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On April 08 2011 10:51 Snipinpanda wrote:Show nested quote +On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). If I had this question on the test, I would ask for clarification because it's not unambiguous. No test questions are ever structured like this for a reason.
It is unambiguous. It's ok to admit you didn't apply the order of operations correctly  . Being wrong is an integral (no pun intended) part of learning mathematics.
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On April 08 2011 10:50 EscPlan9 wrote:
I never use PEMDAS and got it right. I don't understand how people insert the additional bracket? But I guess that's why I didn't struggle with it. This isn't a test of your math knowledge or intelligence really. It's how well you understand how to properly evaluate a certain math problem more than anything.
Calling this a math problem is lol.
It's more like a more pedantic and arbitrary version of semantics.
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United States10328 Posts
On April 08 2011 10:40 Severedevil wrote:
I love how mathematicians have been pointing out the potential difference between 2*(9+3) and 2(9+3) for the entire fucking thread, and the preferred response is "third grade math LOL".
lol this. I guess everyone just wants to prove how smart they are :/
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On April 08 2011 10:51 Snipinpanda wrote:Show nested quote +On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). If I had this question on the test, I would ask for clarification because it's not unambiguous. No test questions are ever structured like this for a reason.
It is unambiguous. Thinking that 1/2x is the same as 1/(2x) is wrong >.> But I digress. No test would ever be formatted in that way  (but that still doesn't stop some people like the College Board >_________<)
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On April 08 2011 10:49 Zeke50100 wrote:Show nested quote +On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text).
Wow, nobody is arguing that 2 is the correct answer. What is being argued is that it is a bit ambiguous, which is 100% is. When I first saw the question I immediately thought 2 as the answer, simply because 2(9+3) is overwhelmingly thought of as a single unit because of grammatical/syntactical/notational reasons. The second poll is clear evidence of this. Yes 2 is the incorrect answer. Yes 288 is the correct answer. Yes the question is ambiguous. End of discussion.
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Ok this is how not tricky question should look like :
Notation used : Polish notation
We will be working in the field of rational numbers Q.
Calculate: * / 48 2 + 9 3
Now I would love to see how many wrong answers would be to this assignment, but especially how many people with wrong answer would afterward argue that the question was ambiguous. I think the answer would pretty clearly show that in fact original OP was intentionally tricky question that has nothing to do with evaluating the expression but parsing it due to imprecision on part of OP (as some people already noted).
EDIT: changed the field identification from Z to Q
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On April 08 2011 10:53 space_yes wrote:Show nested quote +On April 08 2011 10:51 Snipinpanda wrote:On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). If I had this question on the test, I would ask for clarification because it's not unambiguous. No test questions are ever structured like this for a reason. It is unambiguous. It's ok to admit you didn't apply the order of operations correctly . Being wrong is an integral (no pun intended) part of learning mathematics.
Seriously, 40+ pages and it's "unambiguous"?
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People think the question is ambiguous b/c they don't understand the order of operations. If you do it isn't ambiguous at all.
1/xy = y/x
True or false?
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this question tests not mathematical skill but knowledge of parentheses priorities. good job OP, you just trolled everyone into thinking they were dumb
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On April 08 2011 10:56 space_yes wrote:
People think the question is ambiguous b/c they don't understand the order of operations. If you do it isn't ambiguous at all.
1/xy = y/x
True or false?
True but that's even more ambiguous than the problem in the OP.
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On April 08 2011 10:55 MadVillain wrote:Show nested quote +On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). Wow, nobody is arguing that 2 is the correct answer. What is being argued is that it is a bit ambiguous, which is 100% is. When I first saw the question I immediately thought 2 as the answer, simply because 2(9+3) is overwhelmingly thought of as a single unit because of grammatical/syntactical/notational reasons. The second poll is clear evidence of this. Yes 2 is the incorrect answer. Yes 288 is the correct answer. Yes the question is ambiguous. End of discussion.
They were talking about 1/2x.
And no, it's not ambiguous. What the hell does "there is only one way to interpret this correctly, and only one correct answer" mean? Your own fault does not make it ambiguous.
I believe oranges are not fruits because I look at the color and think of orange shirts, which are not fruits. Does that make the question "is and orange a fruit" ambiguous?
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CS education. Had no idea that the convention was to go from the left to the right and treat multiply and division as equals. Honestly don't care much either, in my head it's all polish notation anyway.
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On April 08 2011 10:55 jalstar wrote:Show nested quote +On April 08 2011 10:53 space_yes wrote:On April 08 2011 10:51 Snipinpanda wrote:On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). If I had this question on the test, I would ask for clarification because it's not unambiguous. No test questions are ever structured like this for a reason. It is unambiguous. It's ok to admit you didn't apply the order of operations correctly . Being wrong is an integral (no pun intended) part of learning mathematics. Seriously, 40+ pages and it's "unambiguous"?
Since when did page count determine ambiguity? Mostly the thread is a bunch of debate between people who think it is ambiguous and people who applied order of operations going from left to right and subsequently got the correct answer. Honestly it's not that big of a deal if you got it wrong.
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On April 08 2011 10:58 space_yes wrote:Show nested quote +On April 08 2011 10:55 jalstar wrote:On April 08 2011 10:53 space_yes wrote:On April 08 2011 10:51 Snipinpanda wrote:On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). If I had this question on the test, I would ask for clarification because it's not unambiguous. No test questions are ever structured like this for a reason. It is unambiguous. It's ok to admit you didn't apply the order of operations correctly . Being wrong is an integral (no pun intended) part of learning mathematics. Seriously, 40+ pages and it's "unambiguous"? Since when did page count determine ambiguity? Mostly the thread is a bunch of debate between people who think it is ambiguous and people who applied order of operations going from left to right and subsequently got the correct answer. Honestly it's not that big of a deal if you got it wrong.
I got it right using simple order of operations after I realized that that was the trick. If you've never seen 1/(2x) written as 1/2x then the problem becomes much more intuitive.
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On April 08 2011 10:53 space_yes wrote:Show nested quote +On April 08 2011 10:51 Snipinpanda wrote:On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). If I had this question on the test, I would ask for clarification because it's not unambiguous. No test questions are ever structured like this for a reason. It is unambiguous. It's ok to admit you didn't apply the order of operations correctly . Being wrong is an integral (no pun intended) part of learning mathematics.
For the record, I answered 288 because I know what question is asking. I'm arguing that the question is ambiguous and ill-posed, not that the answer is 2.
On April 08 2011 10:56 space_yes wrote:
People think the question is ambiguous b/c they don't understand the order of operations. If you do it isn't ambiguous at all.
1/xy = y/x
True or false?
Define your juxtaposition operator.
Notation used : Polish notationWe will be working in the field of rational numbers Q. Calculate: * / 48 2 + 9 3
This is an unambiguous question. There are also easier ways to ask this question.
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On April 08 2011 10:56 space_yes wrote:
People think the question is ambiguous b/c they don't understand the order of operations. If you do it isn't ambiguous at all.
1/xy = y/x
True or false?
What!?! Did you even see the results of the second poll... Obviously people understand the order of operations. However in a setting (such as the University that I'm at) more times than not if you wrote that expression people would assume 2(9+3) as a single unit, that is just how people write it and expect it to be interpreted many times.
The wikipedia article for ambiguity starts with: "Ambiguity is a term used in writing and math, and under conditions where information can be understood or interpreted in more than one way..."
The second poll is EVIDENCE that people can interpret 1/2x as (1/2)x and 1/(2x), which by definition makes it AMBIGUOUS. Get it?
Edit: And your example is even more ambiguous, 99% of regular math users would interpret 1/xy as 1/(x*y) NOT (1/x)*y. I can't even count the number of times that has been on homeworks and in books i've read, and they assume the reader will interpret it that way.
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On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
Where I come from, all my math teachers were very strict on everything, for example you would be deducted marks if you missed any lines. You had to follow the textbook as described.
Hell, calculators were forbidden until grade 11 or 12. I cannot remember exactly, but it must have been when we were learning calculus when you absolutely had to use one. All I remember is it wasn't the first and not the second year either.
When I see a math problem written in the OP's form. The first thing that popped into my head was order of operations. Applied the rules that I recall and vola.
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On April 08 2011 10:55 MadVillain wrote:Show nested quote +On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). Wow, nobody is arguing that 2 is the correct answer. What is being argued is that it is a bit ambiguous, which is 100% is. When I first saw the question I immediately thought 2 as the answer, simply because 2(9+3) is overwhelmingly thought of as a single unit because of grammatical/syntactical/notational reasons. The second poll is clear evidence of this. Yes 2 is the incorrect answer. Yes 288 is the correct answer. Yes the question is ambiguous. End of discussion.
Exactly. Even a multiplication sign between 2 and (9+3) would give the problem much needed clarity.
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Who the hell voted 2 anyway?
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You'll never see 1/(2x) written as 1/2x in any published mathematical text b/c 1) formatting and 2) order of operations. I agree the question is tricky but that doesn't make it ambiguous. If you got the first question right and you apply the same rules to the second question you should also get it right. If you got it wrong you used different rules for each question.
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EPT
