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# Math: 6÷2(1+2) = ?

caper_26

User ID: 32057798
01/19/2013 02:16 AM
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Re: Math: 6÷2(1+2) = ?
wow, this page came alive with some rudimentary stuff. The equation has nothing to do with mnemonics here. Nothing to do with Order of Operations. We all know multiplication and Division are on the same level, as well as add and subtract. Even a step back from that, we don't even have to go left to right if we switch all division to inverse mult. and subt. to adding a negative number.
How do we READ the question? You are not a robot or software. The division symbol is a grouping symbol. Everything on the left divided by everything on the right. You know, Dividend; Divisor; Quotient. Now you will say that is untrue, and you must go left to right, and follow order of ops.
Ask yourself what is a ÷ a ?
Now ask, what is 1a ÷ 1a ?
1a ÷ 1a is not 1 * a ÷ 1 * a.
a ÷ a = 1a ÷ 1a
(a) ÷ (a) = (1a) ÷ (1a)
6 ÷ 2a = (6) ÷ (2a) = 3/a

a = 2+1
6 ÷ 2a = 3/a
6 ÷ 2(2+1) = 3/(2+1)
= 1

Read this if you still disagree and try to keep up: [link to cstl.syr.edu]
"I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
Anonymous Coward
User ID: 3329578
United States
01/19/2013 02:16 AM
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Re: Math: 6÷2(1+2) = ?
I can see why people think it is 9 because the problem would never actually be written like this. It is one and here is why...

Fractions are the same as division for example.

1 ÷ 2 = .5
Or
1/2 = .5

So if you make this problem into a fraction, which is what you should do, then you get :

6
_________
2(2+1)

Because the 2 belongs with (2+1). You cannot separate it because it need to be distributed.

So you get 4+2 when you distribute

6 6
____ = ____ = 1

4+2 6

It's one!
Anonymous Coward
User ID: 3329578
United States
01/19/2013 02:19 AM
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Re: Math: 6÷2(1+2) = ?
^ my above post did not format properly but you get the idea

And also 2a = a + a

So sub (2+1) for a and 2(2+1) = (2+1) + (2+1)= 6
Anonymous Coward
User ID: 3329578
United States
01/19/2013 02:24 AM
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Re: Math: 6÷2(1+2) = ?
wow, this page came alive with some rudimentary stuff. The equation has nothing to do with mnemonics here. Nothing to do with Order of Operations. We all know multiplication and Division are on the same level, as well as add and subtract. Even a step back from that, we don't even have to go left to right if we switch all division to inverse mult. and subt. to adding a negative number.
How do we READ the question? You are not a robot or software. The division symbol is a grouping symbol. Everything on the left divided by everything on the right. You know, Dividend; Divisor; Quotient. Now you will say that is untrue, and you must go left to right, and follow order of ops.
Ask yourself what is a ÷ a ?
Now ask, what is 1a ÷ 1a ?
1a ÷ 1a is not 1 * a ÷ 1 * a.
a ÷ a = 1a ÷ 1a
(a) ÷ (a) = (1a) ÷ (1a)
6 ÷ 2a = (6) ÷ (2a) = 3/a

a = 2+1
6 ÷ 2a = 3/a
6 ÷ 2(2+1) = 3/(2+1)
= 1

Read this if you still disagree and try to keep up: [link to cstl.syr.edu]
Quoting: caper_26

^ this
caper_26

User ID: 32057798
01/19/2013 02:26 AM
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Re: Math: 6÷2(1+2) = ?
It is quite clear the answer is 1. There are NO laws of mathematics that you work left from right. Confirmed by two PhDs in mathematics... my buddy of course but that is hearsay, but also by the Berkely professor in the video I posted.

Besides that, you have the obelisk, which clearly does not mean divide by this next number, which is what my calculator does, but it groups numbers into a numerator and denominator.

Then, you have a/1a = 1...

Then you have every single math problem done in algebra and calc class using variables ever done. This is what really started to let the light in on me and opened my mind. Why the fuck would I do these problems differently than I would do the problem in the OP?
Quoting: Anonymous Coward 31557420

Hey dude, what's happening tonight? There are so many ways of showing the maths to say 1, and blindly using "left to right rule" is the only one that says 9. I actually got in touch with some computer & electrical engineers I graduated with, today, and everyone of them said 1. I am also glad you realize that equations are basically "collapsed" , and there is no "left to right" rule in the real order of operations. This left-to-right thing was introduced by teachers or something. I have a very interesting article for you, that I think you will find interesting. It isn't too long.

Have a great weekend my man...

Last Edited by caper_26 on 01/19/2013 02:27 AM
"I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
Anonymous Coward
User ID: 31557420
United States
01/19/2013 02:31 AM
Report Abusive Post
Re: Math: 6÷2(1+2) = ?
wow, this page came alive with some rudimentary stuff. The equation has nothing to do with mnemonics here. Nothing to do with Order of Operations. We all know multiplication and Division are on the same level, as well as add and subtract. Even a step back from that, we don't even have to go left to right if we switch all division to inverse mult. and subt. to adding a negative number.
How do we READ the question? You are not a robot or software. The division symbol is a grouping symbol. Everything on the left divided by everything on the right. You know, Dividend; Divisor; Quotient. Now you will say that is untrue, and you must go left to right, and follow order of ops.
Ask yourself what is a ÷ a ?
Now ask, what is 1a ÷ 1a ?
1a ÷ 1a is not 1 * a ÷ 1 * a.
a ÷ a = 1a ÷ 1a
(a) ÷ (a) = (1a) ÷ (1a)
6 ÷ 2a = (6) ÷ (2a) = 3/a

a = 2+1
6 ÷ 2a = 3/a
6 ÷ 2(2+1) = 3/(2+1)
= 1

Read this if you still disagree and try to keep up: [link to cstl.syr.edu]
Quoting: caper_26

^ this
Quoting: Anonymous Coward 3329578

Yea he nailed it, and yes it is rudimentary stuff but that is why we are having this problem. Clearly people, including myself, are not as well versed in the rudimentary things as we should be.

Now that PDF from Syracuse is great... problem is I am not sure how true the bold part of this statement is:

"Do the remaining multiplication and division, as you come to them, when working from left to right in the expression. (See below for a discussion of this step.)

Do the remaining addition and subtraction, as you come to them, when working from left to right in the expression. (See below for a discussion of this step.)"
Anonymous Coward
User ID: 31557420
United States
01/19/2013 02:32 AM
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Re: Math: 6÷2(1+2) = ?
It is quite clear the answer is 1. There are NO laws of mathematics that you work left from right. Confirmed by two PhDs in mathematics... my buddy of course but that is hearsay, but also by the Berkely professor in the video I posted.

Besides that, you have the obelisk, which clearly does not mean divide by this next number, which is what my calculator does, but it groups numbers into a numerator and denominator.

Then, you have a/1a = 1...

Then you have every single math problem done in algebra and calc class using variables ever done. This is what really started to let the light in on me and opened my mind. Why the fuck would I do these problems differently than I would do the problem in the OP?
Quoting: Anonymous Coward 31557420

Hey dude, what's happening tonight? There are so many ways of showing the maths to say 1, and blindly using "left to right rule" is the only one that says 9. I actually got in touch with some computer & electrical engineers I graduated with, today, and everyone of them said 1. I am also glad you realize that equations are basically "collapsed" , and there is no "left to right" rule in the real order of operations. This left-to-right thing was introduced by teachers or something. I have a very interesting article for you, that I think you will find interesting. It isn't too long.

Have a great weekend my man...
Quoting: caper_26

haha! Thanks bro! This is just the thing I was getting at and literally as I posted my last post, was wishing I could read more about it!

haha thanks again for all your help you taught me a lot and helped me realize just how wrong I can be despite how adamantly I believe I am right.
Anonymous Coward
User ID: 27550461
United States
01/19/2013 02:34 AM
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Re: Math: 6÷2(1+2) = ?
131 pages just proves very succinctly why this country is lagging so far behind the world at math.
caper_26

User ID: 32057798
01/19/2013 02:35 AM
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Re: Math: 6÷2(1+2) = ?
Right now I am reading up on the distributive property. Hopefully I will learn exactly how parentheses work. Because, apparently I don't know even though I thought I did...
Quoting: Anonymous Coward 31557420

There are no examples showing any operators in front of the term being distributed, that I could find. If you do find one, please let me know. The reason the 6/2 doesn't get distributed is because it is not in parentheses.

(6/2)(2+1) = [(6/2)2 + (6/2)1]
But,
6/2(2+1) we have proven that 2(2+1) is in the denominator, so we have
6
2(2+1)

which is

6
(4+2)

= 1

We can proven the requirement of ( ) using the same Identity Law Proof, where there is no ( ), like in the a / 1a expression
"I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
caper_26

User ID: 32057798
01/19/2013 02:37 AM
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Re: Math: 6÷2(1+2) = ?
g'night. Hopefully we can open some doors to some new people tomorrow. Cheers !

"I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
Anonymous Coward
User ID: 25879973
United States
01/19/2013 02:38 AM
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Re: Math: 6÷2(1+2) = ?
Its 1, durp
Anonymous Coward
User ID: 13652486
United States
01/19/2013 02:39 AM
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Re: Math: 6÷2(1+2) = ?
9
caper_26

User ID: 32057798
01/19/2013 02:46 AM
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Re: Math: 6÷2(1+2) = ?
131 pages just proves very succinctly why this country is lagging so far behind the world at math.
Quoting: Anonymous Coward 27550461

It is just a numbers game. The population of the US is rather large, and the ratio of those people to those who have internet access is quite large as well. There is a high percentage of people who are just "not GREAT at math". This question involves things that go beyond the basics. therefore, you are going to get a LOT of people who will solve this like they were taught in elementary school (left to right, with mult&div first). That is the large percentage of the pop. Then you get people who are well versed in all areas of maths, who are the minority, and show some math facts, and we get called idiot, since we are the "only" one showing that "new" way of doing it, something they never saw before, so they immediately discard it. Anyway, that is MY take on the whole thing, but I am not a philosopher by any means. I actually suck with words, which is why I went the route I did... numbers only!! Ciao.

"I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
Anonymous Coward
User ID: 25949545
United States
01/19/2013 02:56 AM
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Re: Math: 6÷2(1+2) = ?
wow, this page came alive with some rudimentary stuff. The equation has nothing to do with mnemonics here. Nothing to do with Order of Operations. We all know multiplication and Division are on the same level, as well as add and subtract. Even a step back from that, we don't even have to go left to right if we switch all division to inverse mult. and subt. to adding a negative number.
How do we READ the question? You are not a robot or software. The division symbol is a grouping symbol. Everything on the left divided by everything on the right. You know, Dividend; Divisor; Quotient. Now you will say that is untrue, and you must go left to right, and follow order of ops.
Ask yourself what is a ÷ a ?
Now ask, what is 1a ÷ 1a ?
1a ÷ 1a is not 1 * a ÷ 1 * a.
a ÷ a = 1a ÷ 1a
(a) ÷ (a) = (1a) ÷ (1a)
6 ÷ 2a = (6) ÷ (2a) = 3/a

a = 2+1
6 ÷ 2a = 3/a
6 ÷ 2(2+1) = 3/(2+1)
= 1

Read this if you still disagree and try to keep up: [link to cstl.syr.edu]
Quoting: caper_26

^ this
Quoting: Anonymous Coward 3329578

Yea he nailed it, and yes it is rudimentary stuff but that is why we are having this problem. Clearly people, including myself, are not as well versed in the rudimentary things as we should be.

Now that PDF from Syracuse is great... problem is I am not sure how true the bold part of this statement is:

"Do the remaining multiplication and division, as you come to them, when working from left to right in the expression. (See below for a discussion of this step.)

Do the remaing addition and subtraction, as tyou come to them, when working from left to right in the expression. (See below for a discussion of this step.)"
Quoting: Anonymous Coward 31557420

I think they tell people this so they have some organization when doing math. But it misleads people into thinking it is a law and takes precedence.

For example left to right does not matter just order of operators:

10 × 10 + 10 × 10 = 100 no matter if you do right multiplication first or left

But division confuses because EVERYTHING beyond a division sign is included if it is grouped. The inclusion ends if another operator is present

6/3+(2+1) is 5 not 1 because it would be rewritten as

6
______
3 + 2 + 1
Anonymous Coward
User ID: 25949545
United States
01/19/2013 03:04 AM
Report Abusive Post
Re: Math: 6÷2(1+2) = ?
wow, this page came alive with some rudimentary stuff. The equation has nothing to do with mnemonics here. Nothing to do with Order of Operations. We all know multiplication and Division are on the same level, as well as add and subtract. Even a step back from that, we don't even have to go left to right if we switch all division to inverse mult. and subt. to adding a negative number.
How do we READ the question? You are not a robot or software. The division symbol is a grouping symbol. Everything on the left divided by everything on the right. You know, Dividend; Divisor; Quotient. Now you will say that is untrue, and you must go left to right, and follow order of ops.
Ask yourself what is a ÷ a ?
Now ask, what is 1a ÷ 1a ?
1a ÷ 1a is not 1 * a ÷ 1 * a.
a ÷ a = 1a ÷ 1a
(a) ÷ (a) = (1a) ÷ (1a)
6 ÷ 2a = (6) ÷ (2a) = 3/a

a = 2+1
6 ÷ 2a = 3/a
6 ÷ 2(2+1) = 3/(2+1)
= 1

Read this if you still disagree and try to keep up: [link to cstl.syr.edu]
Quoting: caper_26

^ this
Quoting: Anonymous Coward 3329578

Yea he nailed it, and yes it is rudimentary stuff but that is why we are having this problem. Clearly people, including myself, are not as well versed in the rudimentary things as we should be.

Now that PDF from Syracuse is great... problem is I am not sure how true the bold part of this statement is:

"Do the remaining multiplication and division, as you come to them, when working from left to right in the expression. (See below for a discussion of this step.)

Do the remaing addition and subtraction, as tyou come to them, when working from left to right in the expression. (See below for a discussion of this step.)"
Quoting: Anonymous Coward 31557420

I think they tell people this so they have some organization when doing math. But it misleads people into thinking it is a law and takes precedence.

For example left to right does not matter just order of operators:

10 × 10 + 10 × 10 = 100 no matter if you do right multiplication first or left

But division confuses because EVERYTHING beyond a division sign is included if it is grouped. The inclusion ends if another operator is present

6/3+(2+1) is 5 not 1 because it would be rewritten as

6
______
3 + 2 + 1
Quoting: Anonymous Coward 25949545

I can't get the format right on my posts lol

But I meant to post

6
__ + 2 + 1

3
Anonymous Coward
User ID: 32567570
Italy
01/19/2013 05:21 AM
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Re: Math: 6÷2(1+2) = ?
Actually you are incorrect. The answer is 9.
6/2(1+2)
Yes, you do the brackets first
6/2(3)
Then you do multiplication or division...doesn't matter which...it matters that you do it left to right.

6/2(3)
3(3)=9
Quoting: Anonymous Coward 23928068

Where did you find that infos?

.
DUCM900

User ID: 32567570
Italy
01/19/2013 05:33 AM
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Re: Math: 6÷2(1+2) = ?
bottom line:

Is 1(n) = 1n ?

.

Last Edited by IWASTHERE on 01/19/2013 05:39 AM
Citizenperth

User ID: 32253509
Australia
01/19/2013 05:41 AM

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Re: Math: 6÷2(1+2) = ?
nine.. stop it..............
It's life as we know it, but only just.
My Fukushima Site:
sic ut vos es vos should exsisto , denego alius vicis facio vos change , exsisto youself , proprie

“If I had an hour to solve a problem and my life depended on it, I would use the first 55 minutes determining the proper question to ask, for once I knew the proper question, I could solve the problem in less than five minutes.”
- Albert Einstein
Anonymous Coward
User ID: 24530075
United States
01/19/2013 05:53 AM
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Re: Math: 6÷2(1+2) = ?
haven't done maths in over 20 years so might be a bit wrong :)

6÷2(1+2) = ?

2x(1+2)=6

6/6=1

yay
Quoting: acid

This is correct.
Anonymous Coward
User ID: 25949545
United States
01/19/2013 06:03 AM
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Re: Math: 6÷2(1+2) = ?
nine.. stop it..............
Quoting: Citizenperth

It is not 9. It is 1. You stop it.

You cannot separate the 2 from (2+1)

If you were to separate it the answer would be

6/2 × 2 +1 which would be 7 but the () are gone so

6/(2*2)+(2*1) which is 3.5.... wait that's not right either...

Where did you get the idea that you can separate the 2?

2(2+1) = (2+1)+(2+1) = 6

6/6 = 1

If you can explain to me how the 2 is magically separated then I will say 9.

The only way to rid the 2 is dividing the whole problem by 2

Which gives

3/(2+1) still equals 1

Anonymous Coward
User ID: 4239460
United States
01/19/2013 06:09 AM
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Re: Math: 6÷2(1+2) = ?
Why is this 131 pages it's basic algebra, parentheses first to simplify the equation. Answer is 1. [link to www.math.com]
Anonymous Coward
User ID: 4239460
United States
01/19/2013 06:14 AM
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Re: Math: 6÷2(1+2) = ?
nine.. stop it..............
Quoting: Citizenperth

It is not 9. It is 1. You stop it.

You cannot separate the 2 from (2+1)

If you were to separate it the answer would be

6/2 × 2 +1 which would be 7 but the () are gone so

6/(2*2)+(2*1) which is 3.5.... wait that's not right either...

Where did you get the idea that you can separate the 2?

2(2+1) = (2+1)+(2+1) = 6

6/6 = 1

If you can explain to me how the 2 is magically separated then I will say 9.

The only way to rid the 2 is dividing the whole problem by 2

Which gives

3/(2+1) still equals 1

Quoting: Anonymous Coward 25949545

They get 9 by doing the division first instead of clearing parentheses like you're supposed to.
6/2=3
3(2+1)
3*3=9 durp
Syrius (OP)

User ID: 19364503
United States
01/19/2013 07:13 AM
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Re: Math: 6÷2(1+2) = ?
Let's fast forward, will there ever be a conclusive answer that everyone agrees on?

I don't believe our egos are capable of coming together, ever...which is sad because the language of Mathematics was conceived to be universal, in the grander scheme.

Yet, here we are a year later... bickering. The same problem, the same results, some faces familiar... others have just joined the fray.

You must ask yourself... because things of this nature have driven good men insane. Perverse, and lost in their thoughts as if they were peddling the newest drug in the lobby. We should resume this discussion with honorable mentions to all the greats.

I salute you Pythagoras. His theorem was simple, yet beautiful : a² + b² = c²
All around me are familiar faces... Worn out places...Worn out faces...
caper_26

User ID: 32057798
01/19/2013 08:40 AM
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Re: Math: 6÷2(1+2) = ?
bottom line:

Is 1(n) = 1n ?

.
Quoting: DUCM900

It has to, because we cannot replace n with 2+1, for example, without ( ) It would look like 6 ÷ 22+1 which is not allowed.
"I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
caper_26

User ID: 32057798
01/19/2013 09:16 AM
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Re: Math: 6÷2(1+2) = ?
Now you have the likes of this guy, who ONLY teaches "left-right", and changes ALL variables like this:
6x²y²z² ÷ 3xyz to 6*x²*y²*z²÷3*x*y*z equals 2x³y³z³ Really??

6x²y²z² ÷ 3xyz = 2xyz and not 2x³y³z³
because:
6x²y²z² ÷ 3xyz means (6x²y²z²) ÷ (3xyz)
for 2 reasons:
1 - a coefficient is part of the term's value, proven below, and as well with the Identity Law.
2 - The obelus is a grouping symbol. (dividend ÷ divisor)

Both 1 & 2 agree with each other. Why? Because true math always does, and never conflicts. If it does, then something is wrong.

this guy's entire premise is this "2n = 2 * n"
But that is not entirely true. You can evaluate 2n by multiplying, but the VALUE 2n must remain the same. You cannot take 6 the expression 6 ÷ 6 and say it is the same as 6 ÷ 2 * 3. It is so absurd it is deafening.
This proves that 2n = (2 * n) and you cannot split any value by inserting a times. We need more people to comment on this video, so that his students don't end up retarded...

"I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it."
Forgotten

User ID: 29097718
United States
01/21/2013 09:55 AM
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Re: Math: 6÷2(1+2) = ?
It is such a conspiracy in the world that not a SINGLE math site will give you the answer 1.

You cant find a single one. They all must be wrong and the few people here that say 1 must be right?

EVERY MATH SITE IS WRONG? Is that really what Casper, DUCM, etc are saying? Every single site?

If someone can show me 1 math website that comes up with 1 I will agree. Even though I can show 10+ websites with 9.

I just need 1. One website.

Look here. Look how many UP arrows people get for 1. Look how many UP arrows people get for 9.

Not that is proof, but lines up with this thread. For every 10 people 3 will say 1, 7 will say 9.

ALONG WITH EVERY FRIGGIN WEBSITE ABOUT MATH!!!

Last Edited by Forgotten on 01/21/2013 10:36 AM
Forgotten

User ID: 29097718
United States
01/21/2013 10:40 AM
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Re: Math: 6÷2(1+2) = ?

Solve any multiplication and division in the problem. Note that multiplication does not precede division, this is a common mistake while the fact is that they are solved from left to right as they occur.

Example:

5 * 4 - 9 / 3
5 * 4 - 9 / 3
20 - 9 / 3
20 - 9 / 3
20 - 3
Quoting: Article

This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.
Quoting: Article

When children initially learn addition, subtraction, multiplication, and division, they begin by performing operations on two numbers. But what happens when an expression requires multiple operations? Over time, mathematicians have developed a set of rules called the order of operations to determine which operation to do first. The rules are:

Multiply and divide from left to right.
Add and subtract from left to right.
Quoting: Article

I can show about 50+ more sites that all show this same thing.

But I am sure it is all a conspiracy.

5-4+1= 2

Not
5-4+1=0

6÷2*3=9

Not

6÷2*3=1

(We all agree we do parenthesis first... that much I am sure of)

Work from left to right when things are equal.

Last Edited by Forgotten on 01/21/2013 10:45 AM
DUCM900

User ID: 32721565
Italy
01/21/2013 10:44 AM
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Re: Math: 6÷2(1+2) = ?
Just get a scientific calculator, do that equation and you'll see that and what all your **** sites are.

.

Last Edited by IWASTHERE on 01/21/2013 10:50 AM
Forgotten

User ID: 29097718
United States
01/21/2013 10:46 AM
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Re: Math: 6÷2(1+2) = ?
Just get a scientific calculator, do that equation and you'll see that all your **** sites are.

.
Quoting: DUCM900

Still cant find one huh. I am sure they are all conspiring to give the wrong answer.