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# Math: 6÷2(1+2) = ?

Forgotten

User ID: 1448291
United States
01/22/2013 12:42 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?
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.

Good luck "space physicist".

caper_26

User ID: 32057798
01/22/2013 12:45 PM
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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

User ID: 32057798
01/22/2013 12:46 PM
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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

User ID: 4949345
01/22/2013 01:02 PM

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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.

"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

User ID: 32057798
01/22/2013 01:20 PM
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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.

"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

User ID: 32057798
01/22/2013 01:24 PM
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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.

"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

User ID: 4949345
01/22/2013 01:29 PM

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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.

"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.
Anonymous Coward
User ID: 32447952
United Kingdom
01/22/2013 01:32 PM
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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

Anonymous Coward
User ID: 31220830
United States
01/22/2013 01:33 PM
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Re: Math: 6÷2(1+2) = ?
9
caper_26

User ID: 32057798
01/22/2013 01:45 PM
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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."
Syrius (OP)

User ID: 19364503
United States
01/22/2013 01:46 PM
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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

User ID: 32057798
01/22/2013 01:51 PM
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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)

User ID: 19364503
United States
01/22/2013 01:53 PM
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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

User ID: 32057798
01/22/2013 01:54 PM
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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

User ID: 4949345
01/22/2013 01:55 PM

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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

User ID: 32057798
01/22/2013 01:56 PM
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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."
caper_26

User ID: 32057798
01/22/2013 02:00 PM
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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

User ID: 4949345
01/22/2013 02:12 PM

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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
Anonymous Coward
User ID: 17300078
United States
01/22/2013 02:34 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.
Anonymous Coward
User ID: 17300078
United States
01/22/2013 03:08 PM
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Re: Math: 6÷2(1+2) = ?

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.
caper_26

User ID: 32057798
01/22/2013 04:46 PM
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Re: Math: 6÷2(1+2) = ?
125 ÷ 5(5) = ?

is the same as

125 ÷ 5 x 5 = ?

BEDMAS left to right:

25(5) = 125
Quoting: Anubis

Not the same. That is the problem with everyone getting 9. That is why the author wrote the equation the way it is. Anyone not well versed in maths doesn't get it, so they will swear it is 9 because of some "mnemonic". All the 1's WILL understand the implied ( ) or grouping. the 9's will not believe the 1's. Stalemate for the most part.

For example. What is 6 ÷ 6 ?
Is 6 = 2(3) ? Yes.
So 6 ÷ 2(3) = ?

6 ÷ 2 * 3 = ?

"Six divided by 2 three's is 1"
6 ÷ 2(3) = 1

"Six divided by 2 times 3 is 9"
6 ÷ 2 * 3 = 9

Math is a way of expressing real world scenarios.
"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
01/22/2013 04:56 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.
Quoting: Anonymous Coward 17300078

Exactly. Most don't understand the lack of ( ) around the 6 ÷ 2 means that expression cannot be distributed. I derived both equations from scratch, using factoring (the reverse of distribution)

6 ÷ 6 = 1
6 ÷ (4+2) = 1
6 ÷ 2(2+1)= 1 Extra Parentheses not required since we know the 2 was the GCF of 4+2. You can put them in, but it is redundant, just as (6) ÷ (6) = (1) is redundant.

3 * 3 = 9
(6/2)3 = 9 Here, we NEED ( ) because we cannot write 6/23
(6/2)(2+1) = 9

There you have it. Another way:
6 + 3 = 9
(6/2)2 + (6/2)1 = 9; We can't write 6/22 + 6/21
(6/2)(2+1) = 9

There are the 2 proofs of the equations in debate.
"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

User ID: 4949345
01/22/2013 05:26 PM

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Re: Math: 6÷2(1+2) = ?

Last Edited by Anubis on 01/22/2013 05:26 PM
Bent

User ID: 1441871
United States
01/22/2013 05:28 PM
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Re: Math: 6÷2(1+2) = ?
To caper and other 1tards...we actually listened in school.!

caper_26

User ID: 32057798
01/22/2013 05:34 PM
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Re: Math: 6÷2(1+2) = ?

Quoting: Anubis

"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

User ID: 4949345
01/22/2013 05:38 PM

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Re: Math: 6÷2(1+2) = ?
6/2(1+2) = 9

6/(2(1+2)) = 1
caper_26

User ID: 32057798
01/22/2013 05:43 PM
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Re: Math: 6÷2(1+2) = ?
6 ÷ 6 = 1
6 ÷ (3+3) = 1
6 ÷ 3(1 + 1) = 1
6 ÷ (1+1)3 = 1

6 ÷ (4+2) = 1
6 ÷ 2(2+1) = 1
6 ÷ (2+1)2 = 1

6 ÷ 2n = 3/n
6 ÷ n2 = 3/n

1a ÷ 1a = 1 and not some retarded 1 * a ÷ 1 * a = a²
"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
01/22/2013 08:46 PM
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Re: Math: 6÷2(1+2) = ?
Here is a real world example:

Solve:

100mm ÷ 10cm = ?
"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
01/22/2013 09:02 PM
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Re: Math: 6÷2(1+2) = ?
Here is a real world example:

Solve:

100mm ÷ 10cm = ?
Quoting: caper_26

Dont bother responding, because I wont respond. Just wanted to show this "joke of an answer" you gave in other thread.

Which is obviously so wrong it isnt even funny. Redunancy indeed!

That is THE most retarded answer I have ever seen. If you believe that, then no bloody wonder you getting 9 as a response.

"Redundancy Law"

A coefficient of 1 does NOT need to be written. It is ALWAYS implied. a = 1a . Also the Identity Law. You CAN write though, but because of the math LAW stated, it cannot change the outcome of the answer.

Please tell me you see what is wrong with this! I thank you for posting, because I can actually use that as yet ANOTHER way to prove 1 is the answer, as a matter of fact !!

3÷1(1+2)=9 What kind of special math is this??

'1' as a coefficient can be omitted.
that means, according to you:

3÷1(1+2)= 3÷(1+2)
9 = 1

In reality though,
3÷1(1+2)= 3÷(1+2)
1 = 1

Thank you for showing everyone this "proof" and good night. Nothing more to be said here after that one.

Quoting: caper_26

I sincerely hope this is the last time you reply.

You are right, the 1 can be omitted. But that just means you remove the ÷, (the item between the 1 and 3), but that still leaves multiplication there. If you drop the "useless" 1, then you drop the item in between. Not the one after. at a loss for words.

Last Edited by Forgotten on 01/22/2013 09:03 PM
DUCM900

User ID: 32829152
Italy
01/22/2013 09:07 PM
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Re: Math: 6÷2(1+2) = ?
worfram's result:

6÷2(1+2)=1

false

Quoting: DUCM900

Nice one. I already proved wolfram doesn't know how to substitute values for variables.

If I gave you 6÷2n = 3/n, then told you n=2+1; it is mathematically invalid to say 9 = 1

This is what wolfram does. Wolfram is proven useless to solve this equation correctly.

.
Quoting: caper_26

Also take a look at that:

then this one: