48÷2(9+3) = ??? -- VOTE!! Poll Added

[TBTwinsFan]

Ha I wrote it on an index card and handed it to my parents, and they are split on it.

Here is my question though, take a pack of Topps cards, turn it over, read the fine print and look at the math problem... What's that answer?

 

[Mr.1989]

Well, I'll contribute to the debate.






When thinking of math historically, writing math down in a series of operations was and has always simply been a conduit for human interpretation of the intention of any series of equations. What I mean by this is that, basically, what the equation is, is translated from its purpose (what it was made for).

In the equation x=48÷2(9+3), most people will agree that the intention of the parentheses is to isolate the operation going on inside, which in this case is additive. So the first step most people will take is to combine 9 and 3 to get 12. So we get:

x=48÷2(12)

Now, here is where we disagree. As I said earlier, it depends on how the equation was formed to how you get your result. Do we first divide 48 by 2 and then multiply that by 12, or do we multiply 2 by 12 first and then divide 48 by that result?
Well, it depends on how you're looking at it.

If it were set up as:
48
-------------
2 (9+3)

, then your intent is to finish out whatever is being worked out at the bottom, which ends up being 24, and then dividing the top by that would be 2.

But, all of this is dependent on two things: How the equation is set up; and the order of operations.

Most mathematicians I know have PEMDAS as their Order of Operations, (those meaning Parentheses, Exponents, Multiplication, Division, Addition and Subtraction from left to right).

In the equation x=48÷2(9+3), you would first combine 9 and 3 (Parentheses), to get 12, then multiply those by 2 (Multiplication comes before Division in PEMDAS and therefore is done first) to get 24, and then after that you simply divide 48 by 24 to get 2.


But, the reason I brought up intent in the first place is because many mathematicians who have their brains running at very high speeds tend to forget putting one thing or another in parentheses while working out long calculus equations.

If the result were to be 288, if would have to be setup like this:

(48÷2)(9+3)

First work each individual parentheses.

(24)(12)

Now multiply.

288


Now you see, based on the way the equation was presented and using PEMDAS as a standard, the answer to this equation is 2.

If you agree, then please press the "Thank Post" button, as I will know you truly thank me through that.

 

[scotty21690]

THANK YOU!


Another way to look at it is:


48/2(9+3)

2(9+3)

(18+6)

(24)

48/24

2

 

[Mr.1989]

THANK YOU!


Another way to look at it is:


48/2(9+3)

2(9+3)

(18+6)

(24)

48/24

2

Who are you thanking? Me?

 

[ChasHawk]

worst baseball thread, and biggest waste of 14 pages ever

congrats to the OP for getting this to 14 pages without getting it moved

 

[scotty21690]

Yes. Very nice job on explaining it!

 

[Mr.1989]

Yes. Very nice job on explaining it!

Well thank you!
The only thing is.......all of the people out there who want to debate PEMDAS.

 

[TBTwinsFan]

worst baseball thread, and biggest waste of 14 pages ever

congrats to the OP for getting this to 14 pages without getting it moved

If you do write in NPN with Topps, it really makes you think.

 

[scotty21690]

worst baseball thread, and biggest waste of 14 pages ever

congrats to the OP for getting this to 14 pages without getting it moved

If you do write in NPN with Topps, it really makes you think.

I thought only Canadians had to do that?

 

[TBTwinsFan]

Lemme check.

Yup. Only Canadians.

Oh well, we have some Canadian members.

 

[Anthony K.]

Yes. Very nice job on explaining it!

Well thank you!
The only thing is.......all of the people out there who want to debate PEMDAS.

A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right.

No debating PEMDAS. The problem is, people argue that multiplication goes BEFORE division, when, clearly stated above, they are equal, so when they are both present, you go from left to right.

 

[Therion]

It actually presents an interesting issue if you take into account the distributive property.

Either answer could be considered legitimately correct.

 

[vwnut13]

worst baseball thread, and biggest waste of 14 pages ever

congrats to the OP for getting this to 14 pages without getting it moved

If you do write in NPN with Topps, it really makes you think.

I thought only Canadians had to do that?

Maybe he sent in a NPN Request when he fled to Canada to avoid the football team.

 

[scotty21690]

It actually presents an interesting issue if you take into account the distributive property.

Either answer could be considered legitimately correct.

That is what I was showing with my last post, forgot the name of the method though, lol.

 

[rehmus]

we really need to start doing something to get this thread locked.

8========================================D

((()))

( )*( )

 

[TBTwinsFan]

worst baseball thread, and biggest waste of 14 pages ever

congrats to the OP for getting this to 14 pages without getting it moved

If you do write in NPN with Topps, it really makes you think.

I thought only Canadians had to do that?

Maybe he sent in a NPN Request when he fled to Canada to avoid the football team.

'
I don't get the joke.

But I thought all people had to send in the math question when they did the send-in route for NPN. I know UD at least had an online system, but I don't do NPN so I don't know how Topps did it.

 

[TramFan3]

Now that im drunk i figure ill weigh in again.

I taught at a University for 3 years.

In fact, one of the first things i taught in my beginning algebra class was order of operations.

If you got 2 instead of 288, you are doing one of the following things wrong

1. misunderstanding the syntax.

or

2. misunderstanding the order of operations.

Since an arithmetic problem doesnt have more than one answer, those who get 2 are doing it wrong. Congrats, youve failed a 9th grade math class.

 

[markakis8]

8========================================D

Well saying 8 = D just makes you look like a *******.

 

[thelesquad]

8========================================D

Well saying 8 = D just makes you look like a *******.

No, saying 8=D makes him look like a d***.

 

[Mighty Bombjack]

The choices on the poll should be changed from "2" and "288" to "Thinks that there can only be one answer" and "Thinks that mathematics, like any other language, has some ambiguity"

That would cut to the heart of the problem.