What is the answer ?

8/2(2+2) = ?


I say it's 42.

16

Are you sure ?

Yes

*LOL*

Where did you get 42 from? Google AI?

Life, the universe, and everything.

Hitchhiker’s Guide to the Galaxy.

Maybe I’ll read that next.

https://phys.org/news/2022-08-simple-viral-math-equation-stumped.html

However, I agree with this

https://ysu.edu/magazine/fall-2019/8-2-22

"O’Mellan says it’s neither.

When all is said and done, it’s a vaguely-written, ambiguous and faulty equation intentionally designed to confound and stew internet chaos, similar to the viral black-and-blue dress and the Laurel vs. Yanny phenomenon. Remember those?

“No mathematician would write this equation this way,” O’Mellan said.

So, there it is: There is no definitive answer. As Steven Strogatz, a professor of Mathematics at Cornell, wrote in the Times: “You say tomayto, I say tomahto."

:)

But 42, tho?

"“No mathematician would write this equation this way,” O’Mellan said."

Is O'Mellan Scotch? There's no True Irishman fallacy.

Been drinking scotch ?

please excuse my dear aunt sally

Which isn’t like 100% accurate, because multiplication and division are the same thing as well as addition and subtraction, but do the addition in the parens first and then outside parens, then 4*4.

Infix precedence rules should give 16 like Beth says. Precedence rules in the example are confusing due to conflicting standards. Such confusion can be cleared up by adding more parenthesis. Otherwise it might not give a consistent answer (PEMDAS vs BEDMAS).

RPN (reverse polish notation) has no precedence rules or parentheses, just left to right evaluation like the HP35 calculator.

2 2 + 8 2 / *



Edited 2 time(s). Last edit at 04/29/2024 03:07AM by bradley.

bradley Wrote:
-------------------------------------------------------

>
> RPN (reverse polish notation) has no precedence
> rules or parentheses, just left to right
> evaluation like the HP35 calculator.
>
> 2 2 + 8 2 / *

Minor correction, this is not quite left to right.


Assuming 8/2(2+2) = (8/2)*(2+2),

It would be 8­­­↑2/2↑2+*.

If you wanted (8/(2*(2+2)),

It would be 8­­­↑2↑2↑2+*/.

Both of which are going left to right in RPN.

Long live Jan Lukasiewicz, the P in RPN!!!

https://en.wikipedia.org/wiki/Jan_%C5%81ukasiewicz

And in case any of you want to be the life of the party this weekend, you can further explain how HP et al made his Polish logic go in reverse.

https://en.wikipedia.org/wiki/Polish_notation

On a nerd note, every math major on the planet is familiar with this notation because of their intro to Abstract Algebra classes.

My God, I am cool!!



Edited 1 time(s). Last edit at 04/29/2024 01:01PM by wowbagger.

> My God, I am cool!!

Indeed.

Definitive answer.

Math is evil.

I’ll drink to that!

Susan I/S Wrote:
-------------------------------------------------------
> Definitive answer.
>
> Math is evil.


... and hard
I know, Barbie told me...

Susan I/S Wrote:
-------------------------------------------------------
> Definitive answer.
>
> Math is evil.

Yes. This.

Why did I open this thread? I need a shot of Irish whiskey tout de suite.

My phobia of numbers started out with arithmetic in grade school and went south from there.

I'm surprised our resident math teacher hasn't weighed in yet. For sure I'd take his opinion on a topic like this. If I could bear to read it that is. Or even better, actually understand it.

My thing is words. Words are good. Words are great. I can do words.

PS: Oh wait - I see the math teacher has bellied up on it, below. I should have read the whole thread before jumping in. I might stop here tho...



Edited 1 time(s). Last edit at 04/29/2024 04:20PM by Nightingale.

When you write (8/2) as a fraction, as you did here, instead of using the division symbol, there is no ambiguity. You first simplify the fraction to “4” and then, after removing the parentheses in the second term, multiple 4X4 to get 16. The ambiguity arising from the use of the division operator is avoided because a fraction is not an operator, and the division symbol is.

In other words, you missed the point of this exercise by using a fraction instead of a division symbol. (See related links where the division symbol is used to establish the ambiguity.)

BofJ will tell you this is correct. (Unless it is just too painful for him to admit I am right about something.)(:-)

First of all, this is not a math question, it is a grammar question. the grammar for precedence in math expressions is ambiguous. The ambiguity here is that an implied multiply has a higher precedence than an explicit multiply. The implied multiply is 2(2+2). That should be done before the preceding divide operation.

OTOH, in standard expression evaluation, divide and multiply have the same precedence, and should be evaluated left to right, unless overridden by parentheses.

A common example is the dreaded quadratic formula that the math illiterati love to mock. x=(-b+-sqrt(b^2-4ac)/2a. Should the "2a" at the end be evaluated as "divide the preceding expression by 2, then multiply the result by a", or "multiply 2 times a, then divide that into the preceding expression".

An argument can be made for either interpretation. With the expression written out horizontally, like here, the 2a would be enclosed in parens to eliminate the ambiguity. If the expression were typeset with the part before the divide printed on top, a divide symbol under it, and the 2a under the divide symbol, the parens would not be used because it would be obvious that 2a should be multiplied first, followed by the division.

It is really irritating to see nonsense like this proposed as "math" problems. It's a grammar problem, and the traditional grammar for algebraic expressions has several ambiguities.

All the computer languages that I am familiar with get around this particular ambiguity by simply not allowing implied multiplies (that is, a multiply symbol must be used), and requiring a strict left-right precedence for consecutive multiply and divide operations.

It is also considered good form to use parentheses to make the evaluation order obvious, even when the parentheses are not actually required.

"The man the dog the boy owned bit died" is technically grammatically correct, and is also extraordinarily poor form because it is unreadable. Nobody except possibly James Joyce would actually write that.

BTW. readers can generally handle two levels of nesting in a sentence. "The man the dog bit died", while kind of clumsy, is parsable by most readers. Adding a third level makes it unreadable. Creating an unreadable sentence is not clever, it is just bad form. The same is true for creating an unreadable math expression.

James Joyce told me the answer is 1. You just have to see it his way.

Was he in a Dubliners mood when he said that or did it take him 800 pages?

It's one of those unusual narrative voices from Ulysses.

That's what I feared.

I’m having a hard time getting through it.

You mean the math problem or the book? ;-)

Years ago, I read the book while listening to the audio, while stopping to read the study guide. It took months to slog through it. It's a weird book. Who else would work in a different organ and different style for each chapter? I ended up reading a biography about him. He was a weird dude.

Haha! The book.

Yesterday I read North Woods by Daniel Mason. I liked it a lot. Also enjoyed The Saint of Bright Doors by Vajra Chandrasekera.

Finally reading The Hitchhiker's Guide to the Galaxy so I can get Dave’s jokes (when he has them).

Okay…this book is super silly fun and exactly what I need.

Taking note of your comments above, I would ask the following question:

What is the difference (conceptually and functionally) between the slash "/" functioning in a mathematical equation as a division *operator*, and the slash functioning as defining a *ratio*, as in the identification of a fraction? Obviously, this is an important distinction because it relates to the difference between (a) what must be done to solve an equation (operator); and (2) a distinct ratio or quantity that is simply a term of the equation.

In the OP we have 8/2(2+2)=? So, is the slash telling us to divide 8 by 2(2+2) (operator), or to multiply the fraction 8/2 (ratio) by (2+2)? The problem is that we don't have any values on the right side of the equation from which to determine the correct answer. If there was a "16" there, the ambiguity would be resolved. Ditto if there was a 1 there.

Notwithstanding this ambiguity, it would seem to me that the use of the slash here is best viewed as a ratio, and not to dictate an operation. That conclusion is for one reason only: So interpreting the 8/2 as a ratio entirely resolves the ambiguity, by immediately simplifying to 4. If you interpret it as an operator, the ambiguity remains, because the answer could be *either* (1) 8/(2(2+2)=1, or (2) (8/2)(2+2)=16.

Compare this to your example of the quadratic formula:

x=(-b+-sqrt(b^2-4ac)/2a, where you suggest the slash is intended as a division operator in order to solve for x. Here, in words, it states (basically) that if you want to find x, then do this, which includes the slash as the division operator. In this case, there is no ambiguity between the slash as an operator or as a ratio, and thus no danger of interpreting the slash in either way. The operator interpretation is demanded by the context. If you want to find x, you better treat the slash as an operator.

Now you may think I am being too nit-picky here. (Who me?) After all, all you have to do is get clear in your notation in the first place. On the other hand, if you are solving a more complex equation, or attempting a proof, what do you do if some ambiguity surfaces? Well, it seems to me if you can resolve the ambiguity by a simple interpretation giving a definitive answer, you should do that, and adjust your notation accordingly as may be helpful or necessary. Otherwise, you are just done! (Unless you are in a context legitimately involving multiple solutions for x)

In the computer context, you note:

"All the computer languages that I am familiar with get around this particular ambiguity by simply not allowing implied multiplies (that is, a multiply symbol must be used), and requiring a strict left-right precedence for consecutive multiply and divide operations."

Yes, and this is true for ALL computer programs where potential ambiguities might arise from implied multiples, or for any other reason. In such cases, the resolutions of the ambiguity must be built into the system logic, without consideration of human convention, human intent, or human error.

In short, the answer to the OP is 16! It may indeed at root be a "grammar question." But, just as in English discourse, when you confront an ambiguity in mathematics, I assume you attempt to resolve it rationally, by logic, context, parsimony, etc.

Nice try. There is no difference between a slash as a ratio and a slash as a divide operator. There is no way to distinguish them other than an external directive telling the user not to carry out the division, leave the expression as a ratio.

And there is still an ambiguity.
STUFF
--------
2a

In the quadratic formula (simplified :) above, is it the ratio of STUFF over 2a, or STUFF over 2, and then figure out what to do with the a? It is STUFF over 2a, and the multiply has to be performed before the divide, even though the linear form of that expression is STUFF / 2*a, In the linear form, you must insert a set of parens to clear up the ambiguity. In the typeset version, by convention, the multiply has higher priority than the divide, which is a violation of PEMDAS. That's why PEMDAS is ambiguous - there are frequently used and accepted exceptions to PEMDAS.

It is also pretty easy to create grammatically correct, but very difficult to parse expressions in PEMDAS, just as it is possible to do that in English. Writers in either discipline ought not write perversely confusing statements. Except James Joyce.

For those not familiar with the acronym,
Parenthese
Exponentiation
MultiplyDivide
AddSubract

Multiply and divide have identical precedence, and consecutive Ds or Ms are processed left to right.
Add and subtract also have the same precedence and consecutive occurrences are processed left to right.

Exponentiation is the odd man out. Consecutive exponents are processed right to left unless parentheses override that. Most people are not aware of that, but multiple consecutive exponents happen so rarely in the "real world", that the issue never comes up.

"Nice try. There is no difference between a slash as a ratio and a slash as a divide operator. There is no way to distinguish them other than an external directive telling the user not to carry out the division, leave the expression as a ratio."

COMMENT: It was quite obvious from my post that I was talking about methodology. What the user does with the slash in any given problem context *is* a distinction! And that depends upon the motivations of the mathematician; that is, the end game he is trying to accomplish. It is quite odd to suggest that such inner thoughts and strategies are merely "external directives." Where do these directives come from, if not the mathematicians mind?
______________________________________

In the quadratic formula (simplified :) above, is it the ratio of STUFF over 2a, or STUFF over 2, and then figure out what to do with the a? It is STUFF over 2a, and the multiply has to be performed before the divide, even though the linear form of that expression is STUFF / 2*a, In the linear form, you must insert a set of parens to clear up the ambiguity. In the typeset version, by convention, the multiply has higher priority than the divide, which is a violation of PEMDAS. That's why PEMDAS is ambiguous - there are frequently used and accepted exceptions to PEMDAS.

COMMENT: Again, what you are talking about here seems to be mathematical judgment! This was precisely the point I was making. How a mathematician views, distinguishes, and addresses terms in an equation involves not only the symbols, mathematical objects, and rules of inference themselves, etc. -- all as established by convention (or Platonic reality)-- but also the skill and creativity of the mathematician. Surely you do not deny this. And *that* I suggest is part of mathematics proper!

Do I need to provide YOU with citations for this basic fact?

one?

Remember girls don't need math or algebra, they will be at home with the babies.

Correct answer: what do you want it to be?

Through the gift of the Holy Ghost you can know the truth of all things.

bradley Wrote:
-------------------------------------------------------
> Through the gift of the Holy Ghost you can know
> the truth of all things.

Oh - that's where I went wrong. I see that now.

I think the correct Mormon answer is to build more temples; at least 15.

So, did I win?

16, by PMDAS.

Just shy of 17?

16. PEMDAS is the rule.

But I wish it was 42, as I am always looking for the meaning of life…

Like Beth, I got 16.

I confess. My answer was 16. I was just trying to make Beth doubt her doubts.

Constants aren't.

Variables won't.

And the answer is...... ONE

There can only be only one!


https://youtu.be/_J3VeogFUOs