48÷2(9+3) = ?
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Originally Posted By: wallyuwl
Originally Posted By: mechanicx
But the distributive and associative property argument has already been brought up in this thread long ago and the consensus was these properties have no bearing on the order of operations.
According to the college algebra book on my shelf, they do. As has said earlier in this thread, you need to get rid of the parentheses first before going on to multiplication/division. That is accomplished by using the distributive property.
I've looked at a few algebra books and some online sources and none of them said the distributive property of multiplication addresses the order of operation or takes precedence. They don't say evaluate a(b+c) by distributing the "a" first, instead they say the solution will be the same due to the distributive property but the order of operations say evaluate inside the paratheses first then evaluate by PEMDAS left to right. So it becomes 2(12) and now it is multiplication indicated by proximity to paratheses and nothing has to be distributed first.
This, the order of operations, is what the real debate is all about. You claim the order of operations rule says one thing, but your source is some algebra book that only you can read. There was only one source provided that says the 2 is tied to the paratheses and that was Purplemath.com. Anyway, its clear there's not going to be an agreement here. I wished some people would stop making the same arguments again and then no one would have to debate them
.
Originally Posted By: mechanicx
But the distributive and associative property argument has already been brought up in this thread long ago and the consensus was these properties have no bearing on the order of operations.
According to the college algebra book on my shelf, they do. As has said earlier in this thread, you need to get rid of the parentheses first before going on to multiplication/division. That is accomplished by using the distributive property.
I've looked at a few algebra books and some online sources and none of them said the distributive property of multiplication addresses the order of operation or takes precedence. They don't say evaluate a(b+c) by distributing the "a" first, instead they say the solution will be the same due to the distributive property but the order of operations say evaluate inside the paratheses first then evaluate by PEMDAS left to right. So it becomes 2(12) and now it is multiplication indicated by proximity to paratheses and nothing has to be distributed first.
This, the order of operations, is what the real debate is all about. You claim the order of operations rule says one thing, but your source is some algebra book that only you can read. There was only one source provided that says the 2 is tied to the paratheses and that was Purplemath.com. Anyway, its clear there's not going to be an agreement here. I wished some people would stop making the same arguments again and then no one would have to debate them
Originally Posted By: mechanicx
I wished some people would stop making the same arguments again and then no one would have to debate them
.
I wished some people would stop making the same arguments again and then no one would have to debate them
Originally Posted By: Quattro Pete
Originally Posted By: mechanicx
I wished some people would stop making the same arguments again and then no one would have to debate them
.
I'm not sure if you are laughing with me or at me
. But it's true, this thread was dead for while then it got revived (and not by me) with "new" arguments that were really the same old arguments that have already been debated to a standstill long ago
.
Originally Posted By: mechanicx
I wished some people would stop making the same arguments again and then no one would have to debate them
I'm not sure if you are laughing with me or at me
Originally Posted By: mechanicx
I'm not sure if you are laughing with me or at me
.
With you, of course.
I'm not sure if you are laughing with me or at me
With you, of course.
Here ya go ...
http://knowyourmeme.com/memes/48293
48 ÷ 2(9+3)=
48 ÷ 2(12)=
48 ÷ 24=
2
The example showing the answer as 2 above is wrong because per the order of operations, you do division and multiplication from left to right.
Should really be:
48 ÷ 2(9+3)=
48 ÷ 2(12)=
48 ÷ 2 x 12 =
288
It's kind of fun to see all the confusion and debating of this on the internet.
Quote from link:
"If one strictly uses the standard order of operations to solve mathematical expressions, the answer to the problem would be 288, which is also the same solution provided by WolframAlpha and Google."
http://knowyourmeme.com/memes/48293
48 ÷ 2(9+3)=
48 ÷ 2(12)=
48 ÷ 24=
2
The example showing the answer as 2 above is wrong because per the order of operations, you do division and multiplication from left to right.
Should really be:
48 ÷ 2(9+3)=
48 ÷ 2(12)=
48 ÷ 2 x 12 =
288
It's kind of fun to see all the confusion and debating of this on the internet.
Quote from link:
"If one strictly uses the standard order of operations to solve mathematical expressions, the answer to the problem would be 288, which is also the same solution provided by WolframAlpha and Google."
Physics chat board ... everyone is debating this thing.
http://www.physicsforums.com/showthread.php?t=488334
Decent answer IMO.
http://www.physicsforums.com/showpost.php?p=3235091&postcount=9
http://www.physicsforums.com/showthread.php?t=488334
Decent answer IMO.
http://www.physicsforums.com/showpost.php?p=3235091&postcount=9
Originally Posted By: ZeeOSix
Decent answer IMO.
http://www.physicsforums.com/showpost.php?p=3235091&postcount=9
Yup, and one that was already given here on one of the many prior pages.
But not everyone buys it, because PrupleMath obviously knows better....
Decent answer IMO.
http://www.physicsforums.com/showpost.php?p=3235091&postcount=9
Yup, and one that was already given here on one of the many prior pages.
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
Originally Posted By: ZeeOSix
Originally Posted By: poiuy223
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
Is that the same as 3÷4th grade math?
That would be 0.75 grade < 1(st) grade = even more sad!!!
Originally Posted By: poiuy223
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
Is that the same as 3÷4th grade math?
That would be 0.75 grade < 1(st) grade = even more sad!!!
Originally Posted By: poiuy223
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
As a future math teacher...would you say this equation, as presented, is a good question to be included on a test? And I mean, EXACTLY as it is written in the thread title.
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
As a future math teacher...would you say this equation, as presented, is a good question to be included on a test? And I mean, EXACTLY as it is written in the thread title.
Originally Posted By: LS2JSTS
Originally Posted By: poiuy223
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
As a future math teacher...would you say this equation, as presented, is a good question to be included on a test? And I mean, EXACTLY as it is written in the thread title.
This order of operations quiz has many equations written the same way. Look at #7 in particular. The correct answer will show if it is done the same way that 48÷2(9+3) = ? is done to obtain 288.
http://amby.com/educate/ord-op/pretest.html
Originally Posted By: poiuy223
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
As a future math teacher...would you say this equation, as presented, is a good question to be included on a test? And I mean, EXACTLY as it is written in the thread title.
This order of operations quiz has many equations written the same way. Look at #7 in particular. The correct answer will show if it is done the same way that 48÷2(9+3) = ? is done to obtain 288.
http://amby.com/educate/ord-op/pretest.html
Originally Posted By: ZeeOSix
Originally Posted By: QuadDriver
A lot of people jumped to the conclusion that 2(9+3) = 2*(9+3) but wars have started for less.
If they don't mean the same thing, then why do they give the same answer - I'm all ears ready to learn something new here. Any way you slice it, the answer is the same.
2(9+3) = 24
2*(9+3) = 24
2x(9+3) = 24
It doesn't matter what "symbol" is used to represent multiplication ... it's still multiplication.
No, you aren't willing to learn something new. You don't get that having an expression in isolation is different than if it is included as only part of a larger equation. The three notations you used above come up with the same answer in isolation, but as part of a larger problem they don't because without an "x" or asterisk between the 2 and parentheses you need to use the distributive property. Using the symbol or not does matter, contrary to what you say. But since you aren't willing to learn something new, you won't. It hasn't been just me saying this here, though I'm the most recent.
Originally Posted By: QuadDriver
A lot of people jumped to the conclusion that 2(9+3) = 2*(9+3) but wars have started for less.
If they don't mean the same thing, then why do they give the same answer - I'm all ears ready to learn something new here. Any way you slice it, the answer is the same.
2(9+3) = 24
2*(9+3) = 24
2x(9+3) = 24
It doesn't matter what "symbol" is used to represent multiplication ... it's still multiplication.
No, you aren't willing to learn something new. You don't get that having an expression in isolation is different than if it is included as only part of a larger equation. The three notations you used above come up with the same answer in isolation, but as part of a larger problem they don't because without an "x" or asterisk between the 2 and parentheses you need to use the distributive property. Using the symbol or not does matter, contrary to what you say. But since you aren't willing to learn something new, you won't. It hasn't been just me saying this here, though I'm the most recent.
Originally Posted By: wallyuwl
No, you aren't willing to learn something new. You don't get that having an expression in isolation is different than if it is included as only part of a larger equation. The three notations you used above come up with the same answer in isolation, but as part of a larger problem they don't because without an "x" or asterisk between the 2 and parentheses you need to use the distributive property. Using the symbol or not does matter, contrary to what you say. But since you aren't willing to learn something new, you won't. It hasn't been just me saying this here, though I'm the most recent.
Go read this thread ... maybe you'll learn something new.
http://www.physicsforums.com/showthread.php?t=488334
No, you aren't willing to learn something new. You don't get that having an expression in isolation is different than if it is included as only part of a larger equation. The three notations you used above come up with the same answer in isolation, but as part of a larger problem they don't because without an "x" or asterisk between the 2 and parentheses you need to use the distributive property. Using the symbol or not does matter, contrary to what you say. But since you aren't willing to learn something new, you won't. It hasn't been just me saying this here, though I'm the most recent.
Go read this thread ... maybe you'll learn something new.
http://www.physicsforums.com/showthread.php?t=488334
Originally Posted By: wallyuwl
The three notations you used above come up with the same answer in isolation, but as part of a larger problem they don't because without an "x" or asterisk between the 2 and parentheses you need to use the distributive property.
Forgot to say ... show some proof that the distributive property over rides the order of operations rules. I've searched high and low and can't find anything that talks about it. Can you?
The way the equation 48÷2(9+3) = ? is written, the order of operations says you must resolve what's in parentheses first and then do division and multiplication from left to right.
If you magically decide to do the distributive property 1st, then you are doing multiplication first and then on top of it doing addition before division
, which strictly goes against the O of O.
In order for this equation to equal 2 and follow the O of Os, it would have to be written as 48÷[2(9+3)] = ?
The three notations you used above come up with the same answer in isolation, but as part of a larger problem they don't because without an "x" or asterisk between the 2 and parentheses you need to use the distributive property.
Forgot to say ... show some proof that the distributive property over rides the order of operations rules. I've searched high and low and can't find anything that talks about it. Can you?
The way the equation 48÷2(9+3) = ? is written, the order of operations says you must resolve what's in parentheses first and then do division and multiplication from left to right.
If you magically decide to do the distributive property 1st, then you are doing multiplication first and then on top of it doing addition before division
In order for this equation to equal 2 and follow the O of Os, it would have to be written as 48÷[2(9+3)] = ?
Originally Posted By: LS2JSTS
Originally Posted By: poiuy223
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
As a future math teacher...would you say this equation, as presented, is a good question to be included on a test? And I mean, EXACTLY as it is written in the thread title.
Yes. Because it's questions like these that make students remember their mistakes. Trick questions leave memorable impressions.
Originally Posted By: poiuy223
I find this sad that people don't know simple 3/4th grade math. I'm so going to have fun when I become a math teacher.
As a future math teacher...would you say this equation, as presented, is a good question to be included on a test? And I mean, EXACTLY as it is written in the thread title.
Yes. Because it's questions like these that make students remember their mistakes. Trick questions leave memorable impressions.
In language, including math notation, we adhere to rules only because universality enables communication and progress. That doesn't change the fact that it is essentially arbitrary.
I can't imagine anyone would say that the current notation in this problem is BETTER than, say, (48 / 2) * (9 + 3). Even if you think the original notation is clear, I hope we can all agree that an extra set of parentheses would make it clearer.
I can't imagine anyone would say that the current notation in this problem is BETTER than, say, (48 / 2) * (9 + 3). Even if you think the original notation is clear, I hope we can all agree that an extra set of parentheses would make it clearer.
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