seriously tho wrote:
It is technically ambiguous by some rule or some other rule. If you put multiplication before division, its 1. Intentionally written to obfuscate and be ambiguous so it doesnt make someone dumb or wrong to think it's something else.
Yep, it's literally written ambiguously to get people to argue about it. Math geniuses have weighed in on this in the past and said as much.
This the perfect problem to keep you spectrum cases busy and arguing and name calling.
xczvzxcv wrote:
seriously tho wrote:
This my last post on this thread.
6 ÷ 2(1+2) = 1 or 9
You can simplify to 6 ÷ 2 x 3 and get 9.
You can also simplify 2(1+2) to 2(3) to 6.
"÷" is the only operation outside of parentheses in this equation.
PEMDAS or BODMAS was what they taught you as a strategy to solve equations in school because it worked for those equations at that time. You can use it still. It is not a mathematical law.
When pressed as to why this is ambiguous and why some think that the answer is 1, I would still say the ambiguity is actually right there in the formula, but not because multiplication and division are both the third priority (after parentheses and exponents), since they are co-equivalent, and not because we don't understand that we work from left to right for co-equivalent functions. No, if we have multiplication and division, we work left to right, same for addition or subtraction. Rather, the ambiguity consists in the meaning of doing the parenthetical operation first. The fact that the 2 is next to the parentheses implies that it is so connected to the parentheses that multiplying the parenthetical result by the 2 must be done after adding the numbers in the parentheses.
When you write 2(1+2), the connection seems there, whereas it seems weaker with what should be equivalent, 2*(1+2), yet the notion of dealing first with everything concerning parentheses suggests you should clean that up first, i.e. get 2(3) or 6, and then do the division to get 1. The more I think of it, the less I can remember handling an operation outside parentheses prior to dealing with whatever is directly involved with the parentheses.
You are correct. The goal of Order of Operations is to essentially eliminate each symbol before moving onto the next symbol in the following order: Parentheses (or Bracket), Exponent, Multiplication/Division, Addition/Subtraction. It is incorrect to evaluate 2(1+2) and leave it as 2(3). The parentheses must be eliminated. This leaves 6 / 2(3) = 6 / 6 = 1.
If the problem was expressed as "6 / 2x(1+2)" then the answer would be 6 / 2 x 3 = 3 x 3 = 9.
CountChocula wrote:
xczvzxcv wrote:
When pressed as to why this is ambiguous and why some think that the answer is 1, I would still say the ambiguity is actually right there in the formula, but not because multiplication and division are both the third priority (after parentheses and exponents), since they are co-equivalent, and not because we don't understand that we work from left to right for co-equivalent functions. No, if we have multiplication and division, we work left to right, same for addition or subtraction. Rather, the ambiguity consists in the meaning of doing the parenthetical operation first. The fact that the 2 is next to the parentheses implies that it is so connected to the parentheses that multiplying the parenthetical result by the 2 must be done after adding the numbers in the parentheses.
When you write 2(1+2), the connection seems there, whereas it seems weaker with what should be equivalent, 2*(1+2), yet the notion of dealing first with everything concerning parentheses suggests you should clean that up first, i.e. get 2(3) or 6, and then do the division to get 1. The more I think of it, the less I can remember handling an operation outside parentheses prior to dealing with whatever is directly involved with the parentheses.
You are correct. The goal of Order of Operations is to essentially eliminate each symbol before moving onto the next symbol in the following order: Parentheses (or Bracket), Exponent, Multiplication/Division, Addition/Subtraction. It is incorrect to evaluate 2(1+2) and leave it as 2(3). The parentheses must be eliminated. This leaves 6 / 2(3) = 6 / 6 = 1.
If the problem was expressed as "6 / 2x(1+2)" then the answer would be 6 / 2 x 3 = 3 x 3 = 9.
you're saying one thing and doing the other here though. If you eliminate the parentheses after solving inside you get 6÷2*3=9 . Having a number against the bracket vs. a multiplication sign means the exact same thing. The only way the answer is 1 is if there is a way to prove that the (1+2) is in the denominator by having something like 6÷(2(1+2)) which this equation does not have. You can't arbitrarily add a rule that you must do what's Next to parenthesis after doing what's inside....it's just the multiplying step
your logic is that 6÷2(1+2)=6÷(2(1+2))=1
but 6÷2(1+2) = 6÷2*(1+2) =9
6
___ * (1+2) = 9
2
or
6
_________ = 1
2 (1+2)
Either one of those is how it would be written in a math class.
None of this ÷ or / stuff.
Now / is used in Excel. That gives 9, treating division equal to multiplication going left to right.
People need to understand PEMDAS.
P= parantheses
(1+2)=3.
Now, the equation is 6/2(3).
E=exponents
No exponents are involved here.
MD =multiply and divide - whichever comes first.
6/2(3)= 3(3).
3(3)=9.
AS = add and subtract - whichever comes first. This does not apply here because we arrived at the answer already.
So the answer is 9.
ardour wrote:
People need to understand PEMDAS.
P= parantheses
(1+2)=3.
Now, the equation is 6/2(3).
E=exponents
No exponents are involved here.
MD =multiply and divide - whichever comes first.
6/2(3)= 3(3).
3(3)=9.
AS = add and subtract - whichever comes first. This does not apply here because we arrived at the answer already.
So the answer is 9.
exactly!
Tron wrote:
CountChocula wrote:
You are correct. The goal of Order of Operations is to essentially eliminate each symbol before moving onto the next symbol in the following order: Parentheses (or Bracket), Exponent, Multiplication/Division, Addition/Subtraction. It is incorrect to evaluate 2(1+2) and leave it as 2(3). The parentheses must be eliminated. This leaves 6 / 2(3) = 6 / 6 = 1.
If the problem was expressed as "6 / 2x(1+2)" then the answer would be 6 / 2 x 3 = 3 x 3 = 9.
you're saying one thing and doing the other here though. If you eliminate the parentheses after solving inside you get 6÷2*3=9 . Having a number against the bracket vs. a multiplication sign means the exact same thing. The only way the answer is 1 is if there is a way to prove that the (1+2) is in the denominator by having something like 6÷(2(1+2)) which this equation does not have. You can't arbitrarily add a rule that you must do what's Next to parenthesis after doing what's inside....it's just the multiplying step
your logic is that 6÷2(1+2)=6÷(2(1+2))=1
but 6÷2(1+2) = 6÷2*(1+2) =9
Crazy how people are inventing rules to solve this problem. First a left to right rule, now a rule to eliminate symbols.
Thankfully many of you have the correct answer and understand why.
I am 100% certain that the airplane will not take off and I will fight anyone who disagrees.
Post Hole Digger wrote:
I don't know and I don't care. At a glance I'd say 1, but like others said, it's intentionally ambiguous (which is the whole point of why you see these posted on Facebook and such) unless you rigorously apply some rule.
I'm a engineering professor and do simple arithmetic like this every day, but I haven't used a division symbol in 40 years and have no idea how to do one on the keyboard. The division symbol is shorthand for a fraction, it's a dot over another dot where the things before or after fill in the dots*.
Just use the fraction and use enough parentheses to make it clear if you're typing it in one line. Students still mess it up if I write it in one line even if I have the parentheses correct, so it's much better to use the equation editor and do it right.
*perhaps apocryphal, but it makes sense
I'll add that to my knowledge I've never heard of PEMDAS, although I probably did learn it in grade school. It's sorta pointless. If someone has written something in such a way that it can't be deciphered without some arcane rules, it's likely that they made a mistake anyway. Just write it in a way that communicates it clearly and you wouldn't have an issue.
In this thread I also learned that the division symbol has a name. It's been educational.
Tron wrote:
CountChocula wrote:
You are correct. The goal of Order of Operations is to essentially eliminate each symbol before moving onto the next symbol in the following order: Parentheses (or Bracket), Exponent, Multiplication/Division, Addition/Subtraction. It is incorrect to evaluate 2(1+2) and leave it as 2(3). The parentheses must be eliminated. This leaves 6 / 2(3) = 6 / 6 = 1.
If the problem was expressed as "6 / 2x(1+2)" then the answer would be 6 / 2 x 3 = 3 x 3 = 9.
you're saying one thing and doing the other here though. If you eliminate the parentheses after solving inside you get 6÷2*3=9 . Having a number against the bracket vs. a multiplication sign means the exact same thing. The only way the answer is 1 is if there is a way to prove that the (1+2) is in the denominator by having something like 6÷(2(1+2)) which this equation does not have. You can't arbitrarily add a rule that you must do what's Next to parenthesis after doing what's inside....it's just the multiplying step
your logic is that 6÷2(1+2)=6÷(2(1+2))=1
but 6÷2(1+2) = 6÷2*(1+2) =9
I looked it up, and the answer is that (shocker) it depends on which convention one uses for multiplication by juxtaposition. Thanks for prompting me to learn something new today!
https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplicationCountChocula wrote:
your logic is that 6÷2(1+2)=6÷(2(1+2))=1
but 6÷2(1+2) = 6÷2*(1+2) =9
[/quote]
Computer programming works with the latter and not with the former.
It is maths laziness to leave out the operation in "2(". You would never do that "2 – (" or "2 + (" or "2 ÷ (". Only multiplication has this magic "shortcut". Why it has stay around is odd. Who "invented" the shortcut in the first place? Answer: a dumdum (a troll from hundreds of years ago).
the answer is 1.
2(1+2) is one number. You can't separate the 2 from the parenthesis.
In Excel if you type "=6/2(1+2)" then Excel indicates it's a typo and corrects it to "=6/2*(1+2)". The result is 9.
In Google Sheets if you type "=6/2(1+2)" then the result is #ERROR.
In Google Sheets if you type "=6/2*(1+2)" then the result is 9.
CountChocula wrote:
Tron wrote:
you're saying one thing and doing the other here though. If you eliminate the parentheses after solving inside you get 6÷2*3=9 . Having a number against the bracket vs. a multiplication sign means the exact same thing. The only way the answer is 1 is if there is a way to prove that the (1+2) is in the denominator by having something like 6÷(2(1+2)) which this equation does not have. You can't arbitrarily add a rule that you must do what's Next to parenthesis after doing what's inside....it's just the multiplying step
your logic is that 6÷2(1+2)=6÷(2(1+2))=1
but 6÷2(1+2) = 6÷2*(1+2) =9
I looked it up, and the answer is that (shocker) it depends on which convention one uses for multiplication by juxtaposition. Thanks for prompting me to learn something new today!
https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication
The only people who are wrong are those who assert others are wrong.
It’s like British and Americans arguing over how to spell colo(u)r.
Or whether to use decimal points or commas.
If you can’t write an equation your audience understands unambiguously, it’s your problem not theirs.
Obviously, FOIL is the proper means of arriving at the correct answer. You just need to pay attention to the signs.
This can be rewritten as:
6÷1+6x2÷2x1+2x2
Then you use PEMDAS
6+12÷2x1+2x2
6+6x1+4
6+6+4
The answer is 16
In Excel:
"=6/2*(1+2)" result is 9
"=6/(2*(1+2))" result is 1
Parentheses make a difference.
I think of 2z and 2(z) as 2 x z. However, when I was in algebra class, y/2z would be interpreted as y ÷ (2 x z)
and not y ÷ 2 x z.
So is 2(3) like (2 x 3) or 2 x 3 ?
I think that's where the confusion is.
math is easy wrote:
the answer is 1.
2(1+2) is one number. You can't separate the 2 from the parenthesis.
This is the correct answer.
It's not ambiguous. When you write 2(1+2), that is different than 2 * (1+2). It is intentionally written as 2(1+2) to show that it is one number, not strictly an operational shorthand.
Lenny Leonard wrote:
math is easy wrote:
the answer is 1.
2(1+2) is one number. You can't separate the 2 from the parenthesis.
This is the correct answer.
It's not ambiguous. When you write 2(1+2), that is different than 2 * (1+2). It is intentionally written as 2(1+2) to show that it is one number, not strictly an operational shorthand.
The fact we have 4 pages here shows it is not as unambiguous as you think. Write clearly for your audience. It's not that hard.
I do, however, disagree that implied multiplication takes precedence over other operations. It's not functional evaluation.