6÷2(1+2)=?

reply to post by BadMagician


Yes they are trolls indeed

www.studygs.net...

Evaluating algebraic expressions can be a simple process, but needs to follow an order of operations to get the right answer. The sequence details the order you follow to add, subtract, multiply, and divide. The order is:

P.E.M.D.A.S.

Parenthesis | Exponents | Multiplication | Division | Addition | Subtraction

Perform the operations inside a parenthesis first
Then exponents
Then multiplication and division, from left to right
Then addition and subtraction, from left to right

You can also create a little phrase to memorize the sequence:

Please Excuse My Dear Aunt Sally

There are many websites showing these rules. They are the same as I posted already.

multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication.*

The implication is that juxtaposition (in this case, multiplication without the sign) takes precedence over normal multiplication and division.

This agrees with what I have learnt and also agrees with my uni text books.


It also says on the same page :

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently.

It also sums it up nicely:

The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations.

Therefore 6÷2(1+2) DOES NOT EQUAL 6÷2*(1+2).

This is 6th grade math, people.

Please note that this is talking exactly about our problem, not about some general rule learnt in primary school.

This also implies that if you are using a 'dumb' calculator (windows, google, various programming languages), then you will have to format the equation yourself by bracketing the juxtaposed values, else the calculator will give you a false result.


.

The easiest way to teach a child to do this problem is to solve the bottom of the fraction first. Then once they have the denominator, simplify the fraction.

6/2(1+2)

6
__

2(1+2)

Originally posted by MegaMind
reply to post by Honor93

 

so you believe the answer is 1/9?

what about every thing after the FIRST "/" being the denominator? That was what u said earlier.

6 / 2 (1 + 2) / 9 = ?

edit on 2-5-2011 by MegaMind because: (no reason given)

actually i defined the 1/9 to the decimal .1111111111111111 for as many digits as you'd like.
as for your question, what's the problem ... a little reading comprehension maybe?

same in this equation as the last ... 6/2(1+2)/9 = ? Follow the rules from inside, out ...
in this case a = 6, b = 2, c = (1+2), d = 9
symbol to symbol denotes left/right paradigm if you think that way ...
so, a[6] divided by the sum of, b[2] times the sum of c[3], divided by d[9] = ?[1 divided by 9 or .111111111111~]

even in a complex equation as you presented, the same d/n rule applies ... 6 / the sum of 2(1+2) / 9
... this equation contains 4 separate calculations, independently.
first, the brackets ... second, the order [exponent] by level, hence multiplying the sum of brackets ... third, division from left to right as instructed ... by dividing the sum of 2(1+2) by 6 and then divide that sum by 9 for the result of .11111111111~

actually, what i said earlier is the posted equation does NOT contain a stand alone fraction of any kind.
it is you and others whom insist such, not i.
what i did suggest is ... if you must 'see' it as a fraction (to comprehend the equation) then everything beyond the division symbol (in the posted one) becomes the denominator. Do not make the mistake of twisting my words, it is not i who is confused.

Have a look here. This should clear it up

6÷2(1+2 ), 6÷2*(1+2), 6÷A*(1+2), 6÷A(1+2), A=2 - Wolfram|Alpha

The calculator contradicts itself and gives a different result for (essentially) the same sum.



.

Originally posted by MegaMind

Originally posted by Honor93
as a matter of fact, time's up and i gotta go ... i'll check back in a few hours ... you got your answers but i doubt you'll acquiesce ... we'll see if progress is truly measured by effort or argument.
where it is likely we'll progress in an argument, it would please me much more if the progress were measured by effort, really, you should try it sometime.

edit on 2-5-2011 by Honor93 because: add text

HA! Got you!

6 / 2 (1 + 2) / 9 = ?

the answer, by the way, is 1. Given your logic I expected you to say either 1/9 or 9 depending on how you ordered it. (hint: that's why rules matter)

While I'm at it what about these?

3 / 3 / 3 = ?

3 / 3 * 3 = ?

3 * 3 / 3 = ?

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

3 * 3 * 3 = ?

I think your just trolling and I've been punked!

You log off and star yourself with another account

edit on 2-5-2011 by MegaMind because: (no reason given)

YOU are seriously confused.
maybe one day when you grow up, have responsibilities, a family and daily duties, perhaps then you'll understand what obligations and time constraints are but, until then, could you at least learn some manners?

i don't do trolling but i am courteous and i said i'd be back later ... had obligations then, have time now ... what is your problem and what is being 'punked'?

as for your math questions, do your own homework ... and the whole number 1 does not compute as a result of your first equation ... regardless how many rules you ignore ... talk about bad math.

You log off and star yourself with another account

you must be completely deluded to fantasize such nonsense ... i have and need only one account, ask anyone.
i do not ever star myself (and didn't really realize i could but thanks for the tip)

clearly, you make far too many assumptions to make any real sense, you really should work on that.
and lastly ... i've wasted enough precious time with you ... have a great evening but plz, do your own homework ... many have before you and surprisingly, many of us actually learned something and programmed your machines.

When anyone assumes a machine is infallible, they are seriously deluded and confused. Why? because Humans created and programmed them ... and, humans are extremely fallible, hence, so are machines.
*** Exercise your brain, it is the greatest machine ever created ***

Originally posted by spy66
This is my reply to you Honor93
Well of course its wrong to space out the equation like you did. because you changed it totally.

Spacing does NOT change any calculations what so ever.
The original is not spaced at all so don't pretend spacing changes progression, it does not.

POSTED: 6/2(1+2)=? ... the only difference is the division symbol ... my current keyboard does not have the arithmetic divider, it uses the universal one "/" ... again, i didn't change ANYthing.

You can't take 6/2 and do as you did. You can't take what 6 is divided by and carry it over to (1+2) and create the equation 2(1+2)

Once again, 6/2(1+2) distributes to 6 divided by [(1+2)+(1+2)] or 6/[(1+2)+(1+2)]
i did not create the equation, i answered it.

How is that possible?
Explain to me how that is correct.

standard basic math coupled with rules of combining operations, otherwise known as 'distributive laws.'
source: oakroadsystems.com...

reply to post by GobbledokTChipeater

kudos, well done and explained precisely, in more than one way.
wish i could give you more than 1 star and thank you for sharing.

Reply to post by MegaMind

A (B + C) = AB + AC

1 / 3 (B + C) = (1/3)B + (1/3)C

is that clear? what don't u get? A = 1/3, or 6/2 or whatever the hell else you want it to be.

edit on 2-5-2011 by MegaMind because: (no reason given)

no it's not clear ... you aren't even close.
1/3(B+C) /=/ what you wrote
1/3(B+C) = 1/[3B+3C]
get it?
in your example A = 1, not (1/3) or one third

reply to post by darius2025


it really depends on how you read it...
Or how it's written out..

idk..
Maybe it's a possibility of both?

Originally posted by heavenlysouldier
reply to post by darius2025

 

it really depends on how you read it...
Or how it's written out..

idk..
Maybe it's a possibility of both?

Yes there are two solutions to this problem depending on how you read it.

the equation 6/2(1+2) can be read in two ways:


6
- (1+2) = 9
2

or

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

Honor93 was right

The answer is 1.

Read the following quote from the American Mathematical Society:

We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division.*

I can't find anywhere else that references that rule, but they clearly say it's a rule.

.

reply to post by GobbledokTChipeater


As far as I can tell about Juxtaposition from online searches is that juxtaposition is merely short hand.
So instead of writing a x b x c = d you can just write abc = d.

I don't see a real mention of it having precedence.
Now I do see that there are special cases where if there is a stacked exponents you do those first from the top down. And also the exclamation point ! indicates that you should calculate the expression to the left.

Using juxtaposition. The formula should be done this way 6 ÷ 2 * (1 + 2) = 9.

In algebra, multiplication involving variables is often written as a juxtaposition (e.g. xy for x times y or 5x for five times x). This notation can also be used for quantities that are surrounded by parentheses (e.g. 5(2) or (5)(2) for five times two).

Unless someone can find some concrete evidence about the whole juxtaposition thing. the answer is 9.

This whole equation is very ambiguous.

God i hate math...

This is clearly an issue with BEDMAS or PEDMAS which i've never heard of...

Using Bedmas the answer is 9...

Using PEDMAS the answer is 1...

Now i can't stand math, im not good at it. I haven't taken it since gr 10 and that was at least 15 years ago.

So.....Have the order of operations changed in the past 15 years?

Since when do you ever Divide before you mulitply?

AND WHERE THE F**K DID PEDMAS COME FROM?

The answer is 9 people... Bedmas is the correct order of operations...

Or were all my teachers idiots?

Originally posted by grey580

In algebra, multiplication involving variables is often written as a juxtaposition (e.g. xy for x times y or 5x for five times x). This notation can also be used for quantities that are surrounded by parentheses (e.g. 5(2) or (5)(2) for five times two).

Unless someone can find some concrete evidence about the whole juxtaposition thing. the answer is 9.

This whole equation is very ambiguous.

Agreed here. I have never heard of this rule where juxtaposition carries higher precedence than regular multiplication. It is just a shorter way of writing things. ab=a*b. The notion that a(b) is of a different precedence in the order of operations than a*b is completely new to me. It has always been taught to me as an implied multiplication, carried out the same way as regular multiplication with a sign. Parentheses denote that the arguments inside must be simplified. Once they are taken care of, the parentheses become unnecessary. For example, say a+b=c

(a+b) = (c)

once you simplify (a+b) to (c), the parentheses serve no purpose and can be dropped. This is of course in contradiction to what Honor93 and others seem to be claiming, that parentheses indicate a higher order of multiplication. This has never been taught to me in any school. I am an engineering student, and while granted I am not a math major, I have taken my fair share of math. It should also be noted however, that most problems that would have this issue arise would be explicitly defined as a fraction of some sort and not presented in this uncommon linear fashion.

If anyone can provide some hard evidence for the juxtaposition precedence thing, please do. Otherwise correct order of operations state that multiplication and division carry the same precedence and are carried out left to right, and I am still going with 9.

Edit for clarification and summary:

The notion that the expressions 6/2(1+2) and 6/2*(1+2) are different expressions because of this higher order juxtaposition seems ridiculous to me. To denote everything after the / to be in the denominator another set of parentheses must be used: 6/(2(1+2)). This is obviously the sticking point of the entire argument here.

Reply to post by ASeeker343

This is of course in contradiction to what Honor93 and others seem to be claiming, that parentheses indicate a higher order of multiplication.

If anyone can provide some hard evidence for the juxtaposition precedence thing, please do. Otherwise correct order of operations state that multiplication and division carry the same precedence and are carried out left to right, and I am still going with 9.

first, the rule you request is posted just above this posting ... see American Mathematical Society for clarification.
second, i do not and did not claim the parenthesis/brackets denote any level change or order of operation change ... add/sub is still basement level and the multiplication order upon that level MUST be computed before addressing any other order on that level, ie: division.

To clarify moreso ... the effect of juxtaposition on the stated equations is simple ...
for 6/2(1+2)=? - the order is to multiply the sum of the brackets
for 6/2*(1+2)=? - the order is to compute separately and multiply the sums of each
get it yet?

The notion that the expressions 6/2(1+2) and 6/2*(1+2) are different expressions because of this higher order juxtaposition seems ridiculous to me. To denote everything after the / to be in the denominator another set of parentheses must be used: 6/(2(1+2)).

The sticky point here is the calculators and those who programmed them with linear functionality solely. Juxtaposition is nothing new, nothing changed and nothing confusing when you understand and play by the rules.

did it ever occur to any of you geniuses who swear your teachers taught you wrong that maybe, just maybe ... on the day the effects of juxtaposition may have been discussed at great length, perhaps, you were absent or played hookey or just skipped that day?
especially, as i know soooo many youngins' figure once they have the 'basics', they are good to go.

Originally posted by Honor93
did it ever occur to any of you geniuses who swear your teachers taught you wrong that maybe, just maybe ... on the day the effects of juxtaposition may have been discussed at great length, perhaps, you were absent or played hookey or just skipped that day?
especially, as i know soooo many youngins' figure once they have the 'basics', they are good to go.

I didn't detect a hint of sarcasm in there at all... But to answer your question no I did not. I paid careful attention back in my algebra learning days. The fact is that the rule of juxtaposition was simply taught to me and probably many others on this thread as a*b = a(b). No higher order precedence of multiplication due to the parentheses was ever taught to me. I have simply just followed the order of operations.

I checked that purple math link, it does in fact state your case. I will however point out the following quotes:

This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.

(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)

This leaves much to be desired... A legitimate textbook would be a little more swaying.

I also checked a physics forum thread that was discussing this said link and another discussion they had there.

www.physicsforums.com...

It seems that this exact same discussion was happening on a physics forum as well, with the same results: page after page of back and forth chicken and egg argument and no consensus.

I will talk to one of my previous math professors sometime this week and see ask his thoughts on the issue.

At this point though we are not making much headway. I am not failing to understand your argument at all, I am comprehending it completely. I am just failing to buy into the fact that the argument you are making is the correct way. There doesn't seem to be a final consensus anywhere, including websites, online calculators DESIGNED to take into account order of operations, teachers, and well educated people on this forum. Posted pictures from a legit textbook with author etc. would be a start. Until then, this is going nowhere.

I'll ask my professor about this when I get a chance and report back. I will also look through own textbooks and look for clarification on the issue as well. The fact is though, in any upper level math class you wont even see a problem posed like this. It will be much more explicitly state in some form of fraction, and I have never run into a distribution with division directly adjacent like this in a math class ever. The fact is that our ways of writing equations are not absolute and only a human construct. There may not even be a complete consensus among higher-ups in the math world. At this point It all comes down to interpretation, and I'm sick of arguing about it. And we all know arguing over the internet is like competing in the special olympics... even if you win, you are still retarded...

If I had to bet money on it, Id go with 9. But if I was in Vegas Id pick something better to bet on.
Ill report back once I talk to my professor.

Originally posted by GobbledokTChipeater
This also implies that if you are using a 'dumb' calculator (windows, google, various programming languages), then you will have to format the equation yourself by bracketing the juxtaposed values, else the calculator will give you a false result.
.

edit on 2/5/11 by GobbledokTChipeater because: (no reason given)

Thanks for the confirmation of what I said!

It would be such a weird synchronicity if a similar thread was bouncing on some other domain, and yet neither thread mentioned the other!

Oh fnord the love of God! Haha.

No but serious, OP's Casio does maths differently. You guys are snobbering all over the place. But I bet on that other domain, they'd be even dumber. Haha, math sucks but its fun. Like flagellation or tattoos.