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Math: 6÷2(1+2) = ?

 
Forgotten

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Re: Math: 6÷2(1+2) = ?
I have shown scientific calculator doing the problem and many other websites and programs doing the problem.

All getting 9.

Have you shown anything showing an answer of 1?

[link to imageshack.us]
[link to img255.imageshack.us]
[link to vimeo.com (secure)]
[link to img339.imageshack.us]

Everyone of these websites I typed the equation EXACTLY as the OP had it. Using ÷ not /,x or adding anything after the first 2.
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Re: Math: 6÷2(1+2) = ?


Last Edited by Forgotten on 01/22/2013 09:50 AM
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Re: Math: 6÷2(1+2) = ?
i went through it again and i actually now come up with 1.

Order of operations:

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

6÷2(1+2) =

= 6÷2(3)

= 3(3)

= 1

i respectfully retract my previous answer of 9 i was doing M before D

:s
 Quoting: Anubis


[link to simple.wikipedia.org]

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


[link to www.purplemath.com]

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


[link to www.eduplace.com]
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.


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

Work from left to right when things are equal.
 Quoting: Forgotten

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Re: Math: 6÷2(1+2) = ?
[link to imageshack.us]
[link to img255.imageshack.us]

Video here show me inputting exactly as OP put it.


[link to vimeo.com (secure)]
[link to img339.imageshack.us]


MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
MULTIPLICATION BEFORE DIVISION
X=1
 Quoting: Anonymous Coward 9839140


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


[link to www.purplemath.com]

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


[link to www.eduplace.com]
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.

Last Edited by Forgotten on 01/22/2013 09:54 AM
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Anonymous Coward
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Re: Math: 6÷2(1+2) = ?
Still 9. Multiplication DOES NOT come before Division.
[link to www.factmonster.com]
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01/22/2013 09:59 AM
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Re: Math: 6÷2(1+2) = ?
the input in wolfram alpha is wrong.

the input I saw used a solidus. However, I used a high powered calculator on an electrical engineering website and that also calculated it wrong.
 Quoting: Anonymous Coward 31557420


Check my wolfram image. Input exactly as OP. Cant believe you let Casper's double talk change your mind. Especially after all the proof against 1.

Including your own variable work.

Every image I put in I used 6÷2(1+2)... exactly. I substituted nothing.

[link to imageshack.us]
[link to img255.imageshack.us]

Video of me doing on scientific calculator. And image to prove it was "scientific".

[link to vimeo.com (secure)]
[link to img339.imageshack.us]


this^^^


Funny because Syrius, the original poster is actually aruging there is a difference between...

6÷2(1+2) and 6÷2*(1+2)...

Which is the weakest argument for 1 in this whole thread. Saying he was showing the 2 up against the parenthesis as indication it was the "denominator". WTF!! Even though it would still be wrong, he would of at least put...

6/2(2+1).... I might of bought his story then. The answer would still be 9, but this thread is getting better and better.

OP didnt even know the answer.

Last Edited by Forgotten on 01/22/2013 10:04 AM
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Re: Math: 6÷2(1+2) = ?
The left to right rule really only applies to division and
subtraction. This is because they don't satisfy the associative
property of equality. To be really precise, it is because we are
really "loose" about the definition of subtraction and division. If we
define subtraction properly, it is adding by an inverse. For example,
(3 - 5) + 7, is really 3 + (-5) + 7. By writing it this way, we can
rewrite to get 3 + ((-5)+ 7), since addition is associative. We get
the same result as before.

The same applies to division. By dividing, we are really multiplying
by a multiplicative inverse.
For example 5/3 is really 5 * (1/3).
Written this way, we can use the associative property.
 Quoting: article

[link to mathforum.org]

Division is the inverse of multiplication. This is why the "left to right" rule is in place. To help people who cant see the inverse. We can get rid of "left to right" by making everything multiplication. See below



Which would make this equation.


6 * .5 * (2+1)... this should be really easy for anyone.

6*.5*3=9

Can re-arragne in any order.

.5*6*3=9

Can even distribute.
6 * .5 * (2+1)
6 (1+.5)
6*1.5
9

Anyone want to argue with this?
and multiplicative identity
(multiplying by 1/3 instead of dividing by 3).
 Quoting: article


So instead of dividing by 2 multiple by .5!!!!!

6/1 ÷ 2/1*(2+1) = 6*.5*(2+1)

Last Edited by Forgotten on 01/22/2013 10:19 AM
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caper_26

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01/22/2013 12:37 PM
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Re: Math: 6÷2(1+2) = ?
I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today.
End of debate... hopefully.
 Quoting: Anonymous Coward 944253


It would be nice if they looked at all aspects of math before solving. Nice COPY & PASTE from yahoo... On yahoo, I am a space physicist, didn't you know?
"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."
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Re: Math: 6÷2(1+2) = ?
This is basic Algebra people. It's 1.
 Quoting: Anonymous Coward 27845368


cruise says the tard
caper_26

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Re: Math: 6÷2(1+2) = ?
This is basic Algebra people. It's 1.
 Quoting: Anonymous Coward 27845368


Sure is.

Theses bozos can't even solve the following:
12x²y ÷ 4x + (6x – x)²


Nor can they solve
a ÷ 1a correctly

Nor write "six halves of n" properly
"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."
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Re: Math: 6÷2(1+2) = ?
I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today.
End of debate... hopefully.
 Quoting: Anonymous Coward 944253


It would be nice if they looked at all aspects of math before solving. Nice COPY & PASTE from yahoo... On yahoo, I am a space physicist, didn't you know?
 Quoting: caper_26


Thread: 6÷2(1+2)=? SOLVED by the Professor of Mathematics at California State University [video]

Thread: 6÷2(1+2) = 9 (Page 2)


Pretty overwhelming proof.

My last post to this thread. As other threads show more info/proof on the first post. Not jumbled up over 140 pages.

Good luck "space physicist".

chuckle
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caper_26

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Re: Math: 6÷2(1+2) = ?
Here is how an obelus works: [link to www.freeimagehosting.net]

Here is how grouping in algebra works: [link to cstl.syr.edu]

Here is a link for those who get 9: [link to i48.tinypic.com]
"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

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Re: Math: 6÷2(1+2) = ?
You bozos can't even solve the following:
12x²y ÷ 4x + (6x – x)²


Nor can you solve
a ÷ 1a correctly

Nor write "six halves of n" properly
 Quoting: caper_26


No wonder you can't evaluate this 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."
Anubis
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Re: Math: 6÷2(1+2) = ?
according to how they teach order of ops in Canada (BEDMAS) and that DM are equivalent in precedence, then left to right order is used. i still get 9.

from: [link to math.about.com]

"There are a couple of things to remember when applying the PEDMAS/BEDMAS order of operations. Brackets/Parenthesis always come first and exponents come second. When working with multiplication and division, you do whichever comes first as you work from left to right. If multiplication comes first, do it before dividing."

based on that its 9.
caper_26

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Re: Math: 6÷2(1+2) = ?
according to how they teach order of ops in Canada (BEDMAS) and that DM are equivalent in precedence, then left to right order is used. i still get 9.

from: [link to math.about.com]

"There are a couple of things to remember when applying the PEDMAS/BEDMAS order of operations. Brackets/Parenthesis always come first and exponents come second. When working with multiplication and division, you do whichever comes first as you work from left to right. If multiplication comes first, do it before dividing."

based on that its 9.
 Quoting: Anubis


Except that (2+1) is in the denominator, since 2(2+1) is a single unit
"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

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Re: Math: 6÷2(1+2) = ?
consider 6 ÷ x²
x² is x(x) = x * x
So 6 ÷ x² = 6 ÷ x * x = 6 ?
No because x² = (x²)

Just like 2(2+1) = [2(2+1)], but as x², we don't need to use redundant parentheses. Some "special" people insist on using them though because they are easily confused.

scratching
"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."
Anubis
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Re: Math: 6÷2(1+2) = ?
according to how they teach order of ops in Canada (BEDMAS) and that DM are equivalent in precedence, then left to right order is used. i still get 9.

from: [link to math.about.com]

"There are a couple of things to remember when applying the PEDMAS/BEDMAS order of operations. Brackets/Parenthesis always come first and exponents come second. When working with multiplication and division, you do whichever comes first as you work from left to right. If multiplication comes first, do it before dividing."

based on that its 9.
 Quoting: Anubis


Except that (2+1) is in the denominator, since 2(2+1) is a single unit
 Quoting: caper_26


i see your viewpoint but unless redundant parenthesis are put in then the answer is open to interpretation.

if it was 6÷(2(1+2)) = ?
then it would undeniably be 1.
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Re: Math: 6÷2(1+2) = ?
6/2(1+2)=


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

The only way to get 1 is to write it like this

6/(2(1+3))=


^^^^^^^
This would give 1
 Quoting: Anonymous Coward 32447952


5a
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Re: Math: 6÷2(1+2) = ?
9
caper_26

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Re: Math: 6÷2(1+2) = ?
6÷2(1+2) = 1
6÷(1+2)2 = 1

(6÷2)(1+2)= 9
6(1+2)÷ 2 = 9
"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."
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Re: Math: 6÷2(1+2) = ?



For starters, I'm not arguing 6÷2(1+2) and 6÷2*(1+2).... Look at the post, a few pages back, that you replied to, genius.

I'm going to be blunt with you, pal. Your trolling attempts are weak and on the verge of annoying. And no, I'm not going to give you the pleasure of restating my arguments for the 7th or 8th time. There is no point.

Your oblivious mind will continue reading and interpreting my words wrong. As you have proven on at least two occasions. Personally, I can tell by your posts ALONE that you have a hard time coping with reality and continue repeating yourself with nothing new to add, the same recycled jargon. Let's be honest, what are you afraid of exactly? An empty existence, where in the light of others, you go out of your way to misquote them and pretend they are ignorant for your own sake?

Before you argue with someone, regardless of topic. Listen to their arguments instead of making shit up. It makes you look a dolt.

I really hope you find peace, and maybe some closure in your life. However, it won't be here so gtfo.
All around me are familiar faces... Worn out places...Worn out faces...
caper_26

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Re: Math: 6÷2(1+2) = ?
There is no troll attempts. Only showing math laws and principles to those who do not know about them

the infamous wolfram even knows how to simplify 6 ÷ 2n. However it does not know how to substitute variables with values.

Most people: "It is 9!!!" with no explanation besides "left to right" then they convert 2(2+1) to 2*(2+1) which is incorrect. 2n = (2*n)

Failure to know that the (2+1) is part of the divisor. Which means the multiplicative inverse of it, as well as the 2, must be interpreted.
"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."
Syrius (OP)

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Re: Math: 6÷2(1+2) = ?
There is no troll attempts. Only showing math laws and principles to those who do not know about them

the infamous wolfram even knows how to simplify 6 ÷ 2n. However it does not know how to substitute variables with values.

Most people: "It is 9!!!" with no explanation besides "left to right" then they convert 2(2+1) to 2*(2+1) which is incorrect. 2n = (2*n)

Failure to know that the (2+1) is part of the divisor. Which means the multiplicative inverse of it, as well as the 2, must be interpreted.
 Quoting: caper_26


I was quoting Forgotten, sir.

You are 1 of the few that has took the time to research all possibilities and seen the light.
All around me are familiar faces... Worn out places...Worn out faces...
caper_26

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Re: Math: 6÷2(1+2) = ?
How is any of that "trolling".


Definition: In Internet slang, a troll is someone who posts inflammatory,[1] extraneous, or off-topic messages in an online community, such as a forum, chat room, or blog, with the primary intent of provoking readers into an emotional response[2] or of otherwise disrupting normal on-topic discussion

Where have I done ANY of that ??? Actually, I can find SEVERAL other people trying to do the above, not me.
"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."
Anubis
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Re: Math: 6÷2(1+2) = ?
There is no troll attempts. Only showing math laws and principles to those who do not know about them

the infamous wolfram even knows how to simplify 6 ÷ 2n. However it does not know how to substitute variables with values.

Most people: "It is 9!!!" with no explanation besides "left to right" then they convert 2(2+1) to 2*(2+1) which is incorrect. 2n = (2*n)

Failure to know that the (2+1) is part of the divisor. Which means the multiplicative inverse of it, as well as the 2, must be interpreted.
 Quoting: caper_26


ok..

Last Edited by Anubis on 01/22/2013 01:57 PM
caper_26

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Re: Math: 6÷2(1+2) = ?

I was quoting Forgotten, sir.

You are 1 of the few that has took the time to research all possibilities and seen the light.
 Quoting: caper_26


Apologies !! I was the last post, so I thought you were talking to me !!

Forgotten has banned me from his thread, because he doesn't want me converting anyone on his 9 bandwagon to 1. I am also on his "foe" list too. I find that rather amusing.
"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."
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Re: Math: 6÷2(1+2) = ?

ok..

what is 5(5) = ?
 Quoting: caper_26

5(5) is "five fives"

Question: what is 125 divided by five fives ?
Answer: 125 ÷ 5(5) = 5

We cannot write "55" like "2n" because it looks like fifty five.

5(5) can be evaluated [5 * 5], like distributive property

5(5 + 0) = [5(5) + 5(0)]
"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."
Anubis
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Re: Math: 6÷2(1+2) = ?

ok..

what is 5(5) = ?
 Quoting: caper_26

5(5) is "five fives"

Question: what is 125 divided by five fives ?
Answer: 125 ÷ 5(5) = 5

We cannot write "55" like "2n" because it looks like fifty five.

5(5) can be evaluated [5 * 5], like distributive property

5(5 + 0) = [5(5) + 5(0)]
 Quoting: Anubis


125 ÷ 5(5) = ?

is the same as

125 ÷ 5 x 5 = ?

BEDMAS left to right:

25(5) = 125

Last Edited by Anubis on 01/22/2013 02:13 PM
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Re: Math: 6÷2(1+2) = ?
Looks, I don't know PEMDAS from BEDMAS even though I'm sure I learned them in elementary school or middle school math.

What I do know is writing alebraic expressions in computer programing and how they are evaluated by a computer language such as C.

When you are facing an expression that has distribution in it like 6÷2(1+2) then you must do the distributed part first and then the remainder of the equation after evaluating the distribution.

2(1+2) must be evaluated first as whole before you consider the remainder of 6÷2(1+2).

You can rewrite the equation as 6÷(2(1+2)). The second set of parenthesis is implied when you have a distribution.

You know you have a distribution because the contents inside of the parenthesis has addition in it (2+1). This means the entirety of the contents within the parenthesis must always be multiplied by what immediately precedes it to the the left on the outside of parenthesis. You don't get to do other operations such as addition, subtraction multiplication, etc before you evaluate 2(1+2).

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

Now if the equation was written like this:

6÷2*(1+2)

Then you have a different story, now the parenthesis still implies distribution, but because the * symbol is there then everything to the left of the * symbol is distributed an you can evaluate everything to the left of the * as a whole first.


6÷2*(1+2) = (6÷2)*(1+2) = (3) * (3) = 9

The lack of the * symbol in the original equation makes a ton of difference about how you treat the distribution implited by (2+1).

Answer in the original equation is 1.
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Re: Math: 6÷2(1+2) = ?
Another way to think about this problem is to replace numbers with some real world examples.

6÷2(1+2)= ?

What is this mathematical expression trying to solve in the real world? A real world word problem might be the following:

]ane has a family of 6. She recently picked up two bags of fruit. In each bag of fruit there are 1 apples and 2 oranges. How many pieces of fruit does each person in her family get to eat?


When you read it that way you understand the answer is 1.

If you think the answer is 9 then your word problem is something like this:

Jane has a family of 6. She recently went shopping and gave fruit to only half the members of her family. In each bag of fruit they received there were 2 apples and 1 orange. How many apples an oranges in total did the family received?

In this case the equation would need to be written like this:

(6÷2)(1+2)

or written like this:

6/2 * (1+2)


These would make it clear that what was important was that only 1/2 the family would get bags of fruit and once you understood that have the family got fruit you could then consider what was in each bag for those family members.

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