Simple Math Problem

[AdamJoshua]

Post your answer to this simple math problem.

https://i.imgur.com/HLv5efg.jpg

[markem]

16

[Porch Dweller]

PEMDAS tells me the answer is one. 2+2=4, 4*2=8, 8/8=1



(For non-mathies, PEMDAS is the order of operations for math functions: First is whatever's in Parantheses, then Exponents, Multiplacation, Division, Addition, then lastly Subtraction.)

[Wharf Rat]

PEMDAS tells me the answer is one. 2+2=4, 4*2=8, 8/8=1



(For non-mathies, PEMDAS is the order of operations for math functions: First is whatever's in Parantheses, then Exponents, Multiplacation, Division, Addition, then lastly Subtraction.)

Once you evaluate the parentheses, you go left to right. 16

[AdamJoshua]

PEMDAS tells me the answer is one. 2+2=4, 4*2=8, 8/8=1



(For non-mathies, PEMDAS is the order of operations for math functions: First is whatever's in Parantheses, then Exponents, Multiplacation, Division, Addition, then lastly Subtraction.)

You must be loads of fun at parties :sl

[icehog3]

Once you evaluate the parentheses, you go left to right. 16

I'm lost. I read 8 divided by 2x4 (8) = 1

[Wharf Rat]

I'm lost. I read 8 divided by 2x4 (8) = 1

After you do the parentheses, you go left to right so,

8/2*(2+2)=

8/2*4=

4*4= 16

[icehog3]

After you do the parentheses, you go left to right so,

8/2*(2+2)=

8/2*4=

4*4= 16

Ok, thanks. Glad I don't need to go back for any math classes anytime soon. :lr

[markem]

PEMDAS tells me the answer is one. 2+2=4, 4*2=8, 8/8=1



(For non-mathies, PEMDAS is the order of operations for math functions: First is whatever's in Parantheses, then Exponents, Multiplacation, Division, Addition, then lastly Subtraction.)

well, no. See https://study.com/academy/lesson/what-is-pemdas-definition-rule-examples.html

[The camaro show]

This is why I hate math lol

[longknocker]

I Hate Math, But I Got That One Right!:D:banger:tu "16"

[Porch Dweller]

You must be loads of fun at parties :sl

Well, I'm a misanthropic introvert, so...what is this "parties" you speak of? :D

[Porch Dweller]

well, no. See https://study.com/academy/lesson/what-is-pemdas-definition-rule-examples.html

I forgot all about that. But I'm drinking whiskey and have taken two Benadryl, so I've probably forgotten my dog's name, too.

[hudd]

I say 1

[longknocker]

After Consulting With My "Smart" Work Colleagues, The Answer Is "1".;s:gary

[G G]

Well it would appear that both answers given are right:
https://www.foxnews.com/tech/viral-math-problem-baffles-many-internet

[mosesbotbol]

I say 1

Agree.

[icehog3]

A wise friend told me "t is a loaded question. You can bypass all ambiguities and misunderstanding with a bracket. Modern Western interpretation says 16. Old Eastern says 1. You can just write 8 / [2(2+2)] as is what is accepted, or (8/2)(2+2) as was used to be accepted, in order to resolve this conversation. Therefore, I would place blame on the opacity of the question."

[CigarNut]

You guys have too much time on your hands :)

[Porch Dweller]

Well it would appear that both answers given are right:
https://www.foxnews.com/tech/viral-math-problem-baffles-many-internet

WooHoo, I knew my whiskey- and benedryl-addled brain hadn't let me down!!!

:D

[markem]

PEMDAS and BODMAS are mnemonics, not mathematical rules. Language is fickle and you can't have two letters occupying the same position in a word, so some order must be chosen. This is the ambiguity of these two mnemonics.

It helps to know that any division can be rewritten as a multiplication without loss of meaning and multiplication can be rewritten as division. The same is true for with regards to addition and subtraction. Remember too that multiplication is a shorthand for addition and division for subtraction.

So all this can be reduced to PEMA or PEDS / PODS. PEMA is the dominant form, probably because multiplication and addition are commutative, associative and multiplication has the distributed rule. PEMA stands for parentheses, exponentiation, multiplication, addition. Note that PEMA has no ambiguity since there is only one operation at each evaluation step (or level, if you know about the precedence pyramid: https://www.teacherspayteachers.com/Product/Order-of-Operations-Pyramid-2358878). (Note that the difference between PEMDAS and BODMAS is really just selecting which item at a specific level is listed first, and thus ambiguous).

If we use multiplication for division and addition for subtraction, the solution is unambiguous (aka deterministic). Equivalent maths should give the same answer.

8 / 2(2+2) can be rewritten as
8 / 2 * (2+2) can be rewritten as
8 * (1/2) * (2+2) can be rewritten as
8 * (1/2) * 4 which reduces to
16

How the order of the operations in the final reduction step do not matter because multiplication is both commutative and associative:

(8 * (1/2)) * 4 == 8 * ((1/2) * 4) == 4 * (1/2) * 8

Note that I use (1/2) to indicate one-half, which could just as easily be replaced by 0.5, but that may complicate understanding for some.

The "DM" and "MD" of the mnemonics do not dictate a required ordering, they are just a handy memory device. There are not 6 cases to remember, just 4, since two cases can be recast in terms of other cases.

Here are some useful links:
http://mathforum.org/library/drmath/view/57199.html
http://thomas.tuerke.net/on/tech/?thread=1521859580

Since MD are at the same level of precedence, some method must be found to denote which order the operations will occur, or non-determinism results. Having a mathematical system that yields different results because of ambiguity is not good and would reduce the value of much of mathematics.

The "consensus" of about the last 100 years (yes, resolving this is a newish problem) is that operations at the same level of precedence are unambiguous when evaluated "left-to-right". Note that this is not a rule of mathematics, but a guide for resolving ambiguity.

Precedence plus the left-to-right guide removes the ambiguity. PEMA has no need for the left-to-right guide so is much simpler to get right.

The issue of PEMDAS and BODMAS (why no PEDMAS?) comes about through misunderstanding of the meaning of the mnemonics, not because math is non-deterministic. The underlying rule is PEMA. Any equation resolved with either of the mnemonics must be equivalent to PEMA or the answer is incorrect by mathematical rule, which cannot be changed. Note that you can reduce PEMA to PEA without introducing non-determinism.

So the real problem is NOT that the equation is ambiguous or opaque. It clearly is not under PEMA. The problem is a misunderstanding about the mnemonics being a mathematical rule rather than just a memory device.

[stearns]

I was following up until we got to the clarifying post above :r

[Weelok]

16. Here is the physics link for math orders.

https://en.m.wikipedia.org/wiki/Order_of_operations

Since the division is not a slash, think fractions, then division and multiplication are equal and evaluated left to right.

PEMDAS is flawed and incorrect.

[Weelok]

If we use multiplication for division and addition for subtraction, the solution is unambiguous (aka deterministic). Equivalent maths should give the same answer.

8 / 2(2+2) can be rewritten as
8 / 2 * (2+2) can be rewritten as
8 * (1/2) * (2+2) can be rewritten as
8 * (1/2) * 4 which reduces to
16

2) to indicate one-half, which could just as easily be replaced by 0.5, but that may complicate understanding for some.

.

Wow, so well done. Perfect.

[icehog3]

My brain hurts.

[longknocker]

Everything In My Old Body Hurts, Now, & I Still Don't Know The Answer!:r:D

[longknocker]

Just Looked Up Adam's Original Post On The Internet, And The Bottom Line Of The Article Gives The Correct Answer As "16". :D:noon:banger:tu

[icehog3]

Just Looked Up Adam's Original Post On The Internet, And The Bottom Line Of The Article Gives The Correct Answer As "16". :D:noon:banger:tu

Yeah, and they used to say the Earth was flat. -(P

[Weelok]

Yeah, and they used to say the Earth was flat. -(P

Wait, you mean the Earth isn’t flat?

I once convinced a Sophomore university French class that the planets in our solar system didn’t rotate around the sun which is why it’s so easy to plot a course for a satellite to take pictures of the planet.

[icehog3]

Wait, you mean the Earth isn’t flat?

I once convinced a Sophomore university French class that the planets in our solar system didn’t rotate around the sun which is why it’s so easy to plot a course for a satellite to take pictures of the planet.

I put instant coffee in a microwave oven and almost went back in time.

[markem]

http://www.cigarasylum.com/vb/attachment.php?attachmentid=18695&stc=1&d=1564707628

[Brlesq]

Old math tells me its 1. But new math with spiky haired teenagers? :sl

[mk05]

Microsoft Excel says 16, so it is 16. :D I do agree that the above 2 pages of disagreements, misunderstandings, etc could have been resolved with a clarifying bracket/parenthesis.

I didn't realize that this was an instagram question. Apparently, this has been so widely debated that Popular Science wrote about this today. The spokesman for the American Mathematical Society commented on this:
"According to order of operations, you solve whatever is in the parentheses first. That gives you 4. Then, in PEMDAS, multiplication and division take equal precedence, so you’d do the first that occurs from left to right. So you’d do 8 divided by 2 first, which is 4. Thus, it’s 16 according to classic order of operations.

But the way it’s written, it’s ambiguous. In math, a lot of times there are ambiguities. Mathematicians try to make rules as precise as possible."
A professor from a university wrote that the intent was to be a convention, a question delivered in such a way to obfuscate the reader by design. Specifically:
"Of course this isn't math. This is convention. We have conventions on how to write these things just like we have conventions on how to spell stuff. But still, there are different conventions. Some people spell it as ‘gray’ and others as ‘grey.’ We still understand what's going on. For me, I would write this more explicitly so that there is no confusion. Like this: 8/(2*(2+2)), if that's what you are trying to do. That way no one will get it wrong."

[Weelok]

Microsoft Excel says 16, so it is 16. :D I do agree that the above 2 pages of disagreements, misunderstandings, etc could have been resolved with a clarifying bracket/parenthesis.

I didn't realize that this was an instagram question. Apparently, this has been so widely debated that Popular Science wrote about this today. The spokesman for the American Mathematical Society commented on this:

A professor from a university wrote that the intent was to be a convention, a question delivered in such a way to obfuscate the reader by design. Specifically:

Hah, yes, it was written to be an ambiguous trick but totally cool it’s sparked a national conversation on math!!!!! Much more constructive arguing over an intellectual question then on Bachelorette show drama imho :)

[Brlesq]

Well now I know why I answered "1". From a news article on this today:

"The confusion has to do with the difference between modern and historic interpretations of the order of operations.
The correct answer today is 16. An answer of 1 would have been correct 100 years ago." <--- THAT explains it! :tg

[icehog3]

Well now I know why I answered "1". From a news article on this today:

"The confusion has to do with the difference between modern and historic interpretations of the order of operations.
The correct answer today is 16. An answer of 1 would have been correct 100 years ago." <--- THAT explains it! :tg

I wanna say it was correct 40 years ago as well.

[shilala]

Best. Post. Ever.
I just went around about this with my kid who is a physics major. She insisted it was 1.
I win. Although she still doesn’t agree.
I’m pretty sure that the fact that I make money with math and she takes that money to argue with me about math equals I’m always right. 😁
PEMDAS and BODMAS are mnemonics, not mathematical rules. Language is fickle and you can't have two letters occupying the same position in a word, so some order must be chosen. This is the ambiguity of these two mnemonics.

It helps to know that any division can be rewritten as a multiplication without loss of meaning and multiplication can be rewritten as division. The same is true for with regards to addition and subtraction. Remember too that multiplication is a shorthand for addition and division for subtraction.

So all this can be reduced to PEMA or PEDS / PODS. PEMA is the dominant form, probably because multiplication and addition are commutative, associative and multiplication has the distributed rule. PEMA stands for parentheses, exponentiation, multiplication, addition. Note that PEMA has no ambiguity since there is only one operation at each evaluation step (or level, if you know about the precedence pyramid: https://www.teacherspayteachers.com/Product/Order-of-Operations-Pyramid-2358878). (Note that the difference between PEMDAS and BODMAS is really just selecting which item at a specific level is listed first, and thus ambiguous).

If we use multiplication for division and addition for subtraction, the solution is unambiguous (aka deterministic). Equivalent maths should give the same answer.

8 / 2(2+2) can be rewritten as
8 / 2 * (2+2) can be rewritten as
8 * (1/2) * (2+2) can be rewritten as
8 * (1/2) * 4 which reduces to
16

How the order of the operations in the final reduction step do not matter because multiplication is both commutative and associative:

(8 * (1/2)) * 4 == 8 * ((1/2) * 4) == 4 * (1/2) * 8

Note that I use (1/2) to indicate one-half, which could just as easily be replaced by 0.5, but that may complicate understanding for some.

The "DM" and "MD" of the mnemonics do not dictate a required ordering, they are just a handy memory device. There are not 6 cases to remember, just 4, since two cases can be recast in terms of other cases.

Here are some useful links:
http://mathforum.org/library/drmath/view/57199.html
http://thomas.tuerke.net/on/tech/?thread=1521859580

Since MD are at the same level of precedence, some method must be found to denote which order the operations will occur, or non-determinism results. Having a mathematical system that yields different results because of ambiguity is not good and would reduce the value of much of mathematics.

The "consensus" of about the last 100 years (yes, resolving this is a newish problem) is that operations at the same level of precedence are unambiguous when evaluated "left-to-right". Note that this is not a rule of mathematics, but a guide for resolving ambiguity.

Precedence plus the left-to-right guide removes the ambiguity. PEMA has no need for the left-to-right guide so is much simpler to get right.

The issue of PEMDAS and BODMAS (why no PEDMAS?) comes about through misunderstanding of the meaning of the mnemonics, not because math is non-deterministic. The underlying rule is PEMA. Any equation resolved with either of the mnemonics must be equivalent to PEMA or the answer is incorrect by mathematical rule, which cannot be changed. Note that you can reduce PEMA to PEA without introducing non-determinism.

So the real problem is NOT that the equation is ambiguous or opaque. It clearly is not under PEMA. The problem is a misunderstanding about the mnemonics being a mathematical rule rather than just a memory device.

[longknocker]

Best. Post. Ever.
I just went around about this with my kid who is a physics major. She insisted it was 1.
I win. Although she still doesn’t agree.
I’m pretty sure that the fact that I make money with math and she takes that money to argue with me about math equals I’m always right. 😁

If Scott Says The Answer Is 16, It's 16!:banger:noon:D:tu

[shilala]

16, *****es!!! :tu

[icehog3]

16, *****es!!! :tu

Your favorite number, the age of most of your hose monkeys. -(P

[Subvet642]

I thought you solved the parenthesis first, so the answer would be 1.

8÷2x (2+2)

8÷2x4

8÷8=1

[Weelok]

I thought you solved the parenthesis first, so the answer would be 1.

8÷2x (2+2)

8÷2x4

8÷8=1

Why did you do multiplication before division? That was your mistake.

[T.G]

This thread reminds me of this....

https://www.youtube.com/watch?v=TEj1LLeB_CI&feature=youtu.be&t=5

/oblig

[markem]

Now that we have gotten off-topic, this is a cool video which discusses an area of computer science and mathematics in which I often live and teach.

https://www.youtube.com/watch?v=YX40hbAHx3s

[Subvet642]

Why did you do multiplication before division? That was your mistake.

Because that's how I recall learning it in 1978.