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(Some Guy)   6/2(1+2) = 9 no no, 6/2(1+2) = 1 no no, 6/2(1+2) = 2   (mathmagical.co.uk) divider line 821
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30203 clicks; posted to Main » on 30 Mar 2012 at 9:56 AM (2 years ago)   |  Favorite    |   share:  Share on Twitter share via Email Share on Facebook   more»



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2012-03-30 11:54:07 AM

cyanide64: dittybopper: cyanide64: No calculators? I'd like to see you plow through a stack of papers full of SIN, COS, and TAN in an hour. Don't forget to show ALL your work.

Sure. I'll use one of my slide rules. How many decimal places are you interested in? That determines whether I'm going to use my 6" Pickett N200 Pocket Trig, the 10" Sterling Precision, or the circular slide rule I made from this website.

I'm going have to to print me off one of those, thanks for the link. ;)


I also built that Yokota Log-Log linear rule out of cardboard, and it worked well until it fell apart. I've got to try it using plastic or metal next time.
 
2012-03-30 11:54:52 AM

Lsherm: TNel: No you still have the parenthesis around the 3 so you still need to deal with those you can't drop those parenthesis. 6/2(3) does not mean you drop the parenthesis into 6/2*3 since the parens are still there you must multiple the 2 and the 3 together. The problem is the / . No teacher would give that equation like that if it was meant that the 6/2 was a fraction.

Again, WTF? Operations INSIDE parentheses take precedence. Parentheses don't garner operations outside them a higher priority.


The problem is the stupid / symbol. If you want it to be a fraction then fine but if you mean for it to be a ÷ then it's 1. 6/2*3 is different than 6÷2*3
 
2012-03-30 11:55:21 AM

JamesSirBensonMum: My answer was 9 also. But I now don't understand how we could determine if they meant:

6
----------
2 x (1+2)

or

6
---- x (1 + 2)
2

I read it as the second version, but how would you disambiguate it between these versions? 6/2(1+2) vs 6/(2(1+2))?


Yeah, that's what you would do to differentiate the two.

I work out the situation by changing the division into a multiplication. 6/2(1+2) = 6 * (1/2) * (1+2) = 3 * 3 = 9.

Whereas 6/(2(1+2)) = 6 * (1 / (2 * (1 + 2)) = 6 * (1/6) = 1.
 
2012-03-30 11:55:46 AM
If my so-called Math "teacher" had only taught me PEMDAS I would not be sitting here today counting on my fingers.

Sometimes it isn't the student who is the dummy. I've been pretty much paralyzed by higher math (yes, for me that means simple addition/subtraction with an occasional division problem) ever since grade school. 'Course, we were using abaci back then. :-)

I actually got the answer right but don't remember how I got the answer if that makes sense. Probably I just sensed it couldn't be = 1...too many numbers in the equation.

A sad state of affairs. I think I actually might have enjoyed higher math if I'd Only Known About PEMDAS.
 
2012-03-30 11:56:34 AM
Why do so many people forget that multiplication and division have the same level of precedence. They just remember PEMDAS so they think Multiplication is higher than Division, but they are the same. So It goes left-to-right.

From a software perspective they failed to account for this specific ambiguity in the grammar. It's an easy mistake to make. They probably realized their mistake and fixed it in a later model.
 
Bf+
2012-03-30 11:56:43 AM

Quantumbunny: My android phone calculator yields the correct 9.

My coworkers iPhone yields 2. If you change it to 6÷2*(1+2) it yields 9. So leaving out the multiplication, the iPhone ignores the 2 and divides 6 by (1+2). Ignoring terms is just wrong.



Huh... windows calculator does the same thing:
I type: 6/2(1+2)
The screen reads: 6 / (1 + 2)
Result: 2

WTF?
I apparently never pressed 2.
Thanks Stalin.
/Yeah, I went there.
 
2012-03-30 11:57:32 AM

babysealclubber: inkblot: While drilling "PEMDAS" in our kids' heads over and over again, we forgot to say that multiplication and division have the same priority. If division is on the left side of the equation, it has to be solved first.

That's why we learned it like this:
P
E
MD
AS

So we just learned PEMA, since division and subtraction are forms of multiplication and addition.


Please Enter My Anus?
 
2012-03-30 11:57:54 AM
The answer is 9.
Any other answer means you are an idiot, or were taught incorrectly.
I'm guessing it's both...
 
2012-03-30 11:58:23 AM
I find their explanatory equation really wierd too (though it does lead to the correct response):

Rather than just saying it should be operated as (6/2) * (1+2) = 9, they basically say it should be operated as (6*(1+2)) / 2 = 9.

I mean that's just weird.
 
2012-03-30 11:59:39 AM
The SI specifies that units should never be spelled with multiple divisions, to avoid this kind of confusion. The official SI nomenclature for mass-specific entropy is J/(kg*K), or J kg^-1 K^-1, not J/kg/K.

(Then again, this is just a convention of writing; there's no innate mathematical law that says multiplication and division have equal precedence and associate left-to-right. Or, for that matter, that multiplication when spelled as X has the same precedence as when spelled without an operator. It could be more intuitive for some if it was different. But, for better or worse, convention isn't that way, and so there is only one correct way to do this: the answer is 9 and nothing else. I'm kind of surprised no morons are here arguing for 1. Fark I am surprisingly not disappoint.)
 
2012-03-30 11:59:50 AM

wjllope: A friend was telling me about his adventure at the post office yesterday. He wants to mail many tens of wedding invitations. The young girl at the counter takes one envelope and puts it on the scale and says she can't mail it because it weighs as zero on the scale, so she can't calculate the postage. Something like that...
It took my friend more than ten minutes to carefully explain why she could measure 10 envelopes at the same time, then just divide that result by ten. At some point she even called the Postmaster over. Eventually, she understood, and the letters got mailed. She was even gushing "that is soo coool - I get it now!!"

If you showed "6/2(1+2)" to this one, I am fairly sure that she'd recognize that there were some numbers written there, but there's no way to predict what result she'd get if asked to evaluate that expression - with or without a calculator. cheers


That's nothing. I took my son to an arcade and when he was cashing out his tickets (he had 63) he bought something that cost 60 tickets. The cashier busted out a calculator to find the difference.
 
2012-03-30 12:00:09 PM
The Olympic Games : The Special Olympics :: Academic Decathlon : This thread
 
2012-03-30 12:00:34 PM

TNel: Lsherm: TNel: No you still have the parenthesis around the 3 so you still need to deal with those you can't drop those parenthesis. 6/2(3) does not mean you drop the parenthesis into 6/2*3 since the parens are still there you must multiple the 2 and the 3 together. The problem is the / . No teacher would give that equation like that if it was meant that the 6/2 was a fraction.

Again, WTF? Operations INSIDE parentheses take precedence. Parentheses don't garner operations outside them a higher priority.

The problem is the stupid / symbol. If you want it to be a fraction then fine but if you mean for it to be a ÷ then it's 1. 6/2*3 is different than 6÷2*3


They're the same thing written in that notation. If you want the whole thing to be a fraction, you have to surround the denominator in parens:

6/(2*3) = 1
6/2*3 = 9

There's no special implied parentheses that come with using the / symbol.
 
2012-03-30 12:00:52 PM
 
2012-03-30 12:02:36 PM
A = People who don't understand math
B = Those who do
C = Trolls

A ∪ B ∪ C= {This thread}
 
2012-03-30 12:02:57 PM

TNel: Lsherm: TNel: No you still have the parenthesis around the 3 so you still need to deal with those you can't drop those parenthesis. 6/2(3) does not mean you drop the parenthesis into 6/2*3 since the parens are still there you must multiple the 2 and the 3 together. The problem is the / . No teacher would give that equation like that if it was meant that the 6/2 was a fraction.

Again, WTF? Operations INSIDE parentheses take precedence. Parentheses don't garner operations outside them a higher priority.

The problem is the stupid / symbol. If you want it to be a fraction then fine but if you mean for it to be a ÷ then it's 1. 6/2*3 is different than 6÷2*3



What the fark are you talking about? The brackets around an integer don't give it some kind of mathemagical precedence. Also, point of order: do you notice the similarities between the classic 'fraction' symbol (as you put it), and the division symbol? Perhaps those dots represent something abstract, no..?

/yeah, I probably just got trolled, but I can't stand idly by...
 
2012-03-30 12:03:21 PM

trappedspirit: Nutsac_Jim: This is why you see so many people saying 'Saddam had to do with 9-11', and
"I hate high gas prices, raise taxes on Exxon"

Don't tell me you actually think a company hitting record breaking profits is a good place to sink tax payer subsides into. There's only one political party I know stupid enough to logic that one out.


Wait: Assuming we tax profits on a company at 10% for the sake of argument, how is it a "subsidy" when a company pays 10% of eleventy billion as opposed to 10% seventy billion? They are paying the same rate.

Also, implied in your assumption is that the increased taxes won't eventually be reflected in the retail price at the pump, which is ridiculous: Taxes are an expense, and as such they are built into the retail price. Raise the taxes, retail price is going to increase, or if market conditions are such that it can't do that, the company is going to recoup that cost in some other way, usually to the detriment of it's employees or customers.
 
2012-03-30 12:04:06 PM

Thorndyke Barnhard: I find their explanatory equation really wierd too (though it does lead to the correct response):

Rather than just saying it should be operated as (6/2) * (1+2) = 9, they basically say it should be operated as (6*(1+2)) / 2 = 9.

I mean that's just weird.


I'm glad I'm not the only one who thought that.
 
Bf+
2012-03-30 12:05:27 PM

BurnShrike: A = People who don't understand math
B = Those who do
C = Trolls

A ∪ B ∪ C= {This thread}




There are three types of people in this world:
Those who are good at math, and those who aren't.
 
2012-03-30 12:06:14 PM

Rixel: fredklein: So, who wants to argue 1/2 on the Monty Hall puzzle??

I love explaining that one! The most bullheaded are usually the complete geeks


Have you heard of the Sleeping Beauty puzzle (new window)?
 
2012-03-30 12:06:27 PM

Bf+: BurnShrike: A = People who don't understand math
B = Those who do
C = Trolls

A ∪ B ∪ C= {This thread}



There are three types of people in this world:
Those who are good at math, and those who aren't.


I'm sorry, but there are 10 types of people in this world.
Those who understand binary, and those who don't.
 
2012-03-30 12:06:40 PM
315 posts to discuss basic farking math principles? I weep for fark.

Order of Operations, motherfarkers, do you speak it??

I hope the article's author teaches elementary school math, any other level is outrageous to demonstrate that level of ignorance.

/had the answer instantly as you should have.
 
2012-03-30 12:07:09 PM
ALL OF YOU ARE WRONG, WRONG, WRONG.

There is no mathematical operator between the the 2 and the left parentheses. A parentheses is not an operator, never has been, never will be. The parentheses is a separator, period.

So the correct answer is obvious!

6/2(1+2) = 33
 
2012-03-30 12:08:45 PM

david_gaithersburg: ALL OF YOU ARE WRONG, WRONG, WRONG.

There is no mathematical operator between the the 2 and the left parentheses. A parentheses is not an operator, never has been, never will be. The parentheses is a separator, period.

So the correct answer is obvious!

6/2(1+2) = 33


You must be the guy who programmed the iPhone calculator :)
 
2012-03-30 12:08:55 PM
6/2 (1+2) = 6 * (1/2) * (1+2) = ( 6 * (1 + 2)) / 2 = (6 + 12) / 2 = 18 / 2 = 9

6/2 (1 + 2) = 3 (1 + 2) = 3 + 6 = 9

6/2 (1 + 2) = 9 duh
 
2012-03-30 12:09:13 PM
8.9999...
 
2012-03-30 12:10:51 PM

jigoro: 8.9999...


(For very large values of 9)
 
2012-03-30 12:11:17 PM

Xcott: TWX: Okay, I'll bite. What's the benefit, assuming that the student understands the process and how to apply it, of setting up the problem and then manually performing the calculation to get a less accurate answer, where the student comes to despise the process, as opposed to the student understanding the process, understanding how to do the process manually, but now substituting a tool to allow the student to come up with more accurate answers instantly after correctly setting up the problem?

It's actually SOP for calculus classes to first show students the "hard way" first, towit computing derivatives by taking limits as h->0, and then later pointing out the very simple rules so that they never need to take a limit.

There are many good reasons to have kids compute numerical integrals before teaching them symbolic integration. One is to appreciate the power and ease of what you are about to teach them. Another is to understand at a very concrete level what integration represents---you can *say* it computes area, but there's a huge difference from being told about baseball and actually playing it. A third reason, as stated above, is that you sometimes have to resort to numerical integration; depending on your major, you may even take an entire course in numerical methods before you graduate, so you had better have an understanding.

When I took Calc in high school, we did learn how to manually calculate answers, but once we learned this, we stopped manually calculating answers and instead learned how to program machines to give us the answers based on what we needed. As a consequence, the bulk of students were ready to apply their math to the engineering tools of the day, like spreadsheets, various computer languages, and handheld calculators, where they might need to take the paper version of the equation and turn it into machine-understandable input, as opposed to doing everything by hand for ever and ever.

Last week I built an oven to heat thermoplasti ...


The article and this thread proves that people need to understand math before they use the tools that make it easy. If you just blindly punch equations like this one into your calculator and accept whatever it spits out, you're gonna screw up. You'll put too little fuel in your plane and wind up landing 20 miles short of the airport.
 
2012-03-30 12:12:02 PM

dittybopper: I would actually say that you are looking at it from the wrong direction: Objectively, mathematics exists outside of human experience. You are mistaking the tools we use to measure and define something for the thing itself. A sketch of an elephant isn't actually an elephant, just the representation of one.


I think he had it right. The "thing" which exists outside the human mind is the universe behaving in a ordered, consistent way. Math is a description of that order not a thing unto itself.
 
2012-03-30 12:12:36 PM
Ok, next question: does 0.999.... (repeating) = 1? Discuss.

i.qkme.me

/am continually surprised at how many people cannot accept the correct answer to this
 
2012-03-30 12:13:57 PM

Lsherm:
There's no special implied parentheses that come with using the / symbol.


The fault is with the equation writer not the math. If they wanted the 6/2 to be computed by themselves they should have put a bracket in there.
 
2012-03-30 12:14:16 PM

californiadiver: I'm glad I'm not the only one who thought that.


Cool, me too! High five!

I mean really they are pretty much implying that you should operate the 1st part of the equation against the 3rd and THEN bring in the 2nd... There's just no rule for that method, right?
 
Bf+
2012-03-30 12:14:23 PM

Ambitwistor: Ok, next question: does 0.999.... (repeating) = 1? Discuss.


Yes-- Almost.
 
2012-03-30 12:15:22 PM

Ambitwistor: Ok, next question: does 0.999.... (repeating) = 1? Discuss.

[i.qkme.me image 312x254]

/am continually surprised at how many people cannot accept the correct answer to this


1/3 = .33 repeat

1/3 + 1/3 + 1/3 = 3/3 = 1 | .999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999....999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999...
 
2012-03-30 12:15:23 PM

BurnShrike: A = People who don't understand math
B = Those who do
C = Trolls

A ∪ B ∪ C= {This thread}


i594.photobucket.com
 
2012-03-30 12:16:36 PM

Bf+: Ambitwistor: Ok, next question: does 0.999.... (repeating) = 1? Discuss.

Yes-- Almost.


And so it begins.
 
2012-03-30 12:17:06 PM
strange.. I've always been taught to treat whatever sticks to a bracket as one entity first. i.e.:
a/b(c) = a / [b(c)]
but who does math in one line using implied operators anyway.. bounded to cause problems... and when I do, I make sure to use enough brackets to show the distinctions...

f(x)={k(x)* y^2-k(x^2)/[k(x)]^2}/g(x-abc^2) + 1, something crazy like that...
 
2012-03-30 12:18:59 PM

the dizzle: rudemix: Does any one besides me ever try to use the date to make math equations?

3+(3+0)x(2+0)=12

I try this everyday. Most days I can find something even if it's a stretch, some days I can't math it out at all.

3+(3+0)x(2+0)=9

(3+3+0)x(2x0)=12 0

3+(3+0)^(2+0)=12


FTFY
 
2012-03-30 12:19:55 PM

utsagrad123: BurnShrike: A = People who don't understand math
B = Those who do
C = Trolls

A ∪ B ∪ C= {This thread}

[i594.photobucket.com image 640x340]


Very nicely done.
 
2012-03-30 12:20:32 PM

woodstock827: strange.. I've always been taught to treat whatever sticks to a bracket as one entity first. i.e.:
a/b(c) = a / [b(c)]
but who does math in one line using implied operators anyway.. bounded to cause problems... and when I do, I make sure to use enough brackets to show the distinctions...

f(x)={k(x)* y^2-k(x^2)/[k(x)]^2}/g(x-abc^2) + 1, something crazy like that...


Same here. When I do math inside programs there is always crazy brackets so something like this would never happen
 
2012-03-30 12:20:41 PM
Why are all of you sheep "implying" a multiplication symbol before the left paren?

Why not imply a "c" which equates to the speed of light?

Or how about we imply that chick with the big eyes? or a cat?
 
2012-03-30 12:21:04 PM

Hollie Maea: jigoro: 8.9999...

(For very large values of 9)


No. Just for an infinitely repeating series of them.

Just to throw some more confusion into the mix, one way of representing infinitely repeating decimals when you can't type on over-bar is to put the repeat in parentheses. So...

8.99999... = 8.(9) = 9

ALL rational numbers can be exactly equally represented as an infinitely repeating decimal.

1 = 0.(9)

24 = 23.(9)

0.236 = 0.235(9)

And so on...
 
2012-03-30 12:21:08 PM

Phinn: If we're driving at a speed of eighty miles per hour, how many miles do we travel in one hour?


Holy crap. I am now dumber than I was before watching that.
 
2012-03-30 12:21:37 PM

woodstock827: f(x)={k(x)* y^2-k(x^2)/[k(x)]^2}/g(x-abc^2) + 1

= 2


Sent from my iPhone
 
2012-03-30 12:22:37 PM

dittybopper: /Let's see if your droid is still working 40+ years after it was manufactured.


My HP 12C calculator is still going strong after more than 20 years.

I think it's only on its second set of batteries.

/damn, how HP has fallen from its former glory......
 
2012-03-30 12:24:41 PM

Huck Chaser: You guys are missing the real point here, which is that if the iPhone says it's 2, it's 2.


I believe the parentheses makes it ignore the first 2.

Proof that Apple is quite good at ignoring user input
 
2012-03-30 12:25:16 PM

Hollie Maea: Xcott: but because the only thing a calculator can do for the students is take them up the wrong tree.

Bullshiat.


You didn't even ask what course I was teaching. If a course is mostly mathematical proofs and symbolic manipulation, if every question something like "prove the chain rule for entropy," then a calculator has zero utility. The one thing a calculator can do, calculation, is a thing that is not used on the exam. Once you get into higher mathematics, a calculator is about as useful on a math test as it is on a philosophy test.

Back when I allowed calculators, the kids who pulled them out would invariably get lousy grades, because they wasted a good 10-15 minutes staring at a machine that wasn't going to give them any help proving anything. I'd go further and say that the kids who learned to turn to calculators probably didn't develop the same mental capacity as the other kids.

Calculation is the calisthenics of the mathematical world: using a calculator to do the arithmetic is like driving instead of walking. This is a great convenience for regular people, but if you want to be an athlete you can't replace your daily run with a daily drive.
 
2012-03-30 12:26:30 PM

dittybopper: schivvers: dittybopper: Walker: farkingismybusiness: I was told there would be no math.

THIS! I hate math!

/maths for those in the UK, Australia, etc.

Poor you. The Universe, and everything in it, is math. Even yourself. All of your actions, thoughts, emotions, everything you see, hear, touch, taste, and experience is math. Everything that you are and do is, at some basic and fundamental level, governed my mathematical principles.

All of it.

Dear sir, I regret that you are wrong. Math is a description of the physical world. It is a system that the human mind has invented to describe and predict what is happening in the real world. This is something that math folks and scientists sometimes have a hard time seeing eye to eye on. Math is a tool. A good tool! But nothing more than that. (I love people who build good tools by the way...) This is the reason that the sums always work out in math. We laid the rules down so that they would. In the beginning of math, the rules were laid down as assumptions. Now these are subtle...but it makes a difference. We said, and usually agreed, that 1/0 is null. That 2 points describe a line, that 3 points describe a plane. What if we change any one of those? We get a whole new set of answers to the same problems! and some these "wrong" answers in the old system are actually more right in the real world. (look up non-euclidian geometry and gps/stellar cartography etc) The statement that math GOVERNS the universe is false. Math DESCRIBES the universe. The reason this is such a big deal is that as a scientist I must accept when my data does not fit our model. The math is wrong...not cause I screwed it up, but because the whole model is broken. That happens. I'm not mad, but telling people that the mathematically correct answer is always the "right" answer leads to a rabbit hole where we get a lot of thing WRONG in reality.

Compare the predicted folding of a polymer or protein to it's actual folding. All th ...


Umm, I think you might have missed it a bit. Yes the hydrogen atom vibrates, but to say it is GOVERNED by math is wrongheaded. Yes we build models wrong, sometimes wrong models work the best for certain purposed (see organic chemist and hybrid bonding theory vs. quantum mechanics) The statement that Math rules the universe, or is built into the fabric of the universe isn't inherently honest. It is built into our UNDERSTANDING of the universe. There is a difference, quite slight, but a difference none the less. Mathematics is a made up construct. Just as literature, or any other endeavor, the universe is real and not made up (unless you really want to enter a philosophical debate.)

Does math work? yes it does, quite well. Is it really useful? and sometimes elegant? yeah I do agree. Is it intrinsic to the universe? I don't believe it is. Is it intrinsic in our current understanding of the universe? yup. (I'm just trying to clarify where i stand on this issue--not beg the question.) I'm trying to make sure you see the difference betwixt the actual universe and our understanding of the universe.

The elephant example is close to spot on...I say there is an elephant over there, you draw a picture (the mathematical representation of said elephant.) I'm saying the mathematical representation doesn't govern weather or not the elephant on the plain knocks my jeep over. The actual elephant does. Your math draws a picture that allows you to try and predict what the elephant will do, not tell the elephant what it will do.

again good day, have fun, I've spent years looking at things like this...hobby of mine as i collected many degrees. (not that the degree makes me or anyone else right)

D
 
2012-03-30 12:27:01 PM

SweetSaws: Could someone explain how that could possibly = 2?


This

Can't figure that one out.
 
2012-03-30 12:27:02 PM

BurnShrike: Bf+: BurnShrike: A = People who don't understand math
B = Those who do
C = Trolls

A ∪ B ∪ C= {This thread}



There are three types of people in this world:
Those who are good at math, and those who aren't.

I'm sorry, but there are 10 types of people in this world.
Those who understand binary, and those who don't.


Actually there are three kinds of people in this world:
Those who extrapolate based on incomplete data.
 
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