Here's what someone who sounds confident posted somewhere:
The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.
So this can be rewritten as:
48 / (2*9 + 2*3)
Which leaves us with
48 / 24 = 2
Answer = 2.
Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 *(9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs.
Well, since that explanation makes my guess of 2 right, I'm totally convinced!
Even using the distributive property, you can still end up with 288 due to the ambiguity of the original expression:
[modified from an Ubuntu discussion forum dorkin' out on this problem]
The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.
That's where I was coming from. The way I understood it, resolving the parenthesis of a math equation not only involves dealing with the interior [9+3] of the parenthesis, but also any coefficient [2] as well. Sort of like 48 ?? 2x, where x = 9+3. I was looking at the following website...
Problem 2. In the following expression, how many terms are there? And each term has how many factors?
2a + 4ab + 5a(b + c)
There are three terms. 2a is the first term. It has two factors: 2 and a. 4ab is the second term. It has three factors: 4, a, and b.
And 5a(b + c) is all one term. It also has three factors: 5, a, and (b + c).
To me, just as 5a(b + c) is one term, I feel that 2(9+3) is one term. I don't think it matters if you're dealing with variables or real numbers -- I can't see why that would change the rules. But again, I'm waiting for a bona fide NASA rocket scientist to chime in. I'm not taking the staunch position I was taking earlier, nor will I cast aspersions on the 288 camp.
If you want to draw a line it goes under the 48 and over the two, then you times that times 12. 288 all day. You have to put parentheses around the 2(9 + 3) if you want the Deuce.
Don't panic, that problem is very common in men your age....I just got an email advertising cheap Viagra, I can forward it to you if you wish. :-P
dollar_binI heartily endorse this product and/or event 2,326 Posts
This thread is giving me Asperger's syndrome. It comes down to whether you give x(y) higher Operator Precedence than x*(y), an arbitrary distinction at best. Do what you want, neither answer is Right.
The equation mimics the common shorthand a/bc, where bc is the term in the denominator.
For example, math people would understand that 1/2?? means 1/(2??), not ??/2. (Remember that ?? is a number.)
Also, 2(9 + 3) is structured like another frequently used form, the factored polynomial (albeit w/o variables).
These conventions jump out immediately, and signal Purpose behind the equation.
If the answer is "supposed" to be 288, the equation's only purpose would be obfuscation.
Here's my new favorite solution which, while I don't believe it is the answer, is at the very least less boring than repeating the exact same arguments dozens of times that lead to either 2 or 288.
If, using the distributive property ..
2(9 + 3) is equivalent to "2 * 9 + 2 * 3"
and because this is part of a larger expression and 2(9 +3) is not protected by parantheses, we could have ...
Here's my new favorite solution which, while I don't believe it is the answer, is at the very least less boring than repeating the exact same arguments dozens of times that lead to either 2 or 288.
If, using the distributive property ..
2(9 + 3) is equivalent to "2 * 9 + 2 * 3"
and because this is part of a larger expression and 2(9 +3) is not protected by parantheses, we could have ...
48 ?? 2 * 9 + 2 * 3
following order of operations ...
24 * 9 + 2 * 3
216 + 2 * 3
216 + 6
222
Nope. The way the equation is written, you need to distribute both 2*9 and 2*3 as divisors of 48.
Here's my new favorite solution which, while I don't believe it is the answer, is at the very least less boring than repeating the exact same arguments dozens of times that lead to either 2 or 288.
If, using the distributive property ..
2(9 + 3) is equivalent to "2 * 9 + 2 * 3"
and because this is part of a larger expression and 2(9 +3) is not protected by parantheses, we could have ...
48 ?? 2 * 9 + 2 * 3
following order of operations ...
24 * 9 + 2 * 3
216 + 2 * 3
216 + 6
222
Nope. The way the equation is written, you need to distribute both 2*9 and 2*3 as divisors of 48.
Like I said, I don't actually think it's the answer. Just playing with an ambiguous expression like everyone else.
edit ... though, that would make the answer an even more interesting 10.66.
Also, 2(9 + 3) is structured like another frequently used form, the factored polynomial (albeit w/o variables).
Yeah, I have a vague memory of being drilled endlessly on this in school. So I guess I instinctively approached it that way.
It would probably hurt my brain to try to do some factoring today. But I do have a clear memory that a girl in my class had the rad 'popsicle stick' perm. So that her hair was in zig-zags. Now, THAT I remember like yesterday.
dollar_binI heartily endorse this product and/or event 2,326 Posts
damms said:
who wants a real math problem ?
Yes please. Or perhaps a real meth problem.
Here's one. Is there any time where all three hands of an analog clock are exactly 120?? apart? If not, why not? If not, how close does a continuously sweeping clock come?
Comments
Here's what someone who sounds confident posted somewhere:
The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.
So this can be rewritten as:
48 / (2*9 + 2*3)
Which leaves us with
48 / 24 = 2
Answer = 2.
Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 *(9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs.
Well, since that explanation makes my guess of 2 right, I'm totally convinced!
[modified from an Ubuntu discussion forum dorkin' out on this problem]
48??2(9+3) =
48/2 (9 + 3) =
(48/2 * 9 + 48/2 * 3) =
(432/2 + 144/2) =
216 + 72 =
288
Any other answer is incorrect.
Kindly,
parallax
That's where I was coming from. The way I understood it, resolving the parenthesis of a math equation not only involves dealing with the interior [9+3] of the parenthesis, but also any coefficient [2] as well. Sort of like 48 ?? 2x, where x = 9+3. I was looking at the following website...
http://www.themathpage.com/alg/algebraic-expressions.htm#factors
Problem 2. In the following expression, how many terms are there? And each term has how many factors?
2a + 4ab + 5a(b + c)
There are three terms. 2a is the first term. It has two factors: 2 and a. 4ab is the second term. It has three factors: 4, a, and b.
And 5a(b + c) is all one term. It also has three factors: 5, a, and (b + c).
To me, just as 5a(b + c) is one term, I feel that 2(9+3) is one term. I don't think it matters if you're dealing with variables or real numbers -- I can't see why that would change the rules. But again, I'm waiting for a bona fide NASA rocket scientist to chime in. I'm not taking the staunch position I was taking earlier, nor will I cast aspersions on the 288 camp.
If you want to draw a line it goes under the 48 and over the two, then you times that times 12. 288 all day. You have to put parentheses around the 2(9 + 3) if you want the Deuce.
Don't panic, that problem is very common in men your age....I just got an email advertising cheap Viagra, I can forward it to you if you wish. :-P
Implied Lisa? Or Implode?
For example, math people would understand that 1/2?? means 1/(2??), not ??/2. (Remember that ?? is a number.)
Also, 2(9 + 3) is structured like another frequently used form, the factored polynomial (albeit w/o variables).
These conventions jump out immediately, and signal Purpose behind the equation.
If the answer is "supposed" to be 288, the equation's only purpose would be obfuscation.
If, using the distributive property ..
2(9 + 3) is equivalent to "2 * 9 + 2 * 3"
and because this is part of a larger expression and 2(9 +3) is not protected by parantheses, we could have ...
48 ?? 2 * 9 + 2 * 3
following order of operations ...
24 * 9 + 2 * 3
216 + 2 * 3
216 + 6
222
Nope. The way the equation is written, you need to distribute both 2*9 and 2*3 as divisors of 48.
Like I said, I don't actually think it's the answer. Just playing with an ambiguous expression like everyone else.
edit ... though, that would make the answer an even more interesting 10.66.
Everyone talking about 2 like they knew. PEMDAS AND FOIL, like they knew.
I like the explanation that the division sign should not be in an equation and it should be written 48 over...
I still feel stupid because I don't know what * means in math.
It would probably hurt my brain to try to do some factoring today. But I do have a clear memory that a girl in my class had the rad 'popsicle stick' perm. So that her hair was in zig-zags. Now, THAT I remember like yesterday.
Yes please. Or perhaps a real meth problem.
Here's one. Is there any time where all three hands of an analog clock are exactly 120?? apart? If not, why not? If not, how close does a continuously sweeping clock come?
Lets substitute the 48 for a 1 to make it simpler, you get:
1??2(9+3)
=
1/2(9+3)
Now that would that give you Brains a 1/24 = f.a.i.l.
And 4:00:40.
nope and nope. At 8:00:20 the minute hand is 2?? past the hour so the second and minute hand are 118?? apart, and at 4:00:40, they're 122?? apart.
if you cut a piece of wood one foot long in half how long is each piece?
depends on which direction you cut it.
On second thought, I think it might be 124?? at 4:00:40.
Kerf-related!