculator that only does one calculation at a time, and you get 7, well I'm not even sure if that's possible.
I have a 30 year old calculator that isn't a graphing calculator. If I type in 1 + 2 + 3 =

The display will show as follows:
type 1, display shows [ 1]
type +, display shows [ 1 +]
type 2, display shows [ 2 +]
type +, display shows [ 3 +]
type 3, display shows [ 3 +]
type =, display shows [ 6]

1 + 2 X 3 = yields this:

1 [ 1]
+ [ 1 +]
2 [ 2 +]
X [ 2 X]
3 [ 3 X]
= [ 7]
#36
Old 09-03-2012, 05:07 PM
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Quote:
Originally Posted by Terr View Post
The OP is not, strictly speaking, a "math question". There is nothing inherently, objectively, "right" about the widely adopted order of mathematical operations, it is a convention, nothing else. It's not "math", it can't be proven. In any case, relying on this, both casually and in stuff like programming, is not a good idea. When I code, I always disambiguate with parentheses.
Of course it's a convention. "Convention" means that everyone agrees to use it. The way we write numbers, and the symbols we use to represent mathematical operations are also conventions. It's not like there are competing schools of thought on how to represent and parse mathematical expressions. Alternate notations didn't come into play until electronic calculators where things like reverse Polish notation were introduced as a convention, but a convention only for entering expressions into a machine. I agree with the idea of using parentheses in code to make things clearer, but not because there is ambiguity--because people make errors.
#37
Old 09-03-2012, 06:20 PM
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Originally Posted by Prox View Post
Left-to-Right actually makes the actually process of doing math more complicated. With standard order of operations, something like 3*2+5=5+2*3, which isn't true for left-to-right. And part of the power of standard order of operations is the concept of a term, which I'm not sure has an equivalent in left-to-right order. In many case, such as multiplying polynomials or integrating, you can treat terms separately, and you would lose that with left-to-right order of operations.
No, this is the confusion of superficial notational choices with the underlying mathematics.

A term (in the sense of elementary algebra) is a product of variables and scalars; this exists as a concept independently of how you choose to notate it. Left-to-right vs. conventional order-of-operations has no bearing on this.

Similarly, in left to right order, the equation you intended would instead be written 3 * 2 + 5 = 5 + (2 * 3), expressing the same true fact. Nothing is lost; it's just notated differently. Yes, parentheses would come up, just as they come up when you want to indicate certain things under the current convention. (You can eliminate parentheses altogether if you move away from infix notation [e.g., if we notated addition and multiplication the same way we denote general functions, we'd write +(*(3, 2), 5) = +(5, *(2, 3)), or, just as well, + * 3 2 5 = + 5 * 2 3, as the parentheses and commas would no longer be necessary. Perhaps ideally, we'd write things in their direct tree form, rather than linearizing them...], but if you cling to infix notation, you're stuck with these conflicts of precedence, and whatever convention you pick for deciding them, you will sometimes want to move away from its default)

Last edited by Indistinguishable; 09-03-2012 at 06:24 PM.
#38
Old 09-03-2012, 07:03 PM
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Originally Posted by Dervorin View Post
It was actually taught to me as "BODMAS" as an acronym to remember, which was useful until it just became second nature. This was in the late 80s in India, so it's possible that it's just another colonial artefact that isn't used anywhere else, but I'm pretty sure I've seen the word in some contemporary maths textbooks here in the UK. I will investigate if possible.

On Google, "BODMAS" returns about 220,000 results, against 17,000 for "BOMDAS" and 6,000 for "BIDMAS" so I suspect "BODMAS" is fairly common. For example: http://mathsisfun.com/operation-order-bodmas.html
Yes, I was taught BODMAS in high school in the UK, although that was back in the 1960s. In British English, "brackets" usually means what Americans call parentheses. We would not have understood the word "parentheses". (These things - [] - we call "square brackets", on the rare occasions we need to refer to them.)

I was told the O of BODMAS stands for "of", and was equivalent to multiplication, but I suppose it is really just there for pronouncability. (At that stage of things, I don't think we had been introduced to the term "exponent" at all, though we probably knew about "powers".)

Last edited by njtt; 09-03-2012 at 07:06 PM.
#39
Old 09-03-2012, 09:46 PM
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48,000 Google hits for BEDMAS, which is what I was taught in New Zealand.

The only other order of operations convention that I know of is Polish notation, where the operators are placed to the left of the operands. So 1+2 in conventional notation is expressed as + 1 2. But the equaiton in the OP doesn't make sense in Polish notation.
#40
Old 09-03-2012, 09:51 PM
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Oh and I think the equation in the OP expressed in Polish notation would be:

- 6 * 1 0 + / 2 2
#41
Old 09-03-2012, 11:10 PM
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Originally Posted by lisiate View Post
The only other order of operations convention that I know of is Polish notation, where the operators are placed to the left of the operands. So 1+2 in conventional notation is expressed as + 1 2.
There's the mirror image of that: Reverse Polish Notation, also known as "postfix", where operators follow their operands. RPN is used by some calculators (most famously from Hewlett-Packard), as well as a few computer programming languages like Forth and Postscript.
#42
Old 09-04-2012, 01:16 PM
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Originally Posted by lisiate View Post
Oh and I think the equation in the OP expressed in Polish notation would be:

- 6 * 1 0 + / 2 2
No, this doesn't work. - 6 * 1 0 is perfectly meaningful, but then that + comes out of nowhere (and is only given the one argument / 2 2, rather than the two it needs).

Remember, to create Polish notation, just follow the usual "function(argument1, argument2, etc.)" convention in math, then remove all the (superfluous) parentheses and commas. (Or, in other words, write the expression tree, and then transcribe it in preorder traversal)

So the OP's 6-(1*0)+(2/2) would become +(-(6, *(1, 0)), /(2, 2)) = + - 6 * 1 0 / 2 2.

And the OP's (6-1)*0+2/2 would become +(*(-(6, 1), 0), /(2, 2)) = + * - 6 1 0 / 2 2.

[For reverse Polish notation, you do the same thing, but with function names coming after their arguments (i.e., the expression tree in postorder traversal). This is natural in programming because this reflects how computation actually proceeds: first you evaluate the arguments, then you apply the function to them, eventually evaluating the whole expression this way from the bottom-up.

So in reverse Polish notation, the OP's 6-(1*0)+(2/2) would become 6 1 0 * - 2 2 / +, and the OP's (6-1)*0+2/2 would become 6 1 - 0 * 2 2 / +]

Last edited by Indistinguishable; 09-04-2012 at 01:19 PM. Reason: My favorite convention? Just write the expression tree qua tree, and don't worry about linearizing it...
#43
Old 09-04-2012, 01:30 PM
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Quote:
Originally Posted by Doug K. View Post
I have a 30 year old calculator that isn't a graphing calculator. If I type in 1 + 2 + 3 =

The display will show as follows:
type 1, display shows [ 1]
type +, display shows [ 1 +]
type 2, display shows [ 2 +]
type +, display shows [ 3 +]
type 3, display shows [ 3 +]
type =, display shows [ 6]

1 + 2 X 3 = yields this:

1 [ 1]
+ [ 1 +]
2 [ 2 +]
X [ 2 X]
3 [ 3 X]
= [ 7]
Yes, but it does "let you punch the whole line in," which to clarify means that it has a memory for what you previously typed in. Cheaper ones just know: 2 numbers and an operator. So it's like Windows Calculator's standard mode, not scientific.
#44
Old 09-04-2012, 05:05 PM
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Originally Posted by Indistinguishable View Post
No, this doesn't work. - 6 * 1 0 is perfectly meaningful, but then that + comes out of nowhere (and is only given the one argument / 2 2, rather than the two it needs).

Remember, to create Polish notation, just follow the usual "function(argument1, argument2, etc.)" convention in math, then remove all the (superfluous) parentheses and commas. (Or, in other words, write the expression tree, and then transcribe it in preorder traversal)

So the OP's 6-(1*0)+(2/2) would become +(-(6, *(1, 0)), /(2, 2)) = + - 6 * 1 0 / 2 2.

And the OP's (6-1)*0+2/2 would become +(*(-(6, 1), 0), /(2, 2)) = + * - 6 1 0 / 2 2.

[For reverse Polish notation, you do the same thing, but with function names coming after their arguments (i.e., the expression tree in postorder traversal). This is natural in programming because this reflects how computation actually proceeds: first you evaluate the arguments, then you apply the function to them, eventually evaluating the whole expression this way from the bottom-up.

So in reverse Polish notation, the OP's 6-(1*0)+(2/2) would become 6 1 0 * - 2 2 / +, and the OP's (6-1)*0+2/2 would become 6 1 - 0 * 2 2 / +]
You're right of course, I was unsure about the equation which is why I said "I think..."

Last edited by lisiate; 09-04-2012 at 05:05 PM.
#45
Old 09-04-2012, 05:31 PM
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Originally Posted by WhyNot View Post
Yep, 7. Not having parentheses doesn't mean you throw out all the other order of operations, just that you start with exponents. Not having exponents doesn't mean you throw out all the other order of operations, just that you start with multiplication.

(We learned it PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)
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#46
Old 03-21-2015, 11:39 PM
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Quote:
Originally Posted by Rick View Post
This popped up in my Facebook today.
6-1X0+2/2=?
Half of the answers say the correct answer is 7 as you do the order of operations with multiplication and division first giving you:
6-(1X0)+(2/2)
6-0+1=7

The other half of the people say that sans brackets or parentheses you go left to right.
(6-1)X0+2/2=1
My algebra classes were a loooong time ago, and I'm flat not sure of the correct answer. My first thought was the the latter of the two methods was correct working left to right, but I am not sure.
So mathematical dopers, what is the correct answer?
A number of the other answers gave 5.

I am guessing that they resolved the multiplication and division:

6 - 1X0 + 2/2 becomes 6 - 0 + 1

But then carried forward with addition before subtraction:

6 - 0 + 1 where the addition resolves to 1, leaving 6 - 1 = 5.
#47
Old 03-22-2015, 11:12 AM
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Originally Posted by Indistinguishable View Post
It may be incorrect parsing relative to the orthographic standard, but I hardly see need to call it idiotic...
Really? OoOps is what? 2nd or 3rd grade? If an adult did not know basic primary school English most people would say that's idiotic
#48
Old 03-22-2015, 11:29 AM
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Originally Posted by tomndebb View Post
A number of the other answers gave 5.

I am guessing that they resolved the multiplication and division:

6 - 1X0 + 2/2 becomes 6 - 0 + 1

But then carried forward with addition before subtraction:

6 - 0 + 1 where the addition resolves to 1, leaving 6 - 1 = 5.
Good to know after 3 years we finally got that conundrum resolved.
#49
Old 03-22-2015, 12:19 PM
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Join Date: Feb 2003
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Quote:
Originally Posted by Saint Cad View Post
Really? OoOps is what? 2nd or 3rd grade? If an adult did not know basic primary school English most people would say that's idiotic
Not the best analogy. It's more like ending a sentence in a preposition.

Some pedants will try to claim it's an absolute violation of the laws of English grammar (which don't really exist either, but that's a separate matter) while others will take the more sensible and historically sound argument that sentence ending prepositions occur all the time.

As mentioned ad nauseum at this point, there's no "Academy of Mathematics" that determines absolute rules. We have a few rules of thumb, enforced by nobody in particular, to reduce ambiguity in expressions. But ambiguity still exists.

The "correct" response to this sort of ambiguity, which is not actually addressed by the usual order of operations lessons and if there is a "correct" response at all, is not to blindly rely on non-existent rules but to ask for a clarification from the writer and to gently chide them for writing such an ambiguous expression in the first place.

An equally acceptable but less predictable course of action is to ask your arithmetic teacher the class policy, because the deliberate use of this type of ambiguity is generally as a lesson to a class - in this particularly case a lesson that is unnecessary as the better lesson is to avoid such ambiguities entirely in actual practice.

Last edited by Great Antibob; 03-22-2015 at 12:22 PM.
#50
Old 03-22-2015, 12:24 PM
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Quote:
Originally Posted by thelurkinghorror View Post
o.O or O.o is Internet speak for a sort of befuddled or surprised expression. Therefore, 0.o.0 is obviously a triclops.
With two mouths!
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