48÷2(9+3) = ???

[bruce negro]

Wait, so can the 2s claim victory since no one has been able to disprove the 2 ways of solving we've come up with yet? We can talk about whether ÷ and / are the same after we've won. With the reasoning that's on the second post of this page, the 288s have nothing. So can we claim victory and then get to the other stuff?

 

[bruce negro]

Wait, so can the 2s claim victory since no one has been able to disprove the 2 ways of solving we've come up with yet? We can talk about whether ÷ and / are the same after we've won. With the reasoning that's on the second post of this page, the 288s have nothing. So can we claim victory and then get to the other stuff?

 

[decemberlove]

Originally Posted by bruce negro

Originally Posted by DecemberLove

Originally Posted by bruce negro


The real question is: What would make you think that the parentheses shouldn't be in the denominator when it is CLEARLY behind the division sign. What makes it different from the 2, which is also behind the division sign? Nothing. If you added parentheses so that the problem was (48÷2)x(9+3), then the question would be written like you show above. The only problem is that it ISN'T written like that, so the problem MUST be written as:

48
----
2(9+3)

That is the answer to your question, have I proved it to you well? I would also like to cite that every time Google or WolframAlpha has come up with the answer 288, you can see that the input has been changed to add parentheses like in this question: (48÷2)x(9+3). If you need proof of that, I'll show it to you, but it's already been posted within this thread. This answers your question. Are there any more questions?

I'm not disagreeing with you at all and my initial answer would also be two but I'm trying to say that the original equation is indeed ambiguous.  Are we in agreement that 2(9+3) is one term?

Yes, I would say that 2(9+3) is one term. However, I don't think that the original equation is ambiguous. The reasoning from the original post I made which started this conversation between you and I, and the reasoning within this conversation, points to the fact that the answer is clearly 2, no matter which method you use to solve it.

Ok riddle me this.  I'm sure you're smart enough to know that [h3]48÷2(9+3) is not the same as (48÷2)x(9+3) but I believe 48÷2(9+3) can be written as 48/2 x (9+3) therefore the original question being ambiguous.[/h3]
How would you type in the original question in a calculator?

 

[decemberlove]

Originally Posted by bruce negro

Originally Posted by DecemberLove

Originally Posted by bruce negro


The real question is: What would make you think that the parentheses shouldn't be in the denominator when it is CLEARLY behind the division sign. What makes it different from the 2, which is also behind the division sign? Nothing. If you added parentheses so that the problem was (48÷2)x(9+3), then the question would be written like you show above. The only problem is that it ISN'T written like that, so the problem MUST be written as:

48
----
2(9+3)

That is the answer to your question, have I proved it to you well? I would also like to cite that every time Google or WolframAlpha has come up with the answer 288, you can see that the input has been changed to add parentheses like in this question: (48÷2)x(9+3). If you need proof of that, I'll show it to you, but it's already been posted within this thread. This answers your question. Are there any more questions?

I'm not disagreeing with you at all and my initial answer would also be two but I'm trying to say that the original equation is indeed ambiguous.  Are we in agreement that 2(9+3) is one term?

Yes, I would say that 2(9+3) is one term. However, I don't think that the original equation is ambiguous. The reasoning from the original post I made which started this conversation between you and I, and the reasoning within this conversation, points to the fact that the answer is clearly 2, no matter which method you use to solve it.

Ok riddle me this.  I'm sure you're smart enough to know that [h3]48÷2(9+3) is not the same as (48÷2)x(9+3) but I believe 48÷2(9+3) can be written as 48/2 x (9+3) therefore the original question being ambiguous.[/h3]
How would you type in the original question in a calculator?

 

[bachelor frog]

Wait, so can the 2s claim victory since no one has been able to disprove the 2 ways of solving we've come up with yet? We can talk about whether ÷ and / are the same after we've won. With the reasoning that's on the second post of this page, the 288s have nothing. So can we claim victory and then get to the other stuff?

Nah, just read what I posted, and apply your theory ... it will fail. Oh and 2(9+3) it is the same as 2*(9+3).

Ok ... so how about this:
You got simple 0,5 * 10 = 5 , cool ? ok ...

In other words it's  1÷2 * 10 = 5 , right ? ...

[font=Arial, Helvetica, sans-serif]so you can say it is for instance [/font]1÷2 * (8+2) = 5 ... yeah do the math (pun intended)

 

[bachelor frog]

Wait, so can the 2s claim victory since no one has been able to disprove the 2 ways of solving we've come up with yet? We can talk about whether ÷ and / are the same after we've won. With the reasoning that's on the second post of this page, the 288s have nothing. So can we claim victory and then get to the other stuff?

Nah, just read what I posted, and apply your theory ... it will fail. Oh and 2(9+3) it is the same as 2*(9+3).

Ok ... so how about this:
You got simple 0,5 * 10 = 5 , cool ? ok ...

In other words it's  1÷2 * 10 = 5 , right ? ...

[font=Arial, Helvetica, sans-serif]so you can say it is for instance [/font]1÷2 * (8+2) = 5 ... yeah do the math (pun intended)

 

[bruce negro]

Originally Posted by DecemberLove

Originally Posted by bruce negro

Originally Posted by DecemberLove


I'm not disagreeing with you at all and my initial answer would also be two but I'm trying to say that the original equation is indeed ambiguous.  Are we in agreement that 2(9+3) is one term?

Yes, I would say that 2(9+3) is one term. However, I don't think that the original equation is ambiguous. The reasoning from the original post I made which started this conversation between you and I, and the reasoning within this conversation, points to the fact that the answer is clearly 2, no matter which method you use to solve it.

Ok riddle me this.  I'm sure you're smart enough to know that [h3]48÷2(9+3) is not the same as (48÷2)x(9+3) but I believe 48÷2(9+3) can be written as 48/2 x (9+3) therefore the original question being ambiguous.[/h3]
How would you type in the original question in a calculator?

Writing the question as 48/2x(9+3) makes it a fraction. This fraction would be written like this:

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

It would be solved as such. The problem is not ambiguous. If typed into a calculator, due to the limitations of a calculator, I would type the whole thing in as 48/((2(9+3)). No need to do that though, when it can easily be done by hand the way I posted above.

Bachelor Frog, I'll either edit this post or post another one once I see what you wrote. December, are we good?

 

[certifiedsw]

Originally Posted by pacmagic2002

Originally Posted by CertifiedSW

Originally Posted by pacmagic2002

I want to know what the people that are saying the first answer is 2 have to say.  I want to know if they came up with the same answer for both, or 2 different answers.

The answer to the first one is 2 though.....

and the 2nd one?

I was joking haha

 

[bruce negro]

Originally Posted by DecemberLove

Originally Posted by bruce negro

Originally Posted by DecemberLove


I'm not disagreeing with you at all and my initial answer would also be two but I'm trying to say that the original equation is indeed ambiguous.  Are we in agreement that 2(9+3) is one term?

Yes, I would say that 2(9+3) is one term. However, I don't think that the original equation is ambiguous. The reasoning from the original post I made which started this conversation between you and I, and the reasoning within this conversation, points to the fact that the answer is clearly 2, no matter which method you use to solve it.

Ok riddle me this.  I'm sure you're smart enough to know that [h3]48÷2(9+3) is not the same as (48÷2)x(9+3) but I believe 48÷2(9+3) can be written as 48/2 x (9+3) therefore the original question being ambiguous.[/h3]
How would you type in the original question in a calculator?

Writing the question as 48/2x(9+3) makes it a fraction. This fraction would be written like this:

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

It would be solved as such. The problem is not ambiguous. If typed into a calculator, due to the limitations of a calculator, I would type the whole thing in as 48/((2(9+3)). No need to do that though, when it can easily be done by hand the way I posted above.

Bachelor Frog, I'll either edit this post or post another one once I see what you wrote. December, are we good?

 

[certifiedsw]

Originally Posted by pacmagic2002

Originally Posted by CertifiedSW

Originally Posted by pacmagic2002

I want to know what the people that are saying the first answer is 2 have to say.  I want to know if they came up with the same answer for both, or 2 different answers.

The answer to the first one is 2 though.....

and the 2nd one?

I was joking haha

 

[dmbrhs]

The final answer is that we are all losers and the Internet wins. Moving on....

 

[dmbrhs]

The final answer is that we are all losers and the Internet wins. Moving on....

 

[bruce negro]

Originally Posted by Bachelor frog

Wait, so can the 2s claim victory since no one has been able to disprove the 2 ways of solving we've come up with yet? We can talk about whether ÷ and / are the same after we've won. With the reasoning that's on the second post of this page, the 288s have nothing. So can we claim victory and then get to the other stuff?

Nah, just read what I posted, and apply your theory ... it will fail. Oh and 2(9+3) it is the same as 2*(9+3).

Ok ... so how about this:
You got simple 0,5 * 10 = 5 , cool ? ok ...

In other words it's  1÷2 * 10 = 5 , right ? ...

[font=Arial, Helvetica, sans-serif]so you can say it is for instance [/font]1÷2 * (8+2) = 5 ... yeah do the math (pun intended)

You need to put parentheses around your 1/2 since it's already understood to be .5. Once you do that, you simply multiply (1/2)*(10), and yeah, you'll get 5.

 

[bruce negro]

Originally Posted by Bachelor frog

Wait, so can the 2s claim victory since no one has been able to disprove the 2 ways of solving we've come up with yet? We can talk about whether ÷ and / are the same after we've won. With the reasoning that's on the second post of this page, the 288s have nothing. So can we claim victory and then get to the other stuff?

Nah, just read what I posted, and apply your theory ... it will fail. Oh and 2(9+3) it is the same as 2*(9+3).

Ok ... so how about this:
You got simple 0,5 * 10 = 5 , cool ? ok ...

In other words it's  1÷2 * 10 = 5 , right ? ...

[font=Arial, Helvetica, sans-serif]so you can say it is for instance [/font]1÷2 * (8+2) = 5 ... yeah do the math (pun intended)

You need to put parentheses around your 1/2 since it's already understood to be .5. Once you do that, you simply multiply (1/2)*(10), and yeah, you'll get 5.

 

[bruce negro]

Posting this again in case people don't read the last page:

ATTENTION PLEASE. Read the below before posting any other bull.

ALRIGHT. I've figured out why, without a doubt, 2 is the right answer.

The argument about this problem has gone many places, but I think one of the places where it went wrong was with HoldenMichael (no offense). After watching some pr0n, I thought again about this problem with a clear head, and the answer is apparent.

Here, HoldenMichael tells us why ÷ and / are not the same thing:

Originally Posted by holdenmichael

bruce negro wrote:

I refute your refutation on the grounds that both signs actually hold the same mathematical meaning. They are actually interchangeable in a way.

No, 48÷2 is spoken as 48 divided by 2.
48/2 is spoken as 48 halves.

Just because both 48 halves are 2 wholes and 48 divided by 2 equals 2 doesn't mean that the symbols for division and fraction are interchangeable in an equation.  One is the addition of fractions of a whole ("I have 48 halves.") and the other is the division of a dividend (4 by a divisor (2; "I took away half of my 48.").

I've only read the first page and the last two pages so the sample size is small, but I have yet to read an opinion that would dissuade me from my belief that:

48÷2=48/2

48÷2(9+3)≠48/2(9+3)

After my immediate refutation, I reconsidered this and thought he was right. HOWEVER, I realized soon afterwards that they are indeed the same, and here is why:

The problem states: 48÷2(9+3). We already proved that through distribution, this problem can be written as 48÷((2*9)+(2*3)). This then simplifies to 48÷(18+6), which simplifies to 48÷(24), which is equal to 2.

NOW, we have the issue of, "What if you interpret this as a fraction?" Above, HoldenMichael writes 48/2, and that makes sense.... but the real problem is that Holden forgets to write the rest of the problem in the denominator. There is nothing that separates the (9+3) from being in the denominator along with the 2. So in reality, if one would look at the ÷ as a / sign, the problem would look like this:

48
----
2(9+3)

This would then simplify to

48
----
2(12)

Then

48
----
(24)

Which is equal to

2.

We have now proven that the answer is 2, 2 different ways solidly. We have also given valid reasons and proof as to why calculators and other mathematical engines are unreliable. These methods also are not based on whether Multiplication goes before Division, which I think we are all now in consensus that it doesn't. If you would like to argue further, please disprove both of these methods.

 

[bruce negro]

Posting this again in case people don't read the last page:

ATTENTION PLEASE. Read the below before posting any other bull.

ALRIGHT. I've figured out why, without a doubt, 2 is the right answer.

The argument about this problem has gone many places, but I think one of the places where it went wrong was with HoldenMichael (no offense). After watching some pr0n, I thought again about this problem with a clear head, and the answer is apparent.

Here, HoldenMichael tells us why ÷ and / are not the same thing:

Originally Posted by holdenmichael

bruce negro wrote:

I refute your refutation on the grounds that both signs actually hold the same mathematical meaning. They are actually interchangeable in a way.

No, 48÷2 is spoken as 48 divided by 2.
48/2 is spoken as 48 halves.

Just because both 48 halves are 2 wholes and 48 divided by 2 equals 2 doesn't mean that the symbols for division and fraction are interchangeable in an equation.  One is the addition of fractions of a whole ("I have 48 halves.") and the other is the division of a dividend (4 by a divisor (2; "I took away half of my 48.").

I've only read the first page and the last two pages so the sample size is small, but I have yet to read an opinion that would dissuade me from my belief that:

48÷2=48/2

48÷2(9+3)≠48/2(9+3)

After my immediate refutation, I reconsidered this and thought he was right. HOWEVER, I realized soon afterwards that they are indeed the same, and here is why:

The problem states: 48÷2(9+3). We already proved that through distribution, this problem can be written as 48÷((2*9)+(2*3)). This then simplifies to 48÷(18+6), which simplifies to 48÷(24), which is equal to 2.

NOW, we have the issue of, "What if you interpret this as a fraction?" Above, HoldenMichael writes 48/2, and that makes sense.... but the real problem is that Holden forgets to write the rest of the problem in the denominator. There is nothing that separates the (9+3) from being in the denominator along with the 2. So in reality, if one would look at the ÷ as a / sign, the problem would look like this:

48
----
2(9+3)

This would then simplify to

48
----
2(12)

Then

48
----
(24)

Which is equal to

2.

We have now proven that the answer is 2, 2 different ways solidly. We have also given valid reasons and proof as to why calculators and other mathematical engines are unreliable. These methods also are not based on whether Multiplication goes before Division, which I think we are all now in consensus that it doesn't. If you would like to argue further, please disprove both of these methods.

 

[thehealthinspector]

2 people say: 2(9+3) is one term

288 people say: 2(9+3) is NOT one term

neither side has proven that the opposite is false

edit - "general consensus" sounds like ambiguity to me, i doubt any of those people can point to an actual rule

 

[thehealthinspector]

2 people say: 2(9+3) is one term

288 people say: 2(9+3) is NOT one term

neither side has proven that the opposite is false

edit - "general consensus" sounds like ambiguity to me, i doubt any of those people can point to an actual rule

 

[holdenmichael]

Originally Posted by TheHealthInspector

Originally Posted by holdenmichael

The lack of a mathematical symbol between "2" and "(9+3)" means that they are a single term.

no it doesnt

2(9+3) = (2)(9+3) = (2) * (9+3)

See the last example on the following page: http://www.purplemath.com/modules/orderops2.htm
http://www.purplemath.com/modules/orderops2.htmUsing their example, they'd give priority to "2(12)" over "48÷2" because the parentheses are still there and the "2" is right next to it without a mathematical symbol between the two.

Again, 48÷2(9+3) is not the same as 48÷2•12.

 

[holdenmichael]

Originally Posted by TheHealthInspector

Originally Posted by holdenmichael

The lack of a mathematical symbol between "2" and "(9+3)" means that they are a single term.

no it doesnt

2(9+3) = (2)(9+3) = (2) * (9+3)

See the last example on the following page: http://www.purplemath.com/modules/orderops2.htm
http://www.purplemath.com/modules/orderops2.htmUsing their example, they'd give priority to "2(12)" over "48÷2" because the parentheses are still there and the "2" is right next to it without a mathematical symbol between the two.

Again, 48÷2(9+3) is not the same as 48÷2•12.

 

[bruce negro]

Originally Posted by TheHealthInspector

2 people say: 2(9+3) is one term

288 people say: 2(9+3) is NOT one term

neither side has proven that the opposite is false

One term by juxtaposition. The 2 is juxtaposed with the parentheses. This was proven PAGES ago.

If this is the only thing being argued now, then we'll wait for Monday. But just so you know, they'll say that it is one term because the 2 is juxtaposed with the parentheses. The 2 methods above definitely work, and prove that the 2s have won.

 

[bruce negro]

Originally Posted by TheHealthInspector

2 people say: 2(9+3) is one term

288 people say: 2(9+3) is NOT one term

neither side has proven that the opposite is false

One term by juxtaposition. The 2 is juxtaposed with the parentheses. This was proven PAGES ago.

If this is the only thing being argued now, then we'll wait for Monday. But just so you know, they'll say that it is one term because the 2 is juxtaposed with the parentheses. The 2 methods above definitely work, and prove that the 2s have won.

 

[bachelor frog]

You need to put parentheses around your 1/2 since it's already understood to be .5. Once you do that, you simply multiply (1/2)*(10), and yeah, you'll get 5.

No you don't need to put anything. There is order of opreations :

1. Calculations must be done from left to right.

4. Multiply and divide in the order the operations occur.

http://math.about.com/library/weekly/aa040502a.htm

So first you do the 1:2 , then you multiply

 

[bachelor frog]

You need to put parentheses around your 1/2 since it's already understood to be .5. Once you do that, you simply multiply (1/2)*(10), and yeah, you'll get 5.

No you don't need to put anything. There is order of opreations :

1. Calculations must be done from left to right.

4. Multiply and divide in the order the operations occur.

http://math.about.com/library/weekly/aa040502a.htm

So first you do the 1:2 , then you multiply

 

[thehealthinspector]

Originally Posted by bruce negro

Originally Posted by TheHealthInspector

2 people say: 2(9+3) is one term

288 people say: 2(9+3) is NOT one term

neither side has proven that the opposite is false

One term by juxtaposition. The 2 is juxtaposed with the parentheses. This was proven PAGES ago.

If this is the only thing being argued now, then we'll wait for Monday. But if not, then the 2 methods above definitely work, and prove that the 2s have won.

(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)


its not a RULE, therefore nothing has been proven false