48÷2(9+3) = ??? -- VOTE!! Poll Added

[rehmus]

THINK OUTSIDE THE BOX.

the answer is 288 if you use PEMDAS. anyone who denies this is dumb. most people aren't denying this (i hope).

the answer is 2 if you understand that a precedence is given to the multiplication part of the equation because 2(9+3) is implied to be 2*(9+3)

48÷2(9+3) = 288 via PEMDAS
2(9+3) is equal in priority to 48÷2
2(9+3) is implied to be 2*(9+3) -
2*(9+3) takes precedence over 2(9+3) - 99.99999% of the time this doesn't matter, but it is an absolute fact - look it up.
2*(9+3) therefore takes precedence over 48÷2, which was equal to 2(9+3)
48÷2*(9+3) therefore is 2

Does the question say 48÷2*(9+3)? No. It says 48÷2(9+3).

Therefore, neither answer is wrong. If you want to acknowledge the implication then it's 2. If not it's 288.

Does every person who voted 2 fully understand this concept? Probably not, but subconsciously it just makes sense to us. It is training by PEMDAS which makes us want to eliminate the parentheses. It is human nature to associate the adjacent 2 to the function of eliminating the parentheses.

The problem, quite simply, is missing a set of parentheses. (48÷2)(9+3) is inarguably 288. 48÷(2(9+3)) is inarguably 2. It is a deliberately flawed question as 48÷2(9+3).

Were I a high school math teacher I would never include this question on a quiz/test. Had I foolishly included it I would probably accept 288 as my answer (technically I would accept both, but thats beside the point) as I wouldn't expect mere high school students to understand upper level math concepts as I've outlined today.

Anyone who arrives at 2 using plain PEMDAS is doing it wrong. Anyone who can't see why someone would choose 2 for other reasons is also doing it wrong, whether or not they actually agree with those reasons.

Print out this post and show it to your math teachers, professors or Stephen Gotdam Hawking himself and tell me what they say.

 

[thelesquad]

THINK OUTSIDE THE BOX.

the answer is 288 if you use PEMDAS. anyone who denies this is dumb. most people aren't denying this (i hope).

the answer is 2 if you understand that a precedence is given to the multiplication part of the equation because 2(9+3) is implied to be 2*(9+3)

48÷2(9+3) = 288 via PEMDAS
2(9+3) is equal in priority to 48÷2
2(9+3) is implied to be 2*(9+3) -
2*(9+3) takes precedence over 2(9+3) - 99.99999% of the time this doesn't matter, but it is an absolute fact - look it up.
2*(9+3) therefore takes precedence over 48÷2, which was equal to 2(9+3)
48÷2*(9+3) therefore is 2

Does the question say 48÷2*(9+3)? No. It says 48÷2(9+3).

Therefore, neither answer is wrong. If you want to acknowledge the implication then it's 2. If not it's 288.

Does every person who voted 2 fully understand this concept? Probably not, but subconsciously it just makes sense to us. It is training by PEMDAS which makes us want to eliminate the parentheses. It is human nature to associate the adjacent 2 to the function of eliminating the parentheses.

The problem, quite simply, is missing a set of parentheses. (48÷2)(9+3) is inarguably 288. 48÷(2(9+3)) is inarguably 2. It is a deliberately flawed question as 48÷2(9+3).

Were I a high school math teacher I would never include this question on a quiz/test. Had I foolishly included it I would probably accept 288 as my answer (technically I would accept both, but thats beside the point) as I wouldn't expect mere high school students to understand upper level math concepts as I've outlined today.

Anyone who arrives at 2 using plain PEMDAS is doing it wrong. Anyone who can't see why someone would choose 2 for other reasons is also doing it wrong, whether or not they actually agree with those reasons.

Print out this post and show it to your math teachers, professors or Stephen Gotdam Hawking himself and tell me what they say.

Most of your post makes sense, but explain why 2*(9+3) takes precedence over 48÷2.

 

[CubsFan13]

Read the first two pages, so not sure if this has been said.

I voted 288.

48/2(9+3)
48/2(12) do what is in the parentheses
24(12) Divide. The rules of PEMDAS say you use multiplication and divison left to right. They are equal. The same goes for addition and subtraction.
288 Multiply.

12(12) = 144
12*12 = 144
12x12 = 144

The P in PEMDAS, parenthese, only pertain to what is inside the parenthese. After that, the paranthese simplify signify multiplication.

However, the thing that puzzles me is this:

10/10 =

10÷10=

10
---
10

These all equal one.

So.....

48/2(9+3)
48/2(12)
24(12)
288

48÷2(9+3)
48÷2(12)
24(12)
288

but

48
-------
2(9+3)

48
-----
2(12)

48
-----
24

=2

BUT, if you look at dividing by two as multiplying by half then...

48*.5(9+3)
48*.5(12)
48*6
288


So, i vote 288.

 

[jbhofmann]

put the dry erase marker down....

 

[CubsFan13]

.

 

[rehmus]

THINK OUTSIDE THE BOX.

the answer is 288 if you use PEMDAS. anyone who denies this is dumb. most people aren't denying this (i hope).

the answer is 2 if you understand that a precedence is given to the multiplication part of the equation because 2(9+3) is implied to be 2*(9+3)

48÷2(9+3) = 288 via PEMDAS
2(9+3) is equal in priority to 48÷2
2(9+3) is implied to be 2*(9+3) -
2*(9+3) takes precedence over 2(9+3) - 99.99999% of the time this doesn't matter, but it is an absolute fact - look it up.
2*(9+3) therefore takes precedence over 48÷2, which was equal to 2(9+3)
48÷2*(9+3) therefore is 2

Does the question say 48÷2*(9+3)? No. It says 48÷2(9+3).

Therefore, neither answer is wrong. If you want to acknowledge the implication then it's 2. If not it's 288.

Does every person who voted 2 fully understand this concept? Probably not, but subconsciously it just makes sense to us. It is training by PEMDAS which makes us want to eliminate the parentheses. It is human nature to associate the adjacent 2 to the function of eliminating the parentheses.

The problem, quite simply, is missing a set of parentheses. (48÷2)(9+3) is inarguably 288. 48÷(2(9+3)) is inarguably 2. It is a deliberately flawed question as 48÷2(9+3).

Were I a high school math teacher I would never include this question on a quiz/test. Had I foolishly included it I would probably accept 288 as my answer (technically I would accept both, but thats beside the point) as I wouldn't expect mere high school students to understand upper level math concepts as I've outlined today.

Anyone who arrives at 2 using plain PEMDAS is doing it wrong. Anyone who can't see why someone would choose 2 for other reasons is also doing it wrong, whether or not they actually agree with those reasons.

Print out this post and show it to your math teachers, professors or Stephen Gotdam Hawking himself and tell me what they say.

Most of your post makes sense, but explain why 2*(9+3) takes precedence over 48÷2.

A big part of the problem people who argue 2 have been having is that they think 2(9+3) should be done first because Multiply comes before Divide in PEMDAS. But, as several have pointed out, dividing and multiplying are interchangeable in the order of operations (therefore equal) and thus the problem should be done left to right - which gets you 288.

2*(9+3) being of greater significance than 2(9+3) (which is of equal significance to 48÷2) therefore changes your order of operations.

 

[Pine Tar]

So this is kind of like this
108÷.5 = 216 and not 54
this was actually on a Machinist test once and most got it wrong :shock:

Why does it look like you are missing something from that equation? Why wouldn't that =54?

because 108/2 = 54.

Dividing by 0.5 is the same as multiplying by 2.

And if this is the case then
108X2=216 and not 54

 

[CubsFan13]

Man, now I'm really confused. I just found this article:

http://justifiableanger.blogspot.com/20 ... think.html

The argument seems valid, but middle school was a LONG time ago :lol:

As a side note, is the person who left the comment (Alex) on the article, the same Alex on the board?
The comment was left today.

 

[rehmus]

[quote="Pine Tar":2utoqp6z]So this is kind of like this
108÷.5 = 216 and not 54
this was actually on a Machinist test once and most got it wrong :shock:

Why does it look like you are missing something from that equation? Why wouldn't that =54?

because 108/2 = 54.

Dividing by 0.5 is the same as multiplying by 2.

And if this is the case then
108X2=216 and not 54[/quote:2utoqp6z]

yup.

108x2 is not 54, haha.

108/2 is 54.
108/2 is 216.
108 x 0.5 is 54
108/0.5 is 216

 

[rehmus]

Man, now I'm really confused. I just found this article:

http://justifiableanger.blogspot.com/20 ... think.html

The argument seems valid, but middle school was a LONG time ago :lol:

As a side note, is the person who left the comment (Alex) on the article, the same Alex on the board?
The comment was left today.

hahaha, that article is really, really interesting and much easier to understand than my previous post. also, im beginning to think i may have been wrong in saying 2*(9+3) is more significant than 2(9+3) based on what he just wrote...

ahhhhhhh.

 

[Mighty Bombjack]

Man, now I'm really confused. I just found this article:

http://justifiableanger.blogspot.com/20 ... think.html

The argument seems valid, but middle school was a LONG time ago :lol:

As a side note, is the person who left the comment (Alex) on the article, the same Alex on the board?
The comment was left today.

This blogger makes a great point

48÷2(x+y) does NOT equal 24(x+y), it equals 48÷(2x+2y)

This is why my bachelor's degree in math told me 2 is the answer.

However, it also tells me that mathematics is a language, and my philosophy degree tells me that all language includes built-in ambiguity.

 

[rehmus]

Man, now I'm really confused. I just found this article:

http://justifiableanger.blogspot.com/20 ... think.html

The argument seems valid, but middle school was a LONG time ago :lol:

As a side note, is the person who left the comment (Alex) on the article, the same Alex on the board?
The comment was left today.

ok i just re-read this and straightened out my thoughts. one thing i didnt consider for my post at the top of this page is the can of worms opened by changing 2(9+3) to 2*(9+3). my points are still correct but apparently other problems are created by having a separation between the 2 and the parentheses. That blog post (and the answer of 2) probably wins the thread.

 

[blanning71]

To quote my favorite movie.......


"Who gives a ****? Its gone!!!!"

 

[thefatguy]

To quote my favorite movie.......


"Who gives a ****? Its gone!!!!"

I don't remember that line in Star Wars :?:

 

[pgwtamu]

To all the 288ers.....Suck It!!!!!

 

[maxpower]

Man, now I'm really confused. I just found this article:

http://justifiableanger.blogspot.com/20 ... think.html

The argument seems valid, but middle school was a LONG time ago :lol:

As a side note, is the person who left the comment (Alex) on the article, the same Alex on the board?
The comment was left today.

Alex's blog post is conclusory and wrong. Simply stating that 2(3) <> 2*(3) does not make it so. They are two ways of communicating the exact same thing. Like saying "2 * 2" vs. "2 times 2".

As for his whole discussion of "(x +y)", he is simply misinformed. The fact that x and y cannot be reduced to a single term has no bearing on the order of operations. And either way, you end up with two unknown variables, whether it's (x+y) or (2x+2y).

Admittedly, the problem is tricky, but not at all ambiguous.

 

[Mighty Bombjack]

Man, now I'm really confused. I just found this article:

http://justifiableanger.blogspot.com/20 ... think.html

The argument seems valid, but middle school was a LONG time ago :lol:

As a side note, is the person who left the comment (Alex) on the article, the same Alex on the board?
The comment was left today.

Alex's blog post is conclusory and wrong. Simply stating that 2(3) <> 2*(3) does not make it so. They are two ways of communicating the exact same thing. Like saying "2 * 2" vs. "2 times 2".

As for his whole discussion of "(x +y)", he is simply misinformed. The fact that x and y cannot be reduced to a single term has no bearing on the order of operations. And either way, you end up with two unknown variables, whether it's (x+y) or (2x+2y).

Admittedly, the problem is tricky, but not at all ambiguous.

Are these the same equation?

48÷2 x X

48÷2X

 

[BunchOBull]

What the guy is basically saying is PEDMDAS

Parenthesis, Exponents, Distribute, Multiply, Divide, Add, Subtract

Which in itself works when there are unknowns; however, that's not the case with the original problem.

 

[hive17]

Has anyone put this, as is, into a TI-85/93/95 calculator?

What does Texas Instrument have to say? You can type that equation in as it's written, hit = and tells us what you get...

 

[Mighty Bombjack]

Has anyone put this, as is, into a TI-85/93/95 calculator?

What does Texas Instrument have to say? You can type that equation in as it's written, hit = and tells us what you get...

I sold my TI85 and HG48X long ago (and bought cards with the money!), but here is a quote from one of the first posts in this thread:

http://www.purplemath.com/modules/orderops2.htm

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. 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 "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!