6÷2(1+2)=?

reply to post by Honor93

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.

Honor93 I am curious to your response to the PHD math professor Grey580 posted. Also, I checked your oakroadsystems link again, and the reason I didnt respond to it or reference it at all is because it doesnt mention your "juxtaposition rule" in this form at all, unless I am just missing it, in which case please direct me more precisely. I understand the order of operations. Parentheses take precedence over exponents which take precedence over multiplication and division which take precedence over addition and subtraction. I understand that you have been taught that multiplication by juxtaposition takes precedence, not saying I dont believe you, I am just failing to see any evidene for your claim (aside from the purplemath link and the AMS link, although that was very ambiguous in itself). Any other source I have seen defines a*(b) = a(b) = a*b. Implied multiplication is the same as signed multiplication. I have never heard that multiplication by juxtaposition jumps to the same order of precedence as exponents. That seems ridiculous to me. It is not an exponent, nothing is being taken to a power, its just multiplication. And dont just say you learned it back when you were getting honors in math 40+ years ago. Not saying I doubt it at all, its just a very unsatisfactory ruling on the subject.

Perhaps this is part of the problem. You were educated before computers and calculators were in use, so perhaps conventions and notations have changed since then. Because computers and calculators are used to the extent that they are today, it would make sense for the math taught to be consistent with that. It wouldn't make sense to teach students one convention that will be at odds with convention they will use in electronic devices. It appears to me that both answers can be interpreted as valid, but I have seen very little proof of the "juxtapositon rule", and aside from your posts, nothing that would put it on the order of exponents.

Originally posted by Akragon
So its 9 then?

Yes

Originally posted by Akragon
BEDMAS is correct as i was taught?

BEDMAS is correct

Originally posted by Akragon
PEMDAS is garbage?

No, PEMDAS and BEDMAS are the same.

Originally posted by Akragon
Divide before you multiply in a simple problem?

No. Division and Multiplication are of the same order and neither take precedence over the other. When working a problem do which ever comes first but from left to right. Left to right is the key.

The rule is simply this:

PEMDAS or BEDMAS

Parenthesis / Brackets
Exponents
Multiplication and Division, from left to right
Addition and Subtraction, from left to right

Follow these widely accepted rules and you will get 9.

SH

The equation 6/2(1+2) can be solved in two ways.

6
- (1+2) = 9
2

or

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

Both answers are right, but not in every action. Specific rules apply to specific action to create the observable result. The observable result is always the right clue to how a equation plays out.

If you choose the actions that create 1. You are not wrong because that action created 1. And if that is what you observe physically you know that your equation is the right one.

If the equation was physical and you got a observable result 9. You would know that the equation that created 1 is the wrong action.Because you observe a physical 9.

A better way to say it is; The observed result decides how the problem is solved.

So if you observe 1.

the right equation is the one that gives you 1.

If you observe 9.

the equation that gives you 9 is the right one.

What we are arguing is that we observe different results after the equation is calculated. If we don't observe the same object/result after calculation of course we differ in how to solve the equation. Because the equation can give us two different observable results.

It would be much easier if the equation was written like this; 6/2(1+2) = 1

or

6/2(1+2) = 9

Then the solutions would be clear. Because we would observe the same result.

Got a reply from my cousin who's teaching up in NYU, if i'm not mistaken.

the statement is controversial b/c of how its written, its ambiguous, you could write it as 6/2(1+2), where the 6/2 is written vertically, then you distribute and get 9 or you can do the ( ) first and get 3 and mult by 6/2 and you get 18/2 which is 9. Even another way is to distribute the numerators and you get 18 on top, div by 2 is 9 again. There are at least 5 ways to reword this and still get 9.

The answer is both 1 & 9.

I'm done with this thread.

Originally posted by grey580
Got a reply from my cousin who's teaching up in NYU, if i'm not mistaken.

the statement is controversial b/c of how its written, its ambiguous, you could write it as 6/2(1+2), where the 6/2 is written vertically, then you distribute and get 9 or you can do the ( ) first and get 3 and mult by 6/2 and you get 18/2 which is 9. Even another way is to distribute the numerators and you get 18 on top, div by 2 is 9 again. There are at least 5 ways to reword this and still get 9.

The answer is both 1 & 9.

I'm done with this thread.

your cousin got 9 five different ways but no way as 1

the answer is 9 when applying the rules. 1 when you make $#!^ up.

It is my firm opinion that the answer is 1, however I can see the logic leading to 9.

The problem here is ambiguity. The equation can be taken in multiple ways due to the exclusion of necessary parentheses.

One interpretation of this problem would be:
(6/2)(1+2) where 6/2 is expressed as a fraction
=(3)(3)
=9

An alternate variation of the previous idea:
6(1+2)
2
=(6+12)
.... 2
= 18
... 2
=9

Another could be
__ 6__ where the entire equation is expressed as a fraction
2(1+2)
=_ 6_
.. 2(3)
= 6/6
= 1

Its all in how you look at the division with regard to the order of operations. All of the teachers I had in both elementary and high school had taught BEDMAS, in which Division/Multiplication were interchangable.

Following BEDMAS strictly as written, the problem is simple...

6/2(1+2)
=6/2(3)
=(3)(3)
=9

However, with the interchangability idea presented by all my past teachers, I would proceed as follows:

6/2(1+2)
=6/2(3)
=6/6 Because I tend to think of numbers appended to brackets as a single term
=1

It is a very interesting paradox; both arguments seem to be equally valid. Again, I believe that ambiguity is the issue here. I'm dissappointed that this discussion has, in some areas, degenerated into an immature argument founded on ignorance, which is what we are supposed to be striving to overcome.

Note: Please ignore periods in the above equations as they were added merely for formatting

The argument we have before us is obelus vs. solidus.

Notice, when obelus is typed-out, a red line appears underneath notifying the writer of an error. This is in fact false. I can only deduce that in today's word, we may classify the term as archaic.

The original meaning that many have came to infer when presented with the symbol is outlined here: mathworld.wolfram.com...

If you closely read the following link WITHOUT bias you will come to understand that when presented with the current formula 6÷2(1+2), this is meant to be read as:

__6__ =
2(1+2)

The reason behind it is simple.

Taking the ratio x/y of two numbers x and y , also written x÷y. (Backbone)

Here, x is called the dividend, y is called the divisor, and x/y is called a quotient. The symbol "/" is called a solidus (sometimes, the "diagonal"), and the symbol "÷" is called the obelus. (Extra Info)

If left unevaluated, x/y is called a fraction, with x known as the numerator and y known as the denominator. (Key)

One must, with the above rules, conclude that because this equation is OBVIOUSLY UNEVALUATED it is actually a fraction. Considering this principle, the x is 6, the y is 2(1+2), there can only be one valid and logical answer to this problem.

1

Originally posted by Itop1
Following PEMDAS, you always multiply before you divide

This might have already been said but I can't be assed to read any more, and I suck at maths but...

You always go from left to right so...

6÷2(1+2) which is 6÷2x3 which is 3x3 which is 9.

The mistake you are making is not seeing the 6÷2 and the (1+2) as separate operations, you do both problems THEN multiply them. 3x3=9

e.g.

15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.

www.purplemath.com...

Originally posted by Zarius
The argument we have before us is obelus vs. solidus.

Notice, when obelus is typed-out, a red line appears underneath notifying the writer of an error. This is in fact false. I can only deduce that in today's word, we may classify the term as archaic.

The original meaning that many have came to infer when presented with the symbol is outlined here: mathworld.wolfram.com...

If you closely read the following link WITHOUT bias you will come to understand that when presented with the current formula 6÷2(1+2), this is meant to be read as:

__6__ =
2(1+2)

The reason behind it is simple.

Taking the ratio x/y of two numbers x and y , also written x÷y. (Backbone)

Here, x is called the dividend, y is called the divisor, and x/y is called a quotient. The symbol "/" is called a solidus (sometimes, the "diagonal"), and the symbol "÷" is called the obelus. (Extra Info)

If left unevaluated, x/y is called a fraction, with x known as the numerator and y known as the denominator. (Key)

One must, with the above rules, conclude that because this equation is OBVIOUSLY UNEVALUATED it is actually a fraction. Considering this principle, the x is 6, the y is 2(1+2), there can only be one valid and logical answer to this problem.

1

This is an absurd argument. 6/2 is a fraction is it not? A fraction being multiplied by (1 + 2). You can look at it either way you proved nothing.

The fact that PEMDAS or BEDMAS gives the answer of 9 and no other rule gives 1 should be a major hint as to what the answer is.

9


You guys are really reaching to try and get that 1. Rebels at heart aren't you?

And people wonder why I hate math...

ATS YOU ARE EMBARRASSING ME!!!!!!!!!!!!!! SERIOUSLY WTF!!!
6÷2(1+2)=? Come on people, I learned this in like 3rd grade.
6/2(3)=
6/6=
1
How can anyone get 9 from this??? Parenthesis first.

Originally posted by DocDoyle
ATS YOU ARE EMBARRASSING ME!!!!!!!!!!!!!! SERIOUSLY WTF!!!
6÷2(1+2)=? Come on people, I learned this in like 3rd grade.
6/2(3)=
6/6=
1
How can anyone get 9 from this??? Parenthesis first.

You already did the brackets man...

6/2(3)= 6/2x3

6/2 = 3... x 3

9

sigh.

Valid answers to this equation are both 1 and 9.

The equation is ambiguous.

And you all need to recognize this.

Originally posted by grey580
sigh.

Valid answers to this equation are both 1 and 9.

The equation is ambiguous.

And you all need to recognize this.

NEGATIVE!!

You need to follow the rules PEMDAS/BEDMAS and get 9!! Get with the program. 1 is WRONG!

Originally posted by DocDoyle
ATS YOU ARE EMBARRASSING ME!!!!!!!!!!!!!! SERIOUSLY WTF!!!
6÷2(1+2)=? Come on people, I learned this in like 3rd grade.
6/2(3)=
6/6=
1
How can anyone get 9 from this??? Parenthesis first.

You should be embarrassed!! PEMDAS/BEDMAS

9

Originally posted by DocDoyle
ATS YOU ARE EMBARRASSING ME!!!!!!!!!!!!!! SERIOUSLY WTF!!!
6÷2(1+2)=? Come on people, I learned this in like 3rd grade.
6/2(3)=
6/6=
1
How can anyone get 9 from this??? Parenthesis first.

6÷2(1+2), two separate problems, work them out separately then multiply. 3x3=9.

Multiplying and dividing have the same priority.*

1. Do any math inside grouping symbols first
(parentheses, brackets & braces)

2. Evaluate numbers with exponents
(Whole number exponents will be explained as part of 6th grade lessons. They are not included in this lesson, except to know the correct order.)

3. Multiplication or Division
Multiplying and dividing have the same priority*. When you are reading from left to right, do whichever one you come to first. Skip adding and subtracting until after all multiplication and division has been done.

4. Addition or Subtraction
Adding and subtracting have the same priority. When you are reading from left to right, do whichever one you come to first.

www.helpingwithmath.com...

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Please judge if 6÷2(1+2) is really equal to 1 or 9. =)

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