# 6÷2(1+2) = x Solve for x

## 6÷2(1+2) = x Solve for x

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#### The-Kid

##### Dr. Stratster
The HP-41C is amazing. I think I was in my first year of college. I had been using a Ti-55. I took a summer course called something like "advanced math" which was just a fun course for math geeks who wanted to learn things mathematical outside of the regular curriculum.

The teacher had an HP-41CV. Once I got the hang of RPN I fell in love with that thing. She let me borrow it over a weekend. I was visiting my parents over that weekend and was showing this amazing calculator to my parents.

That Christmas, there was a box with my name on it which contained the usual underwear and that stuff. We laughed and my mother said, "keep looking". At the bottom was an HP-41CV. I freaked out because that was VERY unlike my mother. It's the best gift I have ever received and I still have it today (and it's working).

Being an HP geek, I have simulators for:
HP50g
HP Prime
HP41CX
HP-42S
HP35s
HP12cp
HP-15C
HP 17bII+

They're all free. I have the real hardware for the HP50g, HP Prime, HP41CV and HP-42S.

I guess it's a similar sickness to having all these guitars

Once you get the hang of RPN, there's no turning back. For the expression in question, I did this:

6÷2(1+2) = x Solve for x

6 ENT 2 ENT 1 ENT 2 + X /

Admittedly, I entered the expression how I am seeing it. Others could have done it differently and gotten x = 9.
TI84 Plus guy here yet we still get the same correct answer!!!!

Hi-5!!!

I mean the calculators have nothing to do with it. One actually has to understand and do the real math to get it right after all *_*

#### Andrew Wasson

##### Senior Stratmaster
The HP-41C is amazing. I think I was in my first year of college. I had been using a Ti-55. I took a summer course called something like "advanced math" which was just a fun course for math geeks who wanted to learn things mathematical outside of the regular curriculum.

The teacher had an HP-41CV. Once I got the hang of RPN I fell in love with that thing. She let me borrow it over a weekend. I was visiting my parents over that weekend and was showing this amazing calculator to my parents.

That Christmas, there was a box with my name on it which contained the usual underwear and that stuff. We laughed and my mother said, "keep looking". At the bottom was an HP-41CV. I freaked out because that was VERY unlike my mother. It's the best gift I have ever received and I still have it today (and it's working).

Being an HP geek, I have simulators for:
HP50g
HP Prime
HP41CX
HP-42S
HP35s
HP12cp
HP-15C
HP 17bII+

They're all free. I have the real hardware for the HP50g, HP Prime, HP41CV and HP-42S.

I guess it's a similar sickness to having all these guitars

Once you get the hang of RPN, there's no turning back. For the expression in question, I did this:

6÷2(1+2) = x Solve for x

6 ENT 2 ENT 1 ENT 2 + X /

Admittedly, I entered the expression how I am seeing it. Others could have done it differently and gotten x = 9.

That’s a totally awesome Christmas present. It sounds like you grew up in a time, like I did where those type lavish presents were few and far between.

Christmas was always good in my house but I knew whatever I was going to get, it was going to be modest. That’s why I spent my paper route money to get my Ti55. It was plenty good enough for high school physics which was the only class we were allowed to use a calculator. I bought mine the summer between grade 9 and grade 10. I tried to program it to play games but it didn’t really have enough steps to do anything interactive or fun. I could definitely do simple things like program it to add tax or discounts to purchases.

I have an HP41CX emulator on my phone. I’ve got forth on a few vintage computers. I ought to give them a run too. I’ve got a 1/4 scale PDP8 that runs PDP8 emulation on a Raspberry Pi. It’s fully functional and runs at about the same speed one would run in around 1968.

Good nerdy fun.

##### Strat-Talker
It's only a matter of people using the parentheses differently in different parts of the world.

The actual math hasn't changed at all. It's just a sequencing of operations.

Yeh, that relates to me too.....all the right notes, buy not necessarily in the right order!!!

#### AxemanVR

##### I appreciate, therefore I am...
Silver Member
Start with understanding the distributive property properly and go from there and you will get the correct answer.

Again this ignores the distributive property.

For example simple equation here.

2+2(2+2).

The correct answer is 10 following the distributive property correctly but if you ignore the distributive you get 16 and the wrong answer.

Similarly in this equation in OP ignoring the distributive property gets you the wrong answer.

This is why its important to understand the distributive property whether your doing it on paper or plugging it into a computer or calculator.

Aren't you forgetting the order of operations? Parentheses first THEN multiplication or division (from left to right) THEN addition or subtraction?

Here's a theoretical "distributive property" example using our equation (which is wholly unnecessary and actually doesn't work):

6÷2(1+2)=x
6÷2(1)+2(2)=x
6÷(2)+(4)=x
6÷2+4=x *You must go from left to right here!
(6÷2)+(4)=x
(3)+(4)=x
3+4=7

x=7?

In order to get "1" you'd have to use "your" argument, and in "your" argument "addition" would precede "division":

6÷2(1+2)=x
6÷2(1)+2(2)=x
6÷(2)+(4)=x
6÷2+4=x
6÷6=1 *You didn't go from left to right in the previous step!

x=1 is wrong!!!!!!

Show me a concise, well documented example of a distributive property equation that begins with multiplication or division ahead of it - especially one that also works in your favor (a “real” example, not one of your condescending, unsupported, word-vomit versions).

Otherwise:

a=what
b=part
c=of
d=FO
e=is
f=confusing
you=you (literally)
?=?

a+b+c+d+e+f+you+?=x

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#### FrieAsABird

##### Senior Stratmaster
So, anybody else in here like guitars or…?

#### AxemanVR

##### I appreciate, therefore I am...
Silver Member
Well if ya want to talk about statistics, having a 55:45 pole isn't exactly "far more prevalent". If I told you that you had a 55% of not having some debilitating illness, would that make you comfortable? The very reason why the vote is pretty close is because the question is ambiguous. If it weren't you'd see a single answer leading closer to 66%~72% (which tends to be the median for most standardized testing). This result is essentially a coinflip.

Be that as it may, if it represented some sort of theoretical election result today, that 55% would set the standard. At the very least ambiguity would be diminished and some sort of universal adherence could be established.

BUT, I do actually agree with you that what’s a bit more ambiguous is the interpretation. So, while I can certainly understand how a person can come up with “1” as the solution, I am still free to disagree with the interpretation that got it.

So (for the record) I can see how “1” and “9” are both found, but I chose to follow one interpretation over the other - based on the supporting evidence I’ve actually seen and not the unsubstantiated patronizing words of others here...

...but, that said, I am still looking into it...

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#### The-Kid

##### Dr. Stratster

Aren't you forgetting the order of operations? Parentheses first THEN multiplication or division (from left to right) THEN addition or subtraction?

Here's a theoretical "distributive property" example using our equation (which is wholly unnecessary and actually doesn't work):

6÷2(1+2)=x
6÷2(1)+2(2)=x
6÷(2)+(4)=x
6÷2+4=x *You must go from left to right here!
(6÷2)+(4)=x
(3)+(4)=x
3+4=7

x=7?

In order to get "1" you'd have to use "your" argument, and in "your" argument "addition" would precede "division":

6÷2(1+2)=x
6÷2(1)+2(2)=x
6÷(2)+(4)=x
6÷2+4=x
6÷6=1 *You didn't go from left to right in the previous step!

x=1... which is wrong!!!!!!

Show me an example of a distributive property equation that begins with multiplication or division ahead of it - one that also works in your favor (a “real” example, not one of your condescending, unsupported, word-vomit versions).

Otherwise:

a=what
b=part
c=of
d=FO
e=is
f=confusing
you=you (literally)
?=?

a+b+c+d+e+f+you+?=x

Firstly I didnt invent the distributive property so its not really my argument its just basic simple elementary maths learned in 5th or 6th grade

Secondly distribution isnt an equation............ Its a property of mathematics that applies to a given set.

6 is being divided by 2(2+1) here, since 2(2+1) is a term you cant just go on and divide by just distributing and not adding them before you begin to divide.

Doing it your way not only violates the distributive property since 2(2+1) is a term that 6 is being divided by but I would say doing math your way ignoring the distributive property also tosses out the commutative and associative property out the window one could say.

In any case doing math how your suggesting here works for you or people who do it as such because it makes sense for you and you understand it that way but it does not make it the correct way of doing math and well you will never get a correct answer.

Furthermore, simply put if you wanted to actually pass a college class at a reputable school or use the maths for real world equations where a correct answer is even more important, doing it your way wouldnt yield correct answers because its not how math works.

Your pseudo math is all fun and games but when it comes down to it it just wont work in any respectable school or in applications where real math is needed to get correct results for equations in the real world.

#### AxemanVR

##### I appreciate, therefore I am...
Silver Member
Firstly I didnt invent the distributive property so its not really my argument its just basic simple elementary maths learned in 5th or 6th grade

Secondly distribution isnt an equation............ Its a property of mathematics that applies to a given set.

6 is being divided by 2(2+1) here, since 2(2+1) is a term you cant just go on and divide by just distributing and not adding them before you begin to divide.

Doing it your way not only violates the distributive property since 2(2+1) is a term that 6 is being divided by but I would say doing math your way ignoring the distributive property also tosses out the commutative and associative property out the window one could say.

In any case doing math how your suggesting here works for you or people who do it as such because it makes sense for you and you understand it that way but it does not make it the correct way of doing math and well you will never get a correct answer.

Furthermore, simply put if you wanted to actually pass a college class at a reputable school or use the maths for real world equations where a correct answer is even more important, doing it your way wouldnt yield correct answers because its not how math works.

Your pseudo math is all fun and games but when it comes down to it it just wont work in any respectable school or in applications where real math is needed to get correct results for equations in the real world.
`
Same B.S. - all words, no proof...

Let me ask you something... what did you mean by this?:

Did you mean 6÷(ab)+(ac)?

*or 6÷(2x1)+(2x2) in this thread's equation?

That'd be the same as 6÷2+4, wouldn't it? And wouldn't the order of operations dictate going from left to right and "dividing" first before "adding" at this point?

Please, tell us how you get 6÷6 without adding first...

`

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#### Skychurch

##### Strat-Talk Member
6 is being divided by 2(2+1) here, since 2(2+1) is a term you cant just go on and divide by just distributing and not adding them before you begin to divide.

That's exactly how I'm seeing it and why I keep getting x = 1 no matter what method or calculator I use. I tried a few times to get x = 9 (which I was able to) but the method I had to use to get 9 I found confusing ... like I was forcing something that wasn't there (at least with how I am seeing the expression).

#### AxemanVR

##### I appreciate, therefore I am...
Silver Member
That's exactly how I'm seeing it and why I keep getting x = 1 no matter what method or calculator I use. I tried a few times to get x = 9 (which I was able to) but the method I had to use to get 9 I found confusing ... like I was forcing something that wasn't there (at least with how I am seeing the expression).

Due to the all the controversy on the subject I'll just call this "my interpretation" and see if it makes sense to you...

First of all, forget about "distributive properties" - that has no application here as far as I can see. The rest is following the "order of operations" which actually only involves three of them for this problem: "parentheses", "multiplication or division" and "addition".

So, starting with our mischievous equation:

A) 6÷2(1+2)=x

"Parentheses" first (this just requires adding the numbers inside the parenthesis in this equation):

6÷2(1+2)=x is the same as 6÷2(3)=x

Here's another way to look at it:

6÷2(3)=x is the same as 6÷2x3=x

In this case "addition" came first, but only because they were inside the parenthesis.

B) 6÷2x3=x

So now we do the "multiplication or division" step (from left to right), starting with "division" first in our case:

6÷2x3=x is the same as (6÷2)x3=x

Another way we can look at it is:

(6÷2=3)x(3)=x

Then we simplify it:

(3)x(3)=x

and simplify again in order to get our answer:

3x3=9

Not trying to cause trouble, but the reason the other way doesn't work is because people see everything following the division sign as being one single thing. My understanding is that this is the "pre-1917" way of looking at it, as mentioned somewhere earlier in this thread.

So the "pre-1917" way looks like this:

6÷2(1+2) is the supposedly the same as 6÷(2x3), which lumps the entire second half (to the right of the division sign) together making it seem to be 6÷(6) or 6÷6

The problem lies on whether a person sees it more like or 6÷2x3=x

Anyway, it's clear that following the order of operations can be at odds with each other...

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#### Skychurch

##### Strat-Talk Member
B) 6÷2x3=x

So now we do the "multiplication or division" step (from left to right), starting with "division" first in our case:

6÷2x3=x is the same as (6÷2)x3=x

`

I think that's my problem. I do not see 6÷2x3=x to be the same as (6÷2)x3=x
The first one has 2x3 in the denominator (6/6) where the second has the 3 moved up to the numerator (3x3) but they are not =. ???

I don't see how mathematically one can move the 3 up to the numerator ... at lease not how the original expression was written.

I think these would be equivalent:

6/2x3 = 3/3 = 2/2

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#### AxemanVR

##### I appreciate, therefore I am...
Silver Member
I think that's my problem. I do not see 6÷2x3=x to be the same as (6÷2)x3=x
The first one has 2x3 in the denominator (6/6) where the second has the 3 moved up to the numerator (3x3) but they are not =. ???

I don't see how mathematically one can move the 3 up to the numerator ... at lease not how the original expression was written.
`
The 3 is not being moved up, but more like moved "out" - Here’s where the ambiguity lies:

Can it actually be either or both? This is why it's so contentious and is also why (as I stated earlier) I'm still looking into it.

BUT, as I also stated earlier, modern interpretation seems to refer to the one on the right as being more correct, so that's how I choose to see it for the time being...

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#### Skychurch

##### Strat-Talk Member
`
Here's where the ambiguity lies:

View attachment 501960

Can it actually be either or or both? This is why it's so contentious and is also why (as I stated earlier) I'm still looking into it. BUT, as I also stated earlier, modern interpretation seem to refer to the one on the right as being more correct, so that's how I choose to see it right now...
`
`

Yes, exactly! I'm still stuck on interpreting the original expression as the first example you have. Others are seeing it as in the second example (I think). Who's right??? I have no idea ... but it must be the way I see it
As you're looking into it, if you find anything interesting, let us know. I'm sincerely interested (whether I'm right or wrong).

#### MickeyPicky

##### Strat-Talker
Lol... You can change the size of the text all you like but it still won't make you right. There are no two sides to this equation. There is right and there is wrong.

EDIT for clarity: The reason it will never be 1 is because it isn't written 6/(2(1+2)) it is written as 6/2(1+2)

it’s not written (6/2)(1+2) either. It’s an incomplete format. Question can’t be answered unless you are demanding they follow some specific order, which would be situational at best

#### MickeyPicky

##### Strat-Talker
So...
What's your answer? To the rather awful representation...not the meaning of life. We figured that out decades ago.

Personally I would presume (6/2) * (1+2), but that’s merely my bias. The problem is basically an optical illusion - one would be just as right going the other way.

#### thomquietwolf

##### Dr. Stratster
Gold Supporting Member
Silver Member
It always amazes me how people want to try to redefine absolute truth. These redefinitions cause nothing but division even among the people that scream for tolerance and unity. When all they are showing is their own ignorance.
Enough of that talk about the difference between new and old math.
Math is math and no matter how you look at it, it is 9. Inside the parentheses first then left to right.

In coding...
PEMDAS

Where did this nonsense come from
{
Inside the parentheses first then left to right.
}

#### FrieAsABird

##### Senior Stratmaster
What about cats then? There’s gotta be some common ground on this battlefield of numbers…

#### dbb541

##### Senior Stratmaster
32 pages of comments on a simple math problem that has an obvious answer of 9.

I sent the equation to my school teacher buddy. He quickly responded the answer is 9. I told him 45% of the people on a guitar forum think the answer is 1.

He added, "I wonder what the demographics are for the people polled. Generation I (idiots)"

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