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Subject: Maths "problem' that allegedly stumps 40% of Japanese 20 somethings rss

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Julius Waller
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So I placed double quotes around the word problem because I can hardly believe 40% of 20 anythings get this wrong:



So the answer is of course:

Spoiler (click to reveal)
1


So now be honest did you get this:

Poll
Immediately correct
  Your Answer   Vote Percent Vote Count
Yes
74.4% 99
No
25.6% 34
Voters 133
This poll is now closed.   133 answers
Poll created by TrustyJules
Closes: Thu Feb 2, 2017 6:00 am


Source video from youtube
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Bryan Thunkd
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Ha. I had to think about it because I haven't had my coffee yet and I thought it was going to be...
Spoiler (click to reveal)
...an order of operations problem and not a division by fraction problem
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Matt Brown
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To be fair, I think I always get the division of fractions wrong unless I'm doing them fairly often. I can pass Calc classes but that thing simply trips me up every time.
 
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Christopher Dearlove
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There's lots of these problems floating around. And they all are like the comment that intelligence/knowledge is knowing that the tomato is a fruit, but wisdom is not putting it in a fruit salad. Or in other words, no one sensible would just write this.

(Of course also the quotes in the subject line are around problem, but could almost be round maths. Yes, this is maths. But to use an board games analogy, it's at the noughts and crosses (tic-tac-toe) level. And that's generous.)
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Harmonica
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I had -1 ... First add and then substract, according to the Meneer-Van-Dalen-Wacht-Op-Antwoord Principle.
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Wendell
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It's a bit of a trick question since it doesn't include parentheses which would make the thing a lot clearer...
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John James
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wifwendell wrote:
It's a bit of a trick question since it doesn't include parentheses which would make the thing a lot clearer...

Parentheses are to create an exception, or isolate a section from the natural order of steps.
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Christopher Dearlove
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Doomsword wrote:
wifwendell wrote:
It's a bit of a trick question since it doesn't include parentheses which would make the thing a lot clearer...

Parentheses are to create an exception, or isolate a section from the natural order of steps.


Or simply to make things crystal clear.

If we consider programming, where this sort of thing happens, most people who should be let anywhere near writing code will know that a*b+c (or, better, with meaningful names and spaces) means (a*b)+c. But there are coding standards that require the parentheses. Unnecessarily in my opinion in that case. But clearly to avoid having to make a judgement call when they are needed or not. But make that (in C) a&&b||c and I'll be putting in the parentheses even when that's the case that doesn't need them. (I'm deliberately not saying which - though I know which - as not doing so will probably raise doubts in some people's minds.) In fact one of my compilers will produce a warning without them.

So, no, parentheses are not just to create exceptions.
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Chapel
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I feel like facebook clickbait now.
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John James
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Dearlove wrote:
Doomsword wrote:
wifwendell wrote:
It's a bit of a trick question since it doesn't include parentheses which would make the thing a lot clearer...

Parentheses are to create an exception, or isolate a section from the natural order of steps.


...

So, no, parentheses are not just to create exceptions.

An exception from the order things are supposed to be done in. 4th grade math, not programming language.
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Julius Waller
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MWChapel wrote:
I feel like facebook clickbait now.

Yeah thats pretty much my feeling too - but apparently the quote wasnt far off. Even on BGG there is 30% failure rate...
 
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Christopher Dearlove
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Doomsword wrote:
Dearlove wrote:
Doomsword wrote:
wifwendell wrote:
It's a bit of a trick question since it doesn't include parentheses which would make the thing a lot clearer...

Parentheses are to create an exception, or isolate a section from the natural order of steps.


...

So, no, parentheses are not just to create exceptions.

An exception from the order things are supposed to be done in. 4th grade math, not programming language.


Same logic. You may know, your readers may not. (And quite a lot don't from responses to these questions.) Better to make crystal clear in many (I would say not all, but opinions vary) cases where strictly unnecessary. Because it is essentially as easy to include them.
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John Breckenridge
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Doomsword wrote:
wifwendell wrote:
It's a bit of a trick question since it doesn't include parentheses which would make the thing a lot clearer...

Parentheses are to create an exception, or isolate a section from the natural order of steps.


The real problem here isn't with a lack of parentheses; it's with font size.

If you read it as "three divided by one divided by three" the divisions are both the same priority, so you perform them left to right and that term collapses to 1. However, the only way to get the answer they're looking for is to interpret 1 over 3 as a rational constant rather than an expression, so that it's read as "three divided by one third" which is 9. The usual convention for printing rational numbers is to use a smaller font for the numerator and denominator, so the final number comes out at roughly the same height as an integer, but here the ones and threes are all the same size whether they are intended to be seen as integer constants or components of a rational constant.

There is no convention for interpreting a fraction division as higher priority than a division sign, which is why the two are rarely mixed in an equation that could have mixed interpretations.
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Robert Wesley
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shake Man! Just try "dishing that out" with 'pies' so that you start with 3 whole ones divided into 1/3-portions each from whence NOW resulted with 9 whole 'pies' where there are 1/3-portions? Pretty 'flaky'-encrusted.
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Robert Wesley
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arrrh That would have been best with "treasure divvys" since you make 3 piles then, while divide into 1/3-EACH further, and yet "end up as 9-times" for such!?! surprise
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Mike Bialecki
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Please excuse my dear aunt Sally.

A phrase that for some reason I still remember from middle school.
 
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Robert Wesley
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Tom Patterson
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Took my awhile to figure it out.

Signed,
BFA in drama, New York University (minor in English)
MFA in acting, University of California, San Diego
C in Calculus, John Adams High School which is the last math class I ever took.
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I was hoping this had died out after seeing these posted on Facebook about 800 times. This is not a test of intelligence. This is a poorly written math problem. It is no more a badge of intelligence to have the order of operations memorized than it is to know how to use vi correctly.
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Julius Waller
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Actually I disagree - the prioritisation of operators is a key thing in maths.
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Wendell
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TrustyJules wrote:
Actually I disagree - the prioritisation of operators is a key thing in maths.


So is clarity.
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wifwendell wrote:
TrustyJules wrote:
Actually I disagree - the prioritisation of operators is a key thing in maths.


So is clarity.
Yeah, this sort of thing just adds an artificial stumbling block. To me I would rather put thought into solving the problem instead of figuring out the order. It's pointless and silly and ultimately proves nothing. It's just some secret handshake nonsense that people have latched onto to "prove" how smart they are.
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Matt
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cold_fuzion wrote:
wifwendell wrote:
TrustyJules wrote:
Actually I disagree - the prioritisation of operators is a key thing in maths.


So is clarity.
Yeah, this sort of thing just adds an artificial stumbling block. To me I would rather put thought into solving the problem instead of figuring out the order. It's pointless and silly and ultimately proves nothing. It's just some secret handshake nonsense that people have latched onto to "prove" how smart they are.


Yeah. This isn't really about order of operations. The big trick is that the two different representations of division distract you from the "divide by a fraction" speedbump.

It is really starting to drive me crazy when they use the division symbol in middle- and high-school math books, because it is not commonly used in actual mathematics. It isn't even on my keyboard, for goodness sake, and in most mathematical typesetting it is not a commonly used command.

I suspect the only reason they keep using it is that it allows you to create homework problems that use each letter in PEMDAS. If you rewrote most of those problems in a different way (writing a fraction, for instance, instead of the division symbol) the order of operations would be much easier to figure out.

Wikipedia wrote:
An obelus (symbol: ÷, plural: obeluses or obeli) is a symbol consisting of a short horizontal line with a dot above and below. It is mainly used to represent the mathematical operation of division. It is therefore commonly called the division sign. Division may also be indicated by a horizontal line (fraction bar), or a slash. In ISO 80000-2-9.6 (about division) it says verbatim "The symbol ÷ should not be used."
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Christopher Dearlove
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TrustyJules wrote:
Actually I disagree - the prioritisation of operators is a key thing in maths.


No, it really isn't. It's a notational convention in pretty trivial maths. In practice any real maths is done in symbols, not numbers, and the multiplication and division symbols are rarely used. You need to know that ab+c is a times b, then plus c, but that those appear more tightly bound is clear. Division usually uses a horizontal line, or a negative exponent.
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Christopher Dearlove
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Thanks for the ISO 80000 reference, I should take a look at that (I'm fortunately enough to have access - though there are cheaper ways to get hold of much of what the 80000 series covers).

Computers have changed our notations. I think they are largely what drove out the division sign (if it's hiding as one of the popup symbols on an iOS keyboard I don't know which one). They also changed the use of points. Once upon a time (I am that old) we wrote a decimal point raised above the line. A full stop (period in American) was on the line. Typewriters and later computers used an on the line point for both. Before that, mathematicians did sometimes use an on the line point for multiplication, especially when repeated. For example 1.2.3.4.5 for what is also written 5!

My point is that notations evolve and also aren't always universal (more examples readily available). It's important not to think that the notation is fundamental. Though a good notation helps a lot.
 
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