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# Math: 6÷2(1+2) = ?

Anonymous Coward
User ID: 32057798
01/13/2013 11:29 AM
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Re: Math: 6÷2(1+2) = ?
My 4 year old can type 9 and call people morons. Back it up with something. Read THIS for example:

Distribute 2 into the parentheses. Why? because it is a factor of the original terms INSIDE them, and cannot be ripped apart. I will show you why:
6 = 4+2 = 2(2+1) = 2(3) The 2 is a common factor of 4 & 2.
No matter which way you view it, the value 6 MUST maintain its value. Just as you cannot take the 4 from (4+2) and divide it into a number with the "+ 2". I cannot take the 2 from 2(2+1) and divide it into another number without the (2+1).
You ARE allowed to distribute before division, or any other operator, since you are allowed to simplify any equation first. There are MANY references which state "Remove parentheses by distribution" Try Googling that as a search term.
6÷2(2+1) = 6÷(4+2) = 1
Now, some people have argued that you don't NEED to distribute the 2; you just add the 2+1, and end up with 2(3). Then they go on the say that this is the same as 2*(3). WRONG! You STILL have parentheses and STILL need to distribute that 2 inside them, for the reasons discussed about factoring above. Therefore you have this:
6÷2(3) and must distribute like this:
6÷2(3+0) = 6÷[2(3) + 2(0)] = 6÷6 = 1
These people who get 9 try and rip the 2 away from the parentheses by inserting a times symbol like this:
6÷2*(3), and then do the division of 6÷2 first. I explained the illegalities of doing this, since the 2 is a factor of the 2+1.
Lastly, 6÷2 is NOT (6/2), as in (6/2)(2+1). This is totally incorrect, since it lacks that parentheses in the original equation. Check any online or written text. Leading fractions as a coefficient ALWAYS have ( ) around them.
I hope this clears things up.
Regards.
Quoting: Anonymous Coward 32057798

This is so wrong, it is not even funny. The fact that you wrote up this whole thing is down right hysterical.

I weep for our society.

p.s. I work for a Univeristy. I have comfirmed the answer is 9 from 3 different math professors, excel, and my own solution.

You sir are a nitwit.
Quoting: Anonymous Coward 29097718

Saying it is wrong, doesn't make it so. Proof anything I said to be other than true.
Let me ask you this: Assuming the Identity Law is correct in saying a = 1a = 1(a),
a/1a = ?
Patrick Bateman

User ID: 32018985
01/13/2013 11:30 AM
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Re: Math: 6÷2(1+2) = ?
Lol, this again?
The MAN BEARD is back!!! RESPECT IT!!!!

"You will never be happy if you continue to search for what happiness consists of. You will never live if you are looking for the meaning of life." - Albert Camus
Anonymous Coward
User ID: 32110288
United States
01/13/2013 11:35 AM
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Re: Math: 6÷2(1+2) = ?
If you think the equation should = 9 then it should look like this:

(6/2)(1+2)=

3*3 =9

but we have:

6/2(1+2)=

6/6 =1

because you do the sum in the bracket first.

Quoting: Anonymous Coward 26789708

Correct.
Quoting: Anonymous Coward 29086850

INCORRECT.
Anonymous Coward
User ID: 32110288
United States
01/13/2013 11:36 AM
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Re: Math: 6÷2(1+2) = ?
Mensa posted this on their FB page about a week ago. I can only assume someone has answered it already but I'll give it a go.

6÷2(1+2) = ?
3(1+2) = ?
3(3) = 9

Order of operations are a grade 9 level understanding of math.
Quoting: Person445

Sorry but you divided 6 by 2 before getting rid of the () thus violating the order of operations.
Quoting: Anonymous Coward 28938484

The parenthesis only applies to what is inside of them.
Patrick Bateman

User ID: 32018985
01/13/2013 11:37 AM
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Re: Math: 6÷2(1+2) = ?
If you think the equation should = 9 then it should look like this:

(6/2)(1+2)=

3*3 =9

but we have:

6/2(1+2)=

6/6 =1

because you do the sum in the bracket first.

Quoting: Anonymous Coward 26789708

Correct.
Quoting: Anonymous Coward 29086850

INCORRECT.
Quoting: Anonymous Coward 32110288

It is a poorly written problem in the least needs an extra set of parentheses to get the desired answer.
The MAN BEARD is back!!! RESPECT IT!!!!

"You will never be happy if you continue to search for what happiness consists of. You will never live if you are looking for the meaning of life." - Albert Camus
Anonymous Coward
User ID: 32057798
01/13/2013 11:37 AM
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Re: Math: 6÷2(1+2) = ?
If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ).
Anonymous Coward
User ID: 27301486
01/13/2013 11:39 AM
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Re: Math: 6÷2(1+2) = ?
If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ).
Quoting: Anonymous Coward 32057798

6 : 2 x (1+2)

= 6 : 2 x 3

= 9
Anonymous Coward
User ID: 32057798
01/13/2013 11:39 AM
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Re: Math: 6÷2(1+2) = ?
If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ).
Quoting: Anonymous Coward 32057798

6 : 2 x (1+2)

= 6 : 2 x 3

= 9

Quoting: Anonymous Coward 27301486

Why are you inserting a TIMES symbol so you can ignore Distribution?
Coma Patient #7

User ID: 29804770
United States
01/13/2013 11:41 AM

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Re: Math: 6÷2(1+2) = ?
The answer has been stated, it can be either because it's poorly stated. Here's one of the better explanations I've read, copy/paste.

A similar debate popped up not that long ago and had people arguing non-stop. Check the reference at the bottom. The real answer is that the equation itself is ambiguous and should have been written better. This equation should have been written as...

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

or

6 / [ 2 ( 1 + 2 ) ] =

Using the standardized order of operations...
6 / 2 ( 1 + 2 )
6 / 2 ( 3 ) or 6 / 2 * 3

Using parenthetical implications via multiplication by juxtaposition and the distributive property...
6 / 2 ( 1 + 2 )
6 / [ ( 2 * 1 ) + ( 2 * 2 ) ]
6 / 6

Both of you are correct. Considering the ambiguity and poor nomenclature of the equation, you should ask whomever posed the problem to define his/her notation preferences. No self-respecting mathematician would write the equation in this manner.

Anytime you see ab/cd you will see this disagreement.

Through will of thought we control our emotions and thoughts are often no more difficult to control then we make them to be.
Patrick Bateman

User ID: 32018985
01/13/2013 11:41 AM
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Re: Math: 6÷2(1+2) = ?
If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ).
Quoting: Anonymous Coward 32057798

I agree, but also still believe it is a flawed problem, and could be argued each way. But from what I have been taught, the answer would be 1.

Last Edited by Patrick Bateman on 01/13/2013 11:41 AM
The MAN BEARD is back!!! RESPECT IT!!!!

"You will never be happy if you continue to search for what happiness consists of. You will never live if you are looking for the meaning of life." - Albert Camus
Patrick Bateman

User ID: 32018985
01/13/2013 11:41 AM
Report Abusive Post
Re: Math: 6÷2(1+2) = ?
The answer has been stated, it can be either because it's poorly stated. Here's one of the better explanations I've read, copy/paste.

A similar debate popped up not that long ago and had people arguing non-stop. Check the reference at the bottom. The real answer is that the equation itself is ambiguous and should have been written better. This equation should have been written as...

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

or

6 / [ 2 ( 1 + 2 ) ] =

Using the standardized order of operations...
6 / 2 ( 1 + 2 )
6 / 2 ( 3 ) or 6 / 2 * 3

Using parenthetical implications via multiplication by juxtaposition and the distributive property...
6 / 2 ( 1 + 2 )
6 / [ ( 2 * 1 ) + ( 2 * 2 ) ]
6 / 6

Both of you are correct. Considering the ambiguity and poor nomenclature of the equation, you should ask whomever posed the problem to define his/her notation preferences. No self-respecting mathematician would write the equation in this manner.

Anytime you see ab/cd you will see this disagreement.

Quoting: Coma Patient #7

Exactly!
The MAN BEARD is back!!! RESPECT IT!!!!

"You will never be happy if you continue to search for what happiness consists of. You will never live if you are looking for the meaning of life." - Albert Camus
Anonymous Coward
User ID: 27301486
01/13/2013 11:42 AM
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Re: Math: 6÷2(1+2) = ?
If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ).
Quoting: Anonymous Coward 32057798

6 : 2 x (1+2)

= 6 : 2 x 3

= 9

Quoting: Anonymous Coward 27301486

Why are you inserting a TIMES symbol so you can ignore Distribution?
Quoting: Anonymous Coward 32057798

Because that is what it means.

2(1+2) = 2 x (1+2)
Anonymous Coward
User ID: 32057798
01/13/2013 11:53 AM
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Re: Math: 6÷2(1+2) = ?
Because that is what it means.

2(1+2) = 2 x (1+2)
Quoting: Anonymous Coward 27301486

That does NOT exempt you from applying distribution OR removing parentheses first.

Has NO ONE seen ANY of these references??!?!?!?

Distribute BEFORE "pedmas" used to REMOVE parentheses too: [link to www.algebra.com]

Get Rid of parentheses with Distribution:

If there is some factor multiplying the parentheses, then the only way to get rid of the parentheses is to multiply using the distributive law.

"When simplifying expressions with parentheses, you will be applying the Distributive Property." -purplemath
Anonymous Coward
User ID: 32057798
01/13/2013 11:56 AM
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Re: Math: 6÷2(1+2) = ?
If you get 9, you obviously don't know how to handle parentheses properly and have not had any higher level math education in university... "pemdas" or "dumass" or whatever it is called, and "left to right" is for elementary school children. You later learn the proper "order of operations" and know that equations are essentially collapsed using proper mathematical techniques
Anonymous Coward
User ID: 27301486
01/13/2013 11:58 AM
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Re: Math: 6÷2(1+2) = ?
Because that is what it means.

2(1+2) = 2 x (1+2)
Quoting: Anonymous Coward 27301486

That does NOT exempt you from applying distribution OR removing parentheses first.

Has NO ONE seen ANY of these references??!?!?!?

Distribute BEFORE "pedmas" used to REMOVE parentheses too: [link to www.algebra.com]

Get Rid of parentheses with Distribution:

If there is some factor multiplying the parentheses, then the only way to get rid of the parentheses is to multiply using the distributive law.

"When simplifying expressions with parentheses, you will be applying the Distributive Property." -purplemath
Quoting: Anonymous Coward 32057798

The factor multiplaying the paranthesis is 3.

6 ÷ 2 x (1+2)

= 3 x (1+2)

= 3 x (1) + 3 x (2)

= 9
Anonymous Coward
User ID: 1428208
United States
01/13/2013 12:04 PM
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Re: Math: 6÷2(1+2) = ?
parentheses first, then solve left to right...

9
Anonymous Coward
User ID: 32057798
01/13/2013 12:04 PM
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Re: Math: 6÷2(1+2) = ?
The factor multiplaying the paranthesis is 3.

6 ÷ 2 x (1+2)

= 3 x (1+2)

= 3 x (1) + 3 x (2)

= 9
Quoting: Anonymous Coward 27301486

Do you SEE any parentheses around 6/2 ?? NO ! Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first! Since when is 6÷2 ever factored from a set of terms?? Distribution is factoring in reverse. You to get a handle on other concepts to solve this equation properly.
(4+2) = 2(2+1)
If you want to say this:
(6 + 3) = 3(2+1) = (6/2)*(2+1) you REQUIRE parentheses. Open any book on online PDF math books... they ALL say this.
Anonymous Coward
User ID: 32057798
01/13/2013 12:07 PM
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Re: Math: 6÷2(1+2) = ?
parentheses first, then solve left to right...

9
Quoting: Anonymous Coward 1428208

Yes, but you didn't do step 1. So before anyone else says "Wrong" you may want to actually read something and educate yourself, and then prove ALL of the following references incorrect.

See below:
---------------------------
"We use the distributive property to help us find a way around the order of operations while still being sure that we keep the value of the expression."

Distribute to REMOVE parentheses [link to www.algebra.com]

Get Rid of parentheses with Distribution:

If there is some factor multiplying the parentheses, then the only way to get rid of the parentheses is to multiply using the distributive law.

"When simplifying expressions with parentheses, you will be applying the Distributive Property." -purplemath
These guys got it right, they use "Parentheses" in the order of operations to require Distributive Property.
Ref: Purplemath

The Distributive Property in ALgebra:
The Distributive Property is handy to help you get rid of parentheses.
a(b + c) = ab + ac
Anonymous Coward
User ID: 27301486
01/13/2013 12:09 PM
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Re: Math: 6÷2(1+2) = ?
Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first!
Quoting: Anonymous Coward 32057798

Then you have:

6 ÷ 2 x (1+2)

= 6 ÷ 2 x 3

= 3 x 3

= 9
Anonymous Coward
User ID: 32057798
01/13/2013 12:10 PM
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Re: Math: 6÷2(1+2) = ?
Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first!
Quoting: Anonymous Coward 32057798

Then you have:

6 ÷ 2 x (1+2)

= 6 ÷ 2 x 3

= 3 x 3

= 9

Quoting: Anonymous Coward 27301486

WRONG. I proved that already. Anyone else?
Anonymous Coward
User ID: 27301486
01/13/2013 12:11 PM
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Re: Math: 6÷2(1+2) = ?
Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first!
Quoting: Anonymous Coward 32057798

Then you have:

6 ÷ 2 x (1+2)

= 6 ÷ 2 x 3

= 3 x 3

= 9

Quoting: Anonymous Coward 27301486

WRONG. I proved that already. Anyone else?
Quoting: Anonymous Coward 32057798

It's correct. Where is it wrong?
Anonymous Coward
User ID: 27301486
01/13/2013 12:11 PM
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Re: Math: 6÷2(1+2) = ?
Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first!
Quoting: Anonymous Coward 32057798

Then you have:

6 ÷ 2 x (1+2)

= 6 ÷ 2 x 3

= 3 x 3

= 9

Quoting: Anonymous Coward 27301486

WRONG. I proved that already. Anyone else?
Quoting: Anonymous Coward 32057798

I just applied your own rule, can you not see that?
Anonymous Coward
User ID: 13045367
Netherlands
01/13/2013 12:12 PM
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Re: Math: 6÷2(1+2) = ?
Casio says 1, en Texas Instruments says 9.

It is nine.

That's just 3 because 1 +2 1 +2 brackets.
So we have:

6 ÷ 2 x 3

Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17.

Given multiplication and division rank equally, they are just left to right.
So first 6/2 gives 3 times 3 is 9 and that
In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert:

6 ÷ (2 x 3)

as one would give.
Anonymous Coward
User ID: 32057798
01/13/2013 12:13 PM
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Re: Math: 6÷2(1+2) = ?
Because that is what it means.

2(1+2) = 2 x (1+2)
Quoting: Anonymous Coward 27301486

Actually,
2(3) = 3 + 3 = [(1+1+1) + (1+1+1)]
Therefore
2(2+1), meaning 2 groups of 2+1, is exactly:
[(2+1) + (2+1)]
Anonymous Coward
User ID: 32057798
01/13/2013 12:14 PM
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Re: Math: 6÷2(1+2) = ?
Casio says 1, en Texas Instruments says 9.

It is nine.

That's just 3 because 1 +2 1 +2 brackets.
So we have:

6 ÷ 2 x 3

Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17.

Given multiplication and division rank equally, they are just left to right.
So first 6/2 gives 3 times 3 is 9 and that
In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert:

6 ÷ (2 x 3)

as one would give.
Quoting: Anonymous Coward 13045367

You didn't eliminate parentheses properly, Read the above post with 5 or so references to the proper way of doing math.
Anonymous Coward
User ID: 9645738
United States
01/13/2013 12:14 PM
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Re: Math: 6÷2(1+2) = ?
This is where infinity comes to die...
Anonymous Coward
User ID: 27301486
01/13/2013 12:15 PM
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Re: Math: 6÷2(1+2) = ?
Casio says 1, en Texas Instruments says 9.

It is nine.

That's just 3 because 1 +2 1 +2 brackets.
So we have:

6 ÷ 2 x 3

Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17.

Given multiplication and division rank equally, they are just left to right.
So first 6/2 gives 3 times 3 is 9 and that
In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert:

6 ÷ (2 x 3)

as one would give.
Quoting: Anonymous Coward 13045367

You didn't eliminate parentheses properly, Read the above post with 5 or so references to the proper way of doing math.
Quoting: Anonymous Coward 32057798

You do not apply your own rules properly, that is where your confusion comes from.
Anonymous Coward
User ID: 13045367
Netherlands
01/13/2013 12:15 PM
Report Abusive Post
Re: Math: 6÷2(1+2) = ?
Casio says 1, en Texas Instruments says 9.

It is nine.

That's just 3 because 1 +2 1 +2 brackets.
So we have:

6 ÷ 2 x 3

Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17.

Given multiplication and division rank equally, they are just left to right.
So first 6/2 gives 3 times 3 is 9 and that
In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert:

6 ÷ (2 x 3)

as one would give.
Quoting: Anonymous Coward 13045367

You didn't eliminate parentheses properly, Read the above post with 5 or so references to the proper way of doing math.
Quoting: Anonymous Coward 32057798

It's the answer from an einstein proffessor in math so dont act you are right.
Anonymous Coward
User ID: 32057798
01/13/2013 12:16 PM
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Re: Math: 6÷2(1+2) = ?
It's correct. Where is it wrong?
Quoting: Anonymous Coward 27301486

Are yous serious? Did you not see any of the references? Maybe if they are in BLUE, you may see them better...
Anonymous Coward
User ID: 32057798
01/13/2013 12:16 PM
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Re: Math: 6÷2(1+2) = ?
Here you go...in BLUE.

parentheses first, then solve left to right...

9
Quoting: Anonymous Coward 1428208

Yes, but you didn't do step 1. So before anyone else says "Wrong" you may want to actually read something and educate yourself, and then prove ALL of the following references incorrect.

See below:
---------------------------
"We use the distributive property to help us find a way around the order of operations while still being sure that we keep the value of the expression."

Distribute to REMOVE parentheses [link to www.algebra.com]

Get Rid of parentheses with Distribution: