6÷2(1+2)=?

Originally posted by Akragon

Using Bedmas the answer is 9...

Using PEDMAS the answer is 1...

I really don't know where you got this from. PEDMAS and BEDMAS are exactly the same. The only difference is some people call them brackets, some people call them parentheses.

Using PEDMAS (or BEDMAS) strictly will give you the incorrect result of 9.

Apparently, most people are unaware of the juxtaposition rule .

Perhaps it should be changed to PEJDMAS?

Originally posted by GobbledokTChipeater

Originally posted by Akragon

Using Bedmas the answer is 9...

Using PEDMAS the answer is 1...

I really don't know where you got this from. PEDMAS and BEDMAS are exactly the same. The only difference is some people call them brackets, some people call them parentheses.

Using PEDMAS (or BEDMAS) strictly will give you the incorrect result of 9.

Apparently, most people are unaware of the juxtaposition rule .

Perhaps it should be changed to PEJDMAS?

I'm thinking you're mistaken.

Formulas. You can help us to reduce production and printing costs by avoiding excessive or unnecessary quotation of complicated formulas. We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. For example, your TeX-coded display
$$[1\over[2\pi i]]\int_\Gamma [f(t)\over (t-z)]dt$$
is likely to be converted to
$(1/2\pi i)\int_\Gamma f(t)(t-z)^[-1]dt$
in our production process.

Your juxtaposition rule is simply something that is a preference for the mathematical review database.
I don't think that this has to do with anything other than math problem for that website.

Everyone needs to look at the quote I posted. This rule has nothing to do with any real math.

reply to post by grey580

Your juxtaposition rule is simply something that is a preference for the mathematical review database.
I don't think that this has to do with anything other than math problem for that website.

Everyone needs to look at the quote I posted. This rule has nothing to do with any real math.

Ah so this is the American mathematical society link Honor93 referred me to. I opened the page and seeing it was a guide for reviewers and not a real discussion on math, I didn't even look at it. I am inclined to agree with you. That is not viable proof for a juxtaposition rule at all. That just has to do with submissions to their website. The only link i have seen explicitly supporting it is the purplemath one:

www.purplemath.com...

This is far from an authoritative source on the matter however. There are other online sources stating the exact opposite. For example the youtube video posted earlier:

www.youtube.com...

A solid textbook example either way would be nice.

Here is a good link:

mathforum.org...

Doesn't look like an authoritative ruling on this issue even exists. If you google "multiplication by juxtaposition" you will find this exact discussion in multiple threads across the internet, page after page of exactly what is going on in this thread, and no definite conclusion anywhere. Seems to be an issue that doesn't have a completely correct answer. It depends on who you ask. If you ask me, I'll tell you PEMDAS and 9!!

Originally posted by ASeeker343

Doesn't look like an authoritative ruling on this issue even exists.

TBH, I do agree with this.

I think the problem arises because people who have done lots of algebra treat it as

6÷(2(1+2)) = 1

the same way Wolfram|Alpha treats algebra.

Whereas people who are familiar with only the BODMAS method, treat it as

(6÷2)(1+2) = 9

the same way Wolfram|Alpha treats sums.

So to people who have done lots of algebra, factoring the equation first (A(B+C)=(AB+AC)) is the most natural way.

I do use the same rule that the American Mathematical Society uses for their reviews. Note that they do call it a rule though. Not a preference, not a guideline, but a rule. That means if I solved the equation using their convention, I would indeed get the answer of 1.


.

Originally posted by GobbledokTChipeater

Originally posted by Akragon

Using Bedmas the answer is 9...

Using PEDMAS the answer is 1...

I really don't know where you got this from. PEDMAS and BEDMAS are exactly the same. The only difference is some people call them brackets, some people call them parentheses.

Using PEDMAS (or BEDMAS) strictly will give you the incorrect result of 9.

Apparently, most people are unaware of the juxtaposition rule .

Perhaps it should be changed to PEJDMAS?

Ya my bad i meant PEMDAS...

this...

Please -- Parenthesis
Excuse -- Exponents
My ------- Multiplication
Dear ----- Division
Aunt ----- Addition
Sally ----- Subtraction

Never heard of it in my life. Of course i have no idea what Juxtaposition is either....*sighs*

And im just to lazy to look it up, and considering its math.....i could honestly care less...

So Bedmas is wrong? Heh, shows what i learned in math class....

Oh right, i was asleep

In my opinion each new multiplication or division clearly separate parts of the formula. There is no need to assume that everything after the "/" is the denominator. To do that, what is in the denominator is would need to be in parenthesis like this:

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

otherwise it may lead to confusion

6 / 2 (1 + 2) (1 + 2) = ? (what is the denominator here?)

The rules of PEDMAS or BEMDAS will give the same answer always, which is the point.

Brackets/ Parenthesis
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)

Notice the "left to right"?

NOT multiplication before division or division before multiplication but rather which ever one is first LEFT to RIGHT!

Also multiplication is not a higher order operation over division - they are equal. There is no "special" multiplication that is a higher order and follows "juxtaposition" that no one has ever heard of before. If you follow the convention and rules that the entire educated world teaches and uses you will all get the same answer. Which is the entire point!!!

so ....

6 / 2 (1 + 2) / (1 + 2) / 3 (1 + 2) / (3 (1 + 2)) = ?

6 / 2 (3) / (3) / 3 (3) / (3(3)) = ? Parenthesis

6 / 2 (3) / 3 / 3 (3) / (9) = ? Parenthesis

3 (3) / 3 / 3 (3) / 9 = ? Multiplication and Division (left to right)

9 / 3 / 3 (3) / 9 = ? Multiplication and Division (left to right)

3 / 3 (3) / 9 = ? Multiplication and Division (left to right)

1 (3) / 9 = ? Multiplication and Division (left to right)

3 / 9 = ? Multiplication and Division (left to right)

1 / 3 or one third

Elementary my dear ... literally!

If you get a different answer you didn't follow the rules.

Oh and ....

3 x 3 = 3 * 3 = 3 (3) = 9

different notation, same meaning, same answer.

The point here is really that this problem has already been discovered and solved a long time ago. It was decided that rules would be applied so all would get the same answer. BEMDAS or PEDMAS is that rule and is taught and used everywhere. If you follow some other "rule" not accepted and taught and used by the vast majority of people then you will not be getting the same answer as everyone else. You may think you are right but what good will that do? Math is a language that has notation and rules accepted by those who use it. Accept that the rules give the answer of 9! or use your own rules that no one else does and be wrong.

ok guys, this is getting boring so for those who may still be cornfused, i'll leave you with this ...

a. i find it interesting that not one of you actually reference the only link I've provided thus far.

b. I referred the American Math Society but provided NO link - someone else did. (i'm more interested in international standards anyway)

c. I 'quoted' the "purple" link provided by ANOTHER poster who uses the link to infer "9" as the correct answer.

For your information, i've been doing math correctly longer than most of you have been alive.
The calculators many are using are not designed to perform such equations without additional manual input to clarify the order or operation. (megamind) arithmetic notations went through a change in the 70s for those who are not aware. (coincidentally, when calculators first arrived)

Yes, there is much disagreement, however, from the same lesson catalog at the "purple" link ... check this.

when you go to e-mail your instructor with a question, or post your question to a math tutoring forum, you can end up with a mess or with something that totally doesn't mean what you meant to say. To deal with this issue, the math community is developing norms for text-only formatting. What follows is not "the" one right way to format math, but is a distillation of what I've seen a lot of math tutors use.

source: www.purplemath.com...

and another quote from same "purple math" link ...

Distributive Property

The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, that 2(3 + 4) = 2×3 + 2×4. Any time they refer in a problem to using the Distributive Property, they want you to take something through the parentheses (or factor something out); any time a computation depends on multiplying through a parentheses (or factoring something out), they want you to say that the computation used the Distributive Property.

Why is the following true? 2(x + y) = 2x + 2y

Since they distributed through the parentheses, this is true by the Distributive Property.

source: www.purplemath.com...

and back to the original and only link i started with ... oakroadsystems.com...

Multiply/Divide over Add/Subtract

You can distribute a multiply or divide over an add or subtract, because multiply and divide are one level above add and subtract:

Right 7(x + y) = 7x + 7y
Right (x + y) / 3 = x/3 + y/3
Right 2x (x − 3) = 2x² − 6x
Right (2x − 8) / 2 = 2x/2 − 8/2 = x − 4

Students sometimes distribute a multiplier over both parts of a fraction, like this:

3 × (2/5) = 6 / 15 WRONG!

You can’t do that because multiply is not one level above divide; they’re at the same level. You can distribute only when moving down one level.

in this case, history should repeat itself ... calculators and digital notating are new, not the other way around.
good luck to all and use your brain first, the calculator second.

ps: i never said to ignore PEDMAS or BEDMAS because they are the same and they are relevant ... what i am saying is the juxtaposition of the "2" next to the brackets/parenthesis has the SAME order sequence as exponents, period.

reply to post by GobbledokTChipeater


As I have posted above. Their rule is simply to shorten long equations.
rather than have a ÷ b * (c + d) they want to have a ÷ b(c+d).

This is particular to them and their method of saving space not to math.

Why anyone would use this for anything is beyond me.

I'm going with the answer of 9.

Originally posted by grey580
reply to post by GobbledokTChipeater

 

As I have posted above. Their rule is simply to shorten long equations.
rather than have a ÷ b * (c + d) they want to have a ÷ b(c+d).

This is particular to them and their method of saving space not to math.

Why anyone would use this for anything is beyond me.

I'm going with the answer of 9.

my apology cause i know you didn't address me specifically, but if you believe what you wrote and both equations are 'equal' ... please, by distributive laws, perform distribution to both ... you will see, they are not the same. not by any rule out there.

reply to post by Honor93


Here is another link on distributive property.

Distributive Property

Again. The equation is ambigous.
Both answers are valid.

oops double post

reply to post by grey580

i asked you to distribute your equations not reference a useless source ... about.com???
the only ambiguity about this equation is the 'digital' interpretation of it.
for those who have performed algebra equations longer than 40yrs, it is quite clear, with only one correct answer.

Originally posted by grey580
reply to post by Honor93

 

Here is another link on distributive property.

Distributive Property

Again. The equation is ambigous.
Both answers are valid.

They are not both valid. You use distributive law. Period. There is no "but if you look at it this way..." or "it depends on if it is math or if it is algebra..."

Neither of those statements make any sense. Algebra is math. There is only one way to look at the expression and that is with the laws of math which include distributive law. There is never a time that you don't use it.

You know what. The more I read and listen to. This freaking equation blows.

Answer From a PHD in Math

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.
The problem as it is written is 6÷2(1+2) , the ÷ cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ÷ is interchangeable with *. therefore the problem must be solved as 6÷2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6÷2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it.
6÷2(3)
(6) ÷(2)(3)
6÷2*3,
or even converting the division to multiplication by a reciprocal (a legal math move)
(6)(1 (over) 2)(3)
are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or
3*3= 9

Just because something is implied rather than written does not give it any special rank in the order of operations.

The problem in it's simplest form, with nothing implied would look like this:
(1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1))
From here, nothing is implied, This again, works out to 9.

If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar.

HOWEVER, because the ÷ symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem.

Once and for all, the answer is 9.

I'm gonna ask my cousin who's a physicist also.

This is getting crazy. I even saw a youtube video where a string theorist when asked the question said that both answers are valid.

sigh.

Originally posted by Cuervo

Originally posted by grey580
reply to post by Honor93

 

Here is another link on distributive property.

Distributive Property

Again. The equation is ambigous.
Both answers are valid.

They are not both valid. You use distributive law. Period. There is no "but if you look at it this way..." or "it depends on if it is math or if it is algebra..."

Neither of those statements make any sense. Algebra is math. There is only one way to look at the expression and that is with the laws of math which include distributive law. There is never a time that you don't use it.

The distributive law states

A (B + C) = AB + AC

In that equation you may substitute any number for A, B and C and the formula will hold true. This is simply what the formula shows. There are no caveats for what A, B and C are.

if A = 3, B = 1 and C = 2 you will have

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

These numbers A, B and C can be any number including fractions.

So ... A = 6/2 a fraction, B = 1 and C = 2 you will have

A (B + C) = A * B + A * C
(6/2)(1 + 2) = (6/2) * 1 + (6/2) * 2 = 9

Note that this is the same answer you get using PEDMAS or BEMDAS. Also note the consistency of Algebraic logic here with the order of operations rule.

I have seen many argue that you cannot make A a fraction. What prevents this from being so?
In Algebra A could be: A = (X + Y) or 0.3333 or a fraction of 1/3, in short anything.

The argument of the distributive law supporting the answer of 1 comes about because of the assumption that the denominator of the formula 6 / 2 (1 + 2) is 2 (1 + 2). Surely then the distributive law gives (2 + 4) = 6. However, the assumption being made is the very assumption that is being debated. I clearly demonstrated above that it may be viewed or assumed that 6 / 2 is a fraction being multiplied by (1 + 2) and thereby give the answer of 9 following the distributive law. Therefore the distributive law does not provide proof of the correct method as some have stated.

I post this to show the distributive law does not confirm one way nor another how to interpret the order of operations. I think the best solution would be to adopt PEDMAS or BEMDAS as it is the most accepted order of operations and being careful to observe the left to right rule. Therefore I conclude the answer should be 9.

SH

Originally posted by SherlockH

I have seen many argue that you cannot make A a fraction. What prevents this from being so?

Nobody has said you can't make A a fraction. I have said however that I think it is not written with A as a fraction, particularly with the '÷' symbol used instead of the '/' symbol.

Originally posted by GobbledokTChipeater
I have said however that I think it is not written with A as a fraction ....

Yes, of course. This is the essence of the debate. I merely meant to show that the distributive law does not provide confirmation one way nor another.

The debate is really which of the following is the correct interpretation of
6 ÷ 2 (1 + 2)

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

or

6
-- (1 + 2)
2

In this I defer to the PEDMAS or BEMDAS rule.

For all purposes I see no difference between "/" or "÷", a fraction is a division of one number by another.

Wiki Fractions ...

Other uses for fractions are to represent ratios, and to represent division. Thus the fraction 3/4 is also used to represent the ratio 3:4 (three to four) and the division 3 ÷ 4 (three divided by four).

I'm sure you know this but I thought I would find a reference for the sake of clarity.

SH

reply to post by Cuervo

They are not both valid. You use distributive law. Period. There is no "but if you look at it this way..." or "it depends on if it is math or if it is algebra..."

Neither of those statements make any sense. Algebra is math. There is only one way to look at the expression and that is with the laws of math which include distributive law. There is never a time that you don't use it.

Distribution is not a law, it is a property of multiplication. It is not a required operation by any means. A(B+C) = AB + AC. When working with real numbers, distribution is not necessary at all. If the argument inside the parentheses is simplified first there is no distribution to be done. For example the expression 3(4+5) can be with or without distribution. 3(9) = 27, or if you distribute, 3*4 + 3*5 = 12+15=27. Distribution is not a law or a requirement to solve the problem. It is simply a property of multiplication that allows simplifications to be made, and can be especially convenient with algebra using variables.

In this case, to properly distribute using the correct order of operations you would distribute 6/2=3 into the argument in parentheses. 3(1+2) = 9. The distributive property can still be used, but it is not necessary. Your argument that the distributive "law" is a requirement to solve the problem correctly is nonsense. People are getting 1 or 9, but either way, distribution is not the ONLY way to get either answer.

Edit: I will direct you to sherlock's post above as well. It lays out the distributive property very nicely. A faction can in fact be distributed across an argument in parentheses, as is the case here if you follow the order of operations.

So its 9 then?

BEDMAS is correct as i was taught?

PEMDAS is garbage?

Divide before you multiply in a simple problem?

Gesus Cryst people