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48÷2(9+3) = ???
- Thread in 'General' Thread starter Started by n1k3b4ller,
- Start date
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its ambiguous because of your notion that 2(9+3) is a single term - which is never 100 percent proven
2(9+3) is no different from (2)(9+3) which = (2) * (9+3)
lets make things even more ambiguous: (4
÷(2)(9+3) = (4 ÷ (2) * (9+3) ..... left to right
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its ambiguous because of your notion that 2(9+3) is a single term - which is never 100 percent proven
2(9+3) is no different from (2)(9+3) which = (2) * (9+3)
lets make things even more ambiguous: (4
÷(2)(9+3) = (4 ÷ (2) * (9+3) ..... left to right
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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)â 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.
Prove to me how it can't be written as
48
------- x (9+3)
2
I stand by my point on claiming it's a stupid question and it can go either way
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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)â 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.
Prove to me how it can't be written as
48
------- x (9+3)
2
I stand by my point on claiming it's a stupid question and it can go either way
240Zestways
formerly mjair
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It is not one term because the equation could be written as 48÷2*12 and since you know how the orders of operations work, then apply it.
240Zestways
formerly mjair
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It is not one term because the equation could be written as 48÷2*12 and since you know how the orders of operations work, then apply it.
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44 pages
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44 pages
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That's the operative word. It's impossible to know whether it is one term or not
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That's the operative word. It's impossible to know whether it is one term or not
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Originally Posted by DecemberLove
Originally Posted by bruce negro
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:
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:Originally Posted by holdenmichael
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
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)â 48/2(9+3)
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.
Prove to me how it can't be written as
48
------- x (9+3)
2
I stand by my point on claiming it's a stupid question and it can go either way
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?
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Originally Posted by DecemberLove
Originally Posted by bruce negro
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:
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:Originally Posted by holdenmichael
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
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)â 48/2(9+3)
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.
Prove to me how it can't be written as
48
------- x (9+3)
2
I stand by my point on claiming it's a stupid question and it can go either way
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?
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Oh LOL
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Oh LOL
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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?
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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?
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Im an engineering major. Its 2.
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Im an engineering major. Its 2.
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Again, it's math. There's no guessing involved.Originally Posted by Millzhouse719
See what your saying with the / and the ÷ sign but do not think it is the issue in this topic. The biggest issue in here is that once we do (9+3) is it just 12 or (12). If it is 48÷2x12= 288 or 48÷2(12). I was taught that the parentheses stays with the sign even after we do the problem. So I will go with 2 for the sake of how I was taught.
48÷2â¢(9+3) isn't the same expression as 48÷2(9+3). The lack of a mathematical symbol between "2" and "(9+3)" means that they are a single term.
To provide a different example:
48÷2^2 (2 squared) = 12
That's different than:
48÷2â¢2=48
You get two different answers even though both 2^2 (2 squared) and 2â¢2 are 4.
That's incorrect. They can mean the same thing, but they don't have to mean the same thing and even then, the symbol that can vary in definition is "/," not "÷."
You can't interpret ÷ as a fraction just because there are two 24s in 48 and 48 halves are two wholes.
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Again, it's math. There's no guessing involved.Originally Posted by Millzhouse719
See what your saying with the / and the ÷ sign but do not think it is the issue in this topic. The biggest issue in here is that once we do (9+3) is it just 12 or (12). If it is 48÷2x12= 288 or 48÷2(12). I was taught that the parentheses stays with the sign even after we do the problem. So I will go with 2 for the sake of how I was taught.
48÷2â¢(9+3) isn't the same expression as 48÷2(9+3). The lack of a mathematical symbol between "2" and "(9+3)" means that they are a single term.
To provide a different example:
48÷2^2 (2 squared) = 12
That's different than:
48÷2â¢2=48
You get two different answers even though both 2^2 (2 squared) and 2â¢2 are 4.
That's incorrect. They can mean the same thing, but they don't have to mean the same thing and even then, the symbol that can vary in definition is "/," not "÷."
You can't interpret ÷ as a fraction just because there are two 24s in 48 and 48 halves are two wholes.
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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.
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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.
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no it doesnt
2(9+3) = (2)(9+3) = (2) * (9+3)
and
except: exponentials before multiplication
1st = exponential solved first, 2nd = left to right, pemdas - theres no guessing here because of rules but youre guessing on that "single term"
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no it doesnt
2(9+3) = (2)(9+3) = (2) * (9+3)
and
except: exponentials before multiplication
1st = exponential solved first, 2nd = left to right, pemdas - theres no guessing here because of rules but youre guessing on that "single term"
