48÷2(9+3) = ???

[kingcrux31]

Originally Posted by megachamploo

Originally Posted by kingcrux31

Originally Posted by il prescelto

Kingcrux31, please take a look at my proof. I'm re-posting it here, and I'm adding a picture of it.

"

Okay, for all the people who think the answer is 2, readthis and let me know what you think.
We start off with 48/2(9+3) = 48/2(12). We add the 9 and 3 first becausethey're in the parenthesis. I think everyone agrees on this step.
Now we have
48/2(12). Let us assume that 48/2(12) = 48/(2(12)) (which is what the peoplewho think the answer is 2 are assuming)
Since multiplication and division are inverse processes (in other words,XY=X(1/Y), we can do the following:
48/(2(12)) = 48(1/(2(12))) = 48 (1/2) (1/12)
Now let us turn those (1/2) and (1/12) back into division sign
48 (1/2) (1/12) = 48/2/12. And 48/2/12 surely does not equal 48/2(12). Therefore,our initial assumption is wrong.

Here’s just the math

48/2(9+3) = 48/2(12). Assume 48/2(12) = 48/(2(12)). Then, 48/2(12)= 48/(2(12)) = 48(1/(2(12))) = 48 (1/2) (1/2) = 48/2/12 =/= 48/2(12). Therefore,our initial assumption is wrong, and 48/2(12) should not be interpreted as48/(2(12)).
If anyone thinks this is wrong, let me know. Andby the way, some guy said people with college education say the answer is 2. MyHarvard, Caltech, MIT, Yale, Stanford, and Cal friends all say 288; I’m the sonof two Cal grads, and I’ve been a student at Cal myself….since we’re talkingabout credentials 

"

Here's where you got it wrong.


Same as what I posted earlier

Why do you think the (9+3) belongs in the denominator? did you read my earlier post quoting you?

Because it wasn't written as 48(9+3)÷2=

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[kingcrux31]

Originally Posted by megachamploo

Originally Posted by kingcrux31

Originally Posted by il prescelto

Kingcrux31, please take a look at my proof. I'm re-posting it here, and I'm adding a picture of it.

"

Okay, for all the people who think the answer is 2, readthis and let me know what you think.
We start off with 48/2(9+3) = 48/2(12). We add the 9 and 3 first becausethey're in the parenthesis. I think everyone agrees on this step.
Now we have
48/2(12). Let us assume that 48/2(12) = 48/(2(12)) (which is what the peoplewho think the answer is 2 are assuming)
Since multiplication and division are inverse processes (in other words,XY=X(1/Y), we can do the following:
48/(2(12)) = 48(1/(2(12))) = 48 (1/2) (1/12)
Now let us turn those (1/2) and (1/12) back into division sign
48 (1/2) (1/12) = 48/2/12. And 48/2/12 surely does not equal 48/2(12). Therefore,our initial assumption is wrong.

Here’s just the math

48/2(9+3) = 48/2(12). Assume 48/2(12) = 48/(2(12)). Then, 48/2(12)= 48/(2(12)) = 48(1/(2(12))) = 48 (1/2) (1/2) = 48/2/12 =/= 48/2(12). Therefore,our initial assumption is wrong, and 48/2(12) should not be interpreted as48/(2(12)).
If anyone thinks this is wrong, let me know. Andby the way, some guy said people with college education say the answer is 2. MyHarvard, Caltech, MIT, Yale, Stanford, and Cal friends all say 288; I’m the sonof two Cal grads, and I’ve been a student at Cal myself….since we’re talkingabout credentials 

"

Here's where you got it wrong.


Same as what I posted earlier

Why do you think the (9+3) belongs in the denominator? did you read my earlier post quoting you?

Because it wasn't written as 48(9+3)÷2=

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[wr]

Originally Posted by inspectah derek


We made it on the list! 

http://knowyourmeme.com/memes/48293

 

[wr]

Originally Posted by inspectah derek


We made it on the list! 

http://knowyourmeme.com/memes/48293

 

[megachamploo]

Originally Posted by kingcrux31

Originally Posted by megachamploo


Why do you think the (9+3) belongs in the denominator? did you read my earlier post quoting you?

Because it wasn't written as 48(9+3)÷2=

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You should read the earlier post I made quoting you. In a situation where it is important to be clear (like this or on a math test), 1/2x = x/2. It doesn't matter what the original writer of the equation meant to say, all that matters, is what the equation (as it is written) means.


3). Because the 2 is next to the (9+3) without a multiplication symbol it belongs in the denominator because of the juxtaposition rule. This is also wrong because even 1/2x = x/2 if you don't explicitly write it as 1/(2x). Yes, people will understand that you meant 1/(2x) when you write 1/2x for simplicity and they know you otherwise would have wrote it x/2. But on a math test, if you write 1/2x on a horizontal line, it means x/2.

 

[megachamploo]

Originally Posted by kingcrux31

Originally Posted by megachamploo


Why do you think the (9+3) belongs in the denominator? did you read my earlier post quoting you?

Because it wasn't written as 48(9+3)÷2=

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[/font]

[font=arial, sans-serif]
[/font]

You should read the earlier post I made quoting you. In a situation where it is important to be clear (like this or on a math test), 1/2x = x/2. It doesn't matter what the original writer of the equation meant to say, all that matters, is what the equation (as it is written) means.


3). Because the 2 is next to the (9+3) without a multiplication symbol it belongs in the denominator because of the juxtaposition rule. This is also wrong because even 1/2x = x/2 if you don't explicitly write it as 1/(2x). Yes, people will understand that you meant 1/(2x) when you write 1/2x for simplicity and they know you otherwise would have wrote it x/2. But on a math test, if you write 1/2x on a horizontal line, it means x/2.

 

[il prescelto]

Originally Posted by il prescelto

Originally Posted by kingcrux31

Originally Posted by il prescelto

Kingcrux31, please take a look at my proof. I'm re-posting it here, and I'm adding a picture of it.

"

Okay, for all the people who think the answer is 2, readthis and let me know what you think.
We start off with 48/2(9+3) = 48/2(12). We add the 9 and 3 first becausethey're in the parenthesis. I think everyone agrees on this step.
Now we have
48/2(12). Let us assume that 48/2(12) = 48/(2(12)) (which is what the peoplewho think the answer is 2 are assuming)
Since multiplication and division are inverse processes (in other words,XY=X(1/Y), we can do the following:
48/(2(12)) = 48(1/(2(12))) = 48 (1/2) (1/12)
Now let us turn those (1/2) and (1/12) back into division sign
48 (1/2) (1/12) = 48/2/12. And 48/2/12 surely does not equal 48/2(12). Therefore,our initial assumption is wrong.

Here’s just the math

48/2(9+3) = 48/2(12). Assume 48/2(12) = 48/(2(12)). Then, 48/2(12)= 48/(2(12)) = 48(1/(2(12))) = 48 (1/2) (1/2) = 48/2/12 =/= 48/2(12). Therefore,our initial assumption is wrong, and 48/2(12) should not be interpreted as48/(2(12)).
If anyone thinks this is wrong, let me know. Andby the way, some guy said people with college education say the answer is 2. MyHarvard, Caltech, MIT, Yale, Stanford, and Cal friends all say 288; I’m the sonof two Cal grads, and I’ve been a student at Cal myself….since we’re talkingabout credentials 

"

Here's where you got it wrong.


Same as what I posted earlier

Okay, I agree that the two aren't equal, that doesn't prove anything, though. As a matter of fact, the last line in my proof STATES that the two aren't equal; I wrote exactly the same thing as you did, so we agree on that...maybe you didn't read it very carefully?
Where in my proof did I ever say that the two WERE equal? Where in my proof did I do something that was wrong?

 

[il prescelto]

Originally Posted by il prescelto

Originally Posted by kingcrux31

Originally Posted by il prescelto

Kingcrux31, please take a look at my proof. I'm re-posting it here, and I'm adding a picture of it.

"

Okay, for all the people who think the answer is 2, readthis and let me know what you think.
We start off with 48/2(9+3) = 48/2(12). We add the 9 and 3 first becausethey're in the parenthesis. I think everyone agrees on this step.
Now we have
48/2(12). Let us assume that 48/2(12) = 48/(2(12)) (which is what the peoplewho think the answer is 2 are assuming)
Since multiplication and division are inverse processes (in other words,XY=X(1/Y), we can do the following:
48/(2(12)) = 48(1/(2(12))) = 48 (1/2) (1/12)
Now let us turn those (1/2) and (1/12) back into division sign
48 (1/2) (1/12) = 48/2/12. And 48/2/12 surely does not equal 48/2(12). Therefore,our initial assumption is wrong.

Here’s just the math

48/2(9+3) = 48/2(12). Assume 48/2(12) = 48/(2(12)). Then, 48/2(12)= 48/(2(12)) = 48(1/(2(12))) = 48 (1/2) (1/2) = 48/2/12 =/= 48/2(12). Therefore,our initial assumption is wrong, and 48/2(12) should not be interpreted as48/(2(12)).
If anyone thinks this is wrong, let me know. Andby the way, some guy said people with college education say the answer is 2. MyHarvard, Caltech, MIT, Yale, Stanford, and Cal friends all say 288; I’m the sonof two Cal grads, and I’ve been a student at Cal myself….since we’re talkingabout credentials 

"

Here's where you got it wrong.


Same as what I posted earlier

Okay, I agree that the two aren't equal, that doesn't prove anything, though. As a matter of fact, the last line in my proof STATES that the two aren't equal; I wrote exactly the same thing as you did, so we agree on that...maybe you didn't read it very carefully?
Where in my proof did I ever say that the two WERE equal? Where in my proof did I do something that was wrong?

 

[wr]

[h2]Mnemonics[/h2]
Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In Canada the acronym BEDMAS is common. It stands for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. In other English speaking countries, Brackets may be called Parentheses, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, and since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms asBIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, PEMDAS, and BPODMAS.

These mnemonics may be misleading, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer.

The correct answer is 9, which is best understood by thinking of the problem as the sum of positive ten, negative three, and positive two.

There is a new mnemonic featured in Danica McKellar's books Math Doesn't Suck[sup][2][/sup] and Kiss My Math[sup][3][/sup] that does address this very issue: "Pandas Eat: Mustard on Dumplings, and Apples with Spice." The intention being that Mustard and Dumplings is a "dinner course" and that Apples and Spice is a "dessert course." Then it becomes not a linear string of operations to do one after the other, but rather the "dinner course" operations are considered together and performed left to right, and then addition and subtraction are considered together, again performed again left to right.

http://en.wikipedia.org/wiki/Order_of_operations

 

[wr]

[h2]Mnemonics[/h2]
Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In Canada the acronym BEDMAS is common. It stands for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. In other English speaking countries, Brackets may be called Parentheses, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, and since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms asBIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, PEMDAS, and BPODMAS.

These mnemonics may be misleading, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer.

The correct answer is 9, which is best understood by thinking of the problem as the sum of positive ten, negative three, and positive two.

There is a new mnemonic featured in Danica McKellar's books Math Doesn't Suck[sup][2][/sup] and Kiss My Math[sup][3][/sup] that does address this very issue: "Pandas Eat: Mustard on Dumplings, and Apples with Spice." The intention being that Mustard and Dumplings is a "dinner course" and that Apples and Spice is a "dessert course." Then it becomes not a linear string of operations to do one after the other, but rather the "dinner course" operations are considered together and performed left to right, and then addition and subtraction are considered together, again performed again left to right.

http://en.wikipedia.org/wiki/Order_of_operations

 

[jchambers]

Without changing the equation to a different form or writing it a different way, can someone here quote a definitive source that states why the 2(12) should be done before the 48/2? What is the rule that leads you to believe this? My interpretation of the equation, the way it is written is accomplished by using strict order of operations that I was taught and are proven to be valid. This is an honest question. Can anyone answer it?

 

[jchambers]

Without changing the equation to a different form or writing it a different way, can someone here quote a definitive source that states why the 2(12) should be done before the 48/2? What is the rule that leads you to believe this? My interpretation of the equation, the way it is written is accomplished by using strict order of operations that I was taught and are proven to be valid. This is an honest question. Can anyone answer it?

 

[bananaboy2601]

Take the Order of Operations test

 

[bananaboy2601]

Take the Order of Operations test

 

[thehealthinspector]

Originally Posted by JChambers

Without changing the equation to a different form or writing it a different way, can someone here quote a definitive source that states why the 2(12) should be done before the 48/2? What is the rule that leads you to believe this? My interpretation of the equation, the way it is written is accomplished by using strict order of operations that I was taught and are proven to be valid. This is an honest question. Can anyone answer it?

thats the thing, they cant, just a website that cant even verify its own claim

the problem is that theyre imagining 2(9+3) as one term when its not, like Danica said - its an illusion

they cant even describe/understand why theyre imagining so other than referencing "the distributive property" which is just a property, not a rule, especially not one that overrides order-of-operations

 

[thehealthinspector]

Originally Posted by JChambers

Without changing the equation to a different form or writing it a different way, can someone here quote a definitive source that states why the 2(12) should be done before the 48/2? What is the rule that leads you to believe this? My interpretation of the equation, the way it is written is accomplished by using strict order of operations that I was taught and are proven to be valid. This is an honest question. Can anyone answer it?

thats the thing, they cant, just a website that cant even verify its own claim

the problem is that theyre imagining 2(9+3) as one term when its not, like Danica said - its an illusion

they cant even describe/understand why theyre imagining so other than referencing "the distributive property" which is just a property, not a rule, especially not one that overrides order-of-operations

 

[wr]

Originally Posted by JChambers

Without changing the equation to a different form or writing it a different way, can someone here quote a definitive source that states why the 2(12) should be done before the 48/2? What is the rule that leads you to believe this? My interpretation of the equation, the way it is written is accomplished by using strict order of operations that I was taught and are proven to be valid. This is an honest question. Can anyone answer it?

[h2]The Solution[/h2]

Inputting the problem on different calculators can lead to different results depending on if the calculator is non-scientific or scientific, and how the calculator interprets order of operations.​

There are considerable arguments for both answers, but the general consensus is that writing ambiguous fractions like “2/6xâ€

 

[wr]

Originally Posted by JChambers

Without changing the equation to a different form or writing it a different way, can someone here quote a definitive source that states why the 2(12) should be done before the 48/2? What is the rule that leads you to believe this? My interpretation of the equation, the way it is written is accomplished by using strict order of operations that I was taught and are proven to be valid. This is an honest question. Can anyone answer it?

[h2]The Solution[/h2]

Inputting the problem on different calculators can lead to different results depending on if the calculator is non-scientific or scientific, and how the calculator interprets order of operations.​

There are considerable arguments for both answers, but the general consensus is that writing ambiguous fractions like “2/6xâ€

 

[jchambers]

Originally Posted by BananaBoy2601


Take the Order of Operations test

Question #4 on that test proves that the answer is 288.

2x9-3(6-1)+1=4

 

[jchambers]

Originally Posted by BananaBoy2601


Take the Order of Operations test

Question #4 on that test proves that the answer is 288.

2x9-3(6-1)+1=4

 

[jchambers]

Originally Posted by TheHealthInspector

Originally Posted by JChambers

Without changing the equation to a different form or writing it a different way, can someone here quote a definitive source that states why the 2(12) should be done before the 48/2? What is the rule that leads you to believe this? My interpretation of the equation, the way it is written is accomplished by using strict order of operations that I was taught and are proven to be valid. This is an honest question. Can anyone answer it?

thats the thing, they cant, just a website that cant even verify its own claim

the problem is that theyre imagining 2(9+3) as one term when its not, like Danica said - its an illusion

they cant even describe/understand why theyre doing so other than referencing "the distributive property" which is just a property, not a rule, especially not one that overrides order-of-operations

I know that and that the distributive property does not override the order of operations. I have found one website that states that the 2(9+3) should be done first, but I can't find any official sources that state this or why.

 

[jchambers]

Originally Posted by TheHealthInspector

Originally Posted by JChambers

Without changing the equation to a different form or writing it a different way, can someone here quote a definitive source that states why the 2(12) should be done before the 48/2? What is the rule that leads you to believe this? My interpretation of the equation, the way it is written is accomplished by using strict order of operations that I was taught and are proven to be valid. This is an honest question. Can anyone answer it?

thats the thing, they cant, just a website that cant even verify its own claim

the problem is that theyre imagining 2(9+3) as one term when its not, like Danica said - its an illusion

they cant even describe/understand why theyre doing so other than referencing "the distributive property" which is just a property, not a rule, especially not one that overrides order-of-operations

I know that and that the distributive property does not override the order of operations. I have found one website that states that the 2(9+3) should be done first, but I can't find any official sources that state this or why.

 

[megachamploo]

Most of the people who think the answer is 2 believe that the (12) belongs under the denominator. They're thinking what the original writer of the question intended for the question to mean instead of what it really means just the way it is written. Most people think of implied multiplication as Wr posted above. But, the way it is written as it is, without an extra parentheses or modifications or consideration of the writer's intention, the answer is 288.

for an test, I would never write 1/(2x) as 1/2x unless I could bet that the grader would understand my intention. Traditionally, as it is written, 1/2x = x/2.

 

[megachamploo]

Most of the people who think the answer is 2 believe that the (12) belongs under the denominator. They're thinking what the original writer of the question intended for the question to mean instead of what it really means just the way it is written. Most people think of implied multiplication as Wr posted above. But, the way it is written as it is, without an extra parentheses or modifications or consideration of the writer's intention, the answer is 288.

for an test, I would never write 1/(2x) as 1/2x unless I could bet that the grader would understand my intention. Traditionally, as it is written, 1/2x = x/2.

 

[thehealthinspector]

edit - yeah, juxtaposition and "implied multiplication" are crocks

its trying to treat 5x as (5x) as if its different and "higher-order" from (5)(x)

same thing thats being done in this thread