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

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61

[quote]chillain wrote:

[quote]Gaius Octavius wrote:
I repeat, it depends on how you read the dash. There is no right or wrong in this matter, it’s just a matter of convention.[/quote]

you forgot to add that only HIGHLY INEXPERIENCED problem-solvers wouldn’t tend to see everything after the dash as the denominator of the entire expression

if you get 9 - that would be you

if you get 1 - your approach mirrors that of the experts

[/quote]

Or people that deal with computers more often, especially programming(which is essentially the entire reason a strict definition of operation is needed).

People that are experts in problem solving don’t deal with horribly formatted text expressions anyway.

62

It’s 9.

Parentheses first: 1+2=3

6/2(3)

Just multiplication and division left, so work left to right

6/2=3

3(3)=9

63

6/2(1+2) is not the same as (6/2)(1+2)

Answering the question as it is written in the title by the original poster would return a value of 1.

If you replace all of the values with variables it forces you to use the order of operations properly.

6 = a, 2 = b, and 1 = c

a/b(c+b)

Distribute the first ‘b’ to what is inside the brackets

a/(bc+b^2)

Which is the same as

    a

(bc + b^2)

Since this is in its most simplest form, replace the variables with their given values

        6

= --------
(2x1 + 2x2)

      6

= ------
( 2 + 4 )

= 6/6

= 1

64

[quote]number10 wrote:
6/2(1+2) is not the same as (6/2)(1+2)

Answering the question as it is written in the title by the original poster would return a value of 1.

If you replace all of the values with variables it forces you to use the order of operations properly.

6 = a, 2 = b, and 1 = c

a/b(c+b)

Distribute the first ‘b’ to what is inside the brackets

a/(bc+b^2)

Which is the same as

    a

(bc + b^2)

Since this is in its most simplest form, replace the variables with their given values

        6

= --------
(2x1 + 2x2)

      6

= ------
( 2 + 4 )

= 6/6

= 1[/quote]
LOL! Use letters or numbers and this is STILL wrong. Brackets come first, then numbers in the order they appear.

65

[quote]Gaius Octavius wrote:
A)My mistake. Sorry about that.
B)No, there can be as many meanings as we want it to have. If I define “/” to be the integral symbol then this sure as hell ain’t 9, it won’t even be a number. The two meanings that make a lick of sense however are that “/” is either a simple divisor or that it means that whatever follows is in a 2nd line.[/quote]

1 (division sign) 2

is the same as

1 over 2

herp derp

66

[quote]red04 wrote:

[quote]chillain wrote:

[quote]Gaius Octavius wrote:
I repeat, it depends on how you read the dash. There is no right or wrong in this matter, it’s just a matter of convention.[/quote]

you forgot to add that only HIGHLY INEXPERIENCED problem-solvers wouldn’t tend to see everything after the dash as the denominator of the entire expression

if you get 9 - that would be you

if you get 1 - your approach mirrors that of the experts

[/quote]

Or people that deal with computers more often, especially programming(which is essentially the entire reason a strict definition of operation is needed).

People that are experts in problem solving don’t deal with horribly formatted text expressions anyway.[/quote]
Yep. Type:

=6/2*(1+2)

into an Excel cell and you get 9.

67

[quote]OBoile wrote:

[quote]red04 wrote:

[quote]chillain wrote:

[quote]Gaius Octavius wrote:
I repeat, it depends on how you read the dash. There is no right or wrong in this matter, it’s just a matter of convention.[/quote]

you forgot to add that only HIGHLY INEXPERIENCED problem-solvers wouldn’t tend to see everything after the dash as the denominator of the entire expression

if you get 9 - that would be you

if you get 1 - your approach mirrors that of the experts

[/quote]

Or people that deal with computers more often, especially programming(which is essentially the entire reason a strict definition of operation is needed).

People that are experts in problem solving don’t deal with horribly formatted text expressions anyway.[/quote]
Yep. Type:

=6/2*(1+2)

into an Excel cell and you get 9.[/quote]

Yeah, but adding the asterisk changes it… It’s written out in a deliberately ambiguous way, do we interpret it as 6/[2(1+2)] = 1, or (6/2)(1+2) = 9?

It’s true though, that were we dealing strictly with variables as earlier posters have pointed out, and were it written with the operators as originally presented, say A/B(x+y), the B(x+y) would be treated as the entire denominator.

68

[quote]RBlue wrote:

[quote]OBoile wrote:

[quote]red04 wrote:

[quote]chillain wrote:

[quote]Gaius Octavius wrote:
I repeat, it depends on how you read the dash. There is no right or wrong in this matter, it’s just a matter of convention.[/quote]

you forgot to add that only HIGHLY INEXPERIENCED problem-solvers wouldn’t tend to see everything after the dash as the denominator of the entire expression

if you get 9 - that would be you

if you get 1 - your approach mirrors that of the experts

[/quote]

Or people that deal with computers more often, especially programming(which is essentially the entire reason a strict definition of operation is needed).

People that are experts in problem solving don’t deal with horribly formatted text expressions anyway.[/quote]
Yep. Type:

=6/2*(1+2)

into an Excel cell and you get 9.[/quote]

Yeah, but adding the asterisk changes it… It’s written out in a deliberately ambiguous way, do we interpret it as 6/[2(1+2)] = 1, or (6/2)(1+2) = 9?

It’s true though, that were we dealing strictly with variables as earlier posters have pointed out, and were it written with the operators as originally presented, say A/B(x+y), the B(x+y) would be treated as the entire denominator.[/quote]
No and No.
Both of your points are incorrect.

69

[quote]OBoile wrote:

[quote]RBlue wrote:

[quote]OBoile wrote:

[quote]red04 wrote:

[quote]chillain wrote:

[quote]Gaius Octavius wrote:
I repeat, it depends on how you read the dash. There is no right or wrong in this matter, it’s just a matter of convention.[/quote]

you forgot to add that only HIGHLY INEXPERIENCED problem-solvers wouldn’t tend to see everything after the dash as the denominator of the entire expression

if you get 9 - that would be you

if you get 1 - your approach mirrors that of the experts

[/quote]

Or people that deal with computers more often, especially programming(which is essentially the entire reason a strict definition of operation is needed).

People that are experts in problem solving don’t deal with horribly formatted text expressions anyway.[/quote]
Yep. Type:

=6/2*(1+2)

into an Excel cell and you get 9.[/quote]

Yeah, but adding the asterisk changes it… It’s written out in a deliberately ambiguous way, do we interpret it as 6/[2(1+2)] = 1, or (6/2)(1+2) = 9?

It’s true though, that were we dealing strictly with variables as earlier posters have pointed out, and were it written with the operators as originally presented, say A/B(x+y), the B(x+y) would be treated as the entire denominator.[/quote]
No and No.
Both of your points are incorrect.[/quote]

Explain why.

70

[quote]RBlue wrote:

[quote]OBoile wrote:

[quote]RBlue wrote:

[quote]OBoile wrote:

[quote]red04 wrote:

[quote]chillain wrote:

[quote]Gaius Octavius wrote:
I repeat, it depends on how you read the dash. There is no right or wrong in this matter, it’s just a matter of convention.[/quote]

you forgot to add that only HIGHLY INEXPERIENCED problem-solvers wouldn’t tend to see everything after the dash as the denominator of the entire expression

if you get 9 - that would be you

if you get 1 - your approach mirrors that of the experts

[/quote]

Or people that deal with computers more often, especially programming(which is essentially the entire reason a strict definition of operation is needed).

People that are experts in problem solving don’t deal with horribly formatted text expressions anyway.[/quote]
Yep. Type:

=6/2*(1+2)

into an Excel cell and you get 9.[/quote]

Yeah, but adding the asterisk changes it… It’s written out in a deliberately ambiguous way, do we interpret it as 6/[2(1+2)] = 1, or (6/2)(1+2) = 9?

It’s true though, that were we dealing strictly with variables as earlier posters have pointed out, and were it written with the operators as originally presented, say A/B(x+y), the B(x+y) would be treated as the entire denominator.[/quote]
No and No.
Both of your points are incorrect.[/quote]

Explain why.[/quote]
Adding the "" is simply so Excel can handle it. It doesn’t change any rule in the equation.
ab+c is exactly the same as ab+c.
Similarly, choosing to write something with letters instead of numbers changes nothing. All that has been changed is the patterns used to symbolize each value, no rules change.
People on this thread are trying to overcomplicate things with rules that don’t exist.

It is somewhat ambiguous, but if the intent was to have the denominator be 2(1+2) then standard practice when writing the formula in a computer environment would be to have 6/[2(1+2)] or 6/(2(1+2)).

71

[quote]RBlue wrote:

[quote]OBoile wrote:

[quote]red04 wrote:

[quote]chillain wrote:

[quote]Gaius Octavius wrote:
I repeat, it depends on how you read the dash. There is no right or wrong in this matter, it’s just a matter of convention.[/quote]

you forgot to add that only HIGHLY INEXPERIENCED problem-solvers wouldn’t tend to see everything after the dash as the denominator of the entire expression

if you get 9 - that would be you

if you get 1 - your approach mirrors that of the experts

[/quote]

Or people that deal with computers more often, especially programming(which is essentially the entire reason a strict definition of operation is needed).

People that are experts in problem solving don’t deal with horribly formatted text expressions anyway.[/quote]
Yep. Type:

=6/2*(1+2)

into an Excel cell and you get 9.[/quote]

Yeah, but adding the asterisk changes it… It’s written out in a deliberately ambiguous way, do we interpret it as 6/[2(1+2)] = 1, or (6/2)(1+2) = 9?

It’s true though, that were we dealing strictly with variables as earlier posters have pointed out, and were it written with the operators as originally presented, say A/B(x+y), the B(x+y) would be treated as the entire denominator.[/quote]

If it were meant to be interpreted with extra parentheses, they would have been included. No?

Claiming this is ambiguous is to completely ignore logic.

72

According to The Order of Operations: Examples | Purplemath it would seem that the standard convention for human interpretation is that multiplication by putting things next to each other has a higher order of precedence than multiplication by “times symbol” or division: “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 “Ã?” sign) indicates that the juxtaposed values must be multiplied together before processing other operations.”

If the claim in the quote above is correct, and if we equate a “general consensus among math people” with “standard convention”, then:

 6/2(1+2)

= 6/2(3)

= 6
‘/’ which is not as strong as “next to”
2
“next to”, which is stronger than ‘/’ or ‘*’
3

= 6/6

= 1

DISCLAIMER: I do not know whether the claim in the quote above is correct.

NOTE: Whether or not there is any computer software that recognizes “next to” multiplicaton as having higher precedence than division or “operand multiplication” is not relevant to the question as originally stated.

73

Replace (1 2) with Y

Therefore, 6/2(Y) or 6/2Y

Anytime you have a number next to a bracket/parenthesis, it gets associated with it.

If it was meant to be interpreted as (6*2)/(1 2), it would have been written that way. No?

74

[quote]NealRaymond2 wrote:
According to The Order of Operations: Examples | Purplemath it would seem that the standard convention for human interpretation is that multiplication by putting things next to each other has a higher order of precedence than multiplication by “times symbol” or division: “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 “Ã??” sign) indicates that the juxtaposed values must be multiplied together before processing other operations.”

If the claim in the quote above is correct, and if we equate a “general consensus among math people” with “standard convention”, then:

 6/2(1+2)

= 6/2(3)

= 6
‘/’ which is not as strong as “next to”
2
“next to”, which is stronger than ‘/’ or ‘*’
3

= 6/6

= 1

DISCLAIMER: I do not know whether the claim in the quote above is correct.

NOTE: Whether or not there is any computer software that recognizes “next to” multiplicaton as having higher precedence than division or “operand multiplication” is not relevant to the question as originally stated.[/quote]
I am a “math person”. Whomever stated that is incorrect. Its as simple as that.

75

[quote]number10 wrote:
Replace (1 2) with Y

Therefore, 6/2(Y) or 6/2Y

Anytime you have a number next to a bracket/parenthesis, it gets associated with it.

If it was meant to be interpreted as (6*2)/(1 2), it would have been written that way. No?

[/quote]
Once again, regardless of whether you use a number, letter or smiley face to represent a value, the rules of mathematics don’t change.
If Y = 3
6/2(Y) is the same 6/2(3) which is the same as 6/23 which is the same as 6/2Y which is the same as 6/2Y. In each case, the order of operations still applies. 6/2Y = 3/1Y = 3Y = 9

76

I’m an engineer which is kind of like a “math person”. How would you approach the problem if it were written as 6/2(Y)?

77

Sorry, I posted that without seeing your reply.

I don’t agree with your logic … “6/2Y = 3/1Y = 3Y = 9”

I’m pretty sure there aren’t many other math people that would agree with that.

78

it equals 9!!! Holy shit why is this even a discussion. So many people have explained it

79

Yup, its ambiguous, there is no right answer

If you put 6/2(1+2) into a calculator, half the time it will give you 9, and half the time it will give you 1.

wait…

80

[quote]NealRaymond2 wrote:
According to The Order of Operations: Examples | Purplemath it would seem that the standard convention for human interpretation is that multiplication by putting things next to each other has a higher order of precedence than multiplication by “times symbol” or division: “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 “Ã???” sign) indicates that the juxtaposed values must be multiplied together before processing other operations.”

If the claim in the quote above is correct, and if we equate a “general consensus among math people” with “standard convention”, then:

 6/2(1+2)

= 6/2(3)

= 6
‘/’ which is not as strong as “next to”
2
“next to”, which is stronger than ‘/’ or ‘*’
3

= 6/6

= 1

DISCLAIMER: I do not know whether the claim in the quote above is correct.

NOTE: Whether or not there is any computer software that recognizes “next to” multiplicaton as having higher precedence than division or “operand multiplication” is not relevant to the question as originally stated.[/quote]

[quote]OBoile wrote:
I am a “math person”. Whomever stated that is incorrect. Its as simple as that.[/quote]

Myself, I am currently not inclined to take any anonymous stranger’s word for it on the standard convention for juxtaposition (“next to”) multiplication precedence. But I absolutely agree that if the claim from purplemath.com is incorrect, then the correct answer to the problem posed in this thread is indeed “9”, and not “1”.