48÷2(9+3) = ???

[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

 

[jchambers]

Originally Posted by 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?

[h5]Implied Multiplication[/h5]
However, the answer 2 could be justified by the principle of implied multiplication. For example, consider the problem "2/5x."

If one strictly follows the standard order of operations, the correct interpretation would be “(2/5)*(x).â€

 

[jchambers]

Originally Posted by 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?

[h5]Implied Multiplication[/h5]
However, the answer 2 could be justified by the principle of implied multiplication. For example, consider the problem "2/5x."

If one strictly follows the standard order of operations, the correct interpretation would be “(2/5)*(x).â€

 

[il prescelto]

Originally Posted by Wr

• University of North Texas
• Northern Michigan University
• Deb Russell
• University of Minnesota Rochester
• Midland College
• Hofstra University

... All great institutions, I'm sure

 

[il prescelto]

Originally Posted by Wr

• University of North Texas
• Northern Michigan University
• Deb Russell
• University of Minnesota Rochester
• Midland College
• Hofstra University

... All great institutions, I'm sure

 

[jchambers]

Originally Posted by 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

Seems that way. I wonder if I am giving some of these posters too much credit by believing that there may be some rule or exception that I am not aware of. Maybe they just honestly don't understand the rules of operations for equations. Someone please prove me wrong with a valid source. I am getting depressed.

 

[jchambers]

Originally Posted by 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

Seems that way. I wonder if I am giving some of these posters too much credit by believing that there may be some rule or exception that I am not aware of. Maybe they just honestly don't understand the rules of operations for equations. Someone please prove me wrong with a valid source. I am getting depressed.

 

[Mactastic4167]

Originally Posted by Mac4167

I'm saying though, 43 pages?

I'm saying though, 86 pages?

 

[thehealthinspector]

Originally Posted by JChambers

Originally Posted by 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

Seems that way. I wonder if I am giving some of these posters too much credit by believing that there may be some rule or exception that I am not aware of. Maybe they just honestly don't understand the rules of operations for equations. Someone please prove me wrong with a valid source. I am getting depressed.

dont feel depressed

whats actually going on is that people are trying to misconstrue our common understanding of 2(9+3)... aka... 2*(9+3)....aka.... (2)(9+3).... aka.... (2)*(9+3) to IMPLY something thats not there

theyre trying to insist implied multiplication just because of how we understand that ^^^ this means multiplication... just because of how its been written without the multiplication symbol

if thats the case, how the hell are we supposed to write "implied division"

countries like china and japan would probably laugh and shake their head at this "implied' !%@$+@%%

 

[Mactastic4167]

Originally Posted by Mac4167

I'm saying though, 43 pages?

I'm saying though, 86 pages?

 

[thehealthinspector]

Originally Posted by JChambers

Originally Posted by 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

Seems that way. I wonder if I am giving some of these posters too much credit by believing that there may be some rule or exception that I am not aware of. Maybe they just honestly don't understand the rules of operations for equations. Someone please prove me wrong with a valid source. I am getting depressed.

dont feel depressed

whats actually going on is that people are trying to misconstrue our common understanding of 2(9+3)... aka... 2*(9+3)....aka.... (2)(9+3).... aka.... (2)*(9+3) to IMPLY something thats not there

theyre trying to insist implied multiplication just because of how we understand that ^^^ this means multiplication... just because of how its been written without the multiplication symbol

if thats the case, how the hell are we supposed to write "implied division"

countries like china and japan would probably laugh and shake their head at this "implied' !%@$+@%%

 

[sole vintage]

This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.

• Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
  • 
    16 ÷ 2[8 – 3(4 – 2)] + 1
        = 16 ÷ 2[8 – 3(2)] + 1
        = 16 ÷ 2[8 – 6] + 1
        = 16 ÷ 2[2] + 1   (**)
        = 16 ÷ 4 + 1
        = 4 + 1
        = 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!
(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!)

please end it

 

[sole vintage]

This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.

• Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
  • 
    16 ÷ 2[8 – 3(4 – 2)] + 1
        = 16 ÷ 2[8 – 3(2)] + 1
        = 16 ÷ 2[8 – 6] + 1
        = 16 ÷ 2[2] + 1   (**)
        = 16 ÷ 4 + 1
        = 4 + 1
        = 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!
(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!)

please end it

 

[inspectah derek]

HERE is the end! If this discussion continues, please quote this for every new page. 

http://www.neogaf.com/for...26053&postcount=2590

by Jocchan

I ended up writing a long post, hoping it can be just quoted to at least try to stop the same ol' cycle from starting over and over again.


The equation source of this discussion is 48÷2(9+3) = ????.

Most people able to solve basic first degree equations come up with two different solutions: 288 and 2. Why two and not one? Because the equation is written ambiguously.

The (9+3) can, in fact, be seen either as a number multiplied by the result of 48÷2, or as part of the denominator, together with the 2, the number 48 is divided by. So:

- The ones coming up with 288 see it as:

48
-- * (9+3)
2

- The ones coming up with 2 see it as:

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

Why both camps are correct:
- The ones coming up with 288 are applying basic math rules, and considering the division sign as a simple division between the two numbers around it. Nothing strange, and nothing worth explaining. It's simply correct.

- The ones coming up with 2 are applying a type of notation commonly used in calculus, physics and chemistry where 1/xy is used to represent on a single line the fraction

1
--
xy
and not (1/x) multiplied by y. In this notation, y is also part of the denominator.
This notation is commonly used with implicit products, and usually with short expressions. Whether or not this is a consequence of implicit products by juxtaposition appearing as prioritary, at least visually since the elements are portrayed as "bound" together, compared to regular multiplications and divisions making the elements appear as more separate, is not really relevant. Fact is it's a real convention and it's commonly used in several textbooks and slides.

Proof: just do a Google search for "1/2

 

[inspectah derek]

HERE is the end! If this discussion continues, please quote this for every new page. 

http://www.neogaf.com/for...26053&postcount=2590

by Jocchan

I ended up writing a long post, hoping it can be just quoted to at least try to stop the same ol' cycle from starting over and over again.


The equation source of this discussion is 48÷2(9+3) = ????.

Most people able to solve basic first degree equations come up with two different solutions: 288 and 2. Why two and not one? Because the equation is written ambiguously.

The (9+3) can, in fact, be seen either as a number multiplied by the result of 48÷2, or as part of the denominator, together with the 2, the number 48 is divided by. So:

- The ones coming up with 288 see it as:

48
-- * (9+3)
2

- The ones coming up with 2 see it as:

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

Why both camps are correct:
- The ones coming up with 288 are applying basic math rules, and considering the division sign as a simple division between the two numbers around it. Nothing strange, and nothing worth explaining. It's simply correct.

- The ones coming up with 2 are applying a type of notation commonly used in calculus, physics and chemistry where 1/xy is used to represent on a single line the fraction

1
--
xy
and not (1/x) multiplied by y. In this notation, y is also part of the denominator.
This notation is commonly used with implicit products, and usually with short expressions. Whether or not this is a consequence of implicit products by juxtaposition appearing as prioritary, at least visually since the elements are portrayed as "bound" together, compared to regular multiplications and divisions making the elements appear as more separate, is not really relevant. Fact is it's a real convention and it's commonly used in several textbooks and slides.

Proof: just do a Google search for "1/2

 

[balloonoboy]

It ain't gonna work, B.

Various posters, myself included, been said this was written poorly to incite such meaningless discussions, over basic %+! algebra.

Dudes flaunting their degrees and those of their distant cousins. Only a middle school certificate is needed.

 

[balloonoboy]

It ain't gonna work, B.

Various posters, myself included, been said this was written poorly to incite such meaningless discussions, over basic %+! algebra.

Dudes flaunting their degrees and those of their distant cousins. Only a middle school certificate is needed.

 

[waystinthyme]

Originally Posted by JChambers

Originally Posted by 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?

[h5]Implied Multiplication[/h5]
However, the answer 2 could be justified by the principle of implied multiplication. For example, consider the problem "2/5x."

If one strictly follows the standard order of operations, the correct interpretation would be “(2/5)*(x).â€

 

[waystinthyme]

Originally Posted by JChambers

Originally Posted by 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?

[h5]Implied Multiplication[/h5]
However, the answer 2 could be justified by the principle of implied multiplication. For example, consider the problem "2/5x."

If one strictly follows the standard order of operations, the correct interpretation would be “(2/5)*(x).â€

 

[jthagreat]

so 2 or 288

 

[jthagreat]

so 2 or 288

 

[DPancakes]

Okay so 288 is the right one. Cool.

 

[DPancakes]

Okay so 288 is the right one. Cool.

 

[jking0821]

Team 2 checking in

or maybe team 288

no team 2....def team 2

i think

 

[jking0821]

Team 2 checking in

or maybe team 288

no team 2....def team 2

i think