Poll: What is the answer to 48/2(9+3)?

[mps4li3n]

I'm not trolling. The two is the coefficient of (9+3), meaning it technically is inside of the parentheses. Look up coefficients, you'll find a bunch of nonsense involving variables and stuff you won't understand. However, it won't matter, because I am not trolling. 2 is involved in the parentheses, therefore (9+3) is part of the denominator.

And that's the thing, you take it as a coefficient while others do not... and if this was given to someone in 8th grade it would have to be (42/2)....

Context is always important, which is why, unless i'm very sure of the intentions of whoever gave it to me i'd always ask about it.

And as i said before, notation can and does differ based on country... saying that because that's the notation you use for that doesn't instantly mean it's what everyone uses... or even that whoever gave you the formula isn't using the lack of * wrong (like he could be asking how much money he would make in 48 days is he's working half a shift and the full shift gave him 9+3 $ per day).

 

[Joseph Webb]

Here is the problem with that...
how does 48/2(9+3) become 48/2*(9+3)?

2(9+3) is NOT 2 * (9+3)
it is the simplified form of
((2*9)+(2*3))

by it your way you break the order of operations and Divide before you complete the Parentheses.

2(9 + 3) is equivalent to 2*(9+3)

2*9 + 2*3 = 18 + 6 = 24

2*(9+3) = 2*12 = 24

But that isn't the question.

The question is 48/2(9+3)

Which is evaluated as such

BEDMAS(or PEMDAS)

Brackets/Parentheses:

48/2(12)

Division & multiplication ( left to right)

24 * 12 = 288


Or if you prefer to distribute

48/2(9/3) = 48/2*9 + 48/2*3 = 288.

Honostly...

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.

Source:
http://www.purplemath.com/modules/orderops2.htm
(bottem half of page)

The fact that you where NOT taught this in basic algebra and that i have to go to 'purplemath' to prove you wrong hurts my brain...

The worst part is that I've already directed them to that page, and they didn't believe me still.

 

[mps4li3n]

Honostly...

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.

Source:
http://www.purplemath.com/modules/orderops2.htm
(bottem half of page)

The fact that you where NOT taught this in basic algebra and that i have to go to 'purplemath' to prove you wrong hurts my brain...

And even closer to the bottom it makes it clear that not everyone uses it like that and you should always ask your teacher...

 

[Joseph Webb]

I'm not trolling. The two is the coefficient of (9+3), meaning it technically is inside of the parentheses. Look up coefficients, you'll find a bunch of nonsense involving variables and stuff you won't understand. However, it won't matter, because I am not trolling. 2 is involved in the parentheses, therefore (9+3) is part of the denominator.

And that's the thing, you take it as a coefficient while others do not... and if this was given to someone in 8th grade it would have to be (42/2)....

Context is always important, which is why, unless i'm very sure of the intentions of whoever gave it to me i'd always ask about it.

And as i said before, notation can and does differ based on country... saying that because that's the notation you use for that doesn't instantly mean it's what everyone uses... or even that whoever gave you the formula isn't using the lack of * wrong (like he could be asking how much money he would make in 48 days is he's working half a shift and the full shift gave him 9+3 um per day).

No, that is what it means to everyone if it were written in the language that they're used to. I'm not even kidding you, you don't understand math if you think that what you're saying makes any sense. It doesn't matter when it comes to context, that's how the problem is written, the answer is 2. Stop arguing dude. The person in 8th grade would be wrong, and the teacher would tell them why the VERY NEXT DAY. Do you know why I know this? It's because that's how MY teacher taught MY class about how these work when considering the order of operations. Like I said, math is a universal language, it doesn't matter if the person is misinterpreting it, it's their fault for doing so, not the equation's, or anyone else's (aside from maybe a bad teacher). The original formula is correct, the answer is 2. If you want it to equal 288, you either need to write the original formula as (48/2)(9+3), or as 48/2*(9+3). There is no other way to look at this situation, stop trying to act like there is and I'm being oblivious. The individuals that are being oblivious are those that don't know what coefficients are, or that don't know what the distributive property is.

 

[Joseph Webb]

Honostly...

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.

Source:
http://www.purplemath.com/modules/orderops2.htm
(bottem half of page)

The fact that you where NOT taught this in basic algebra and that i have to go to 'purplemath' to prove you wrong hurts my brain...

And even closer to the bottom it makes it clear that not everyone uses it like that and you should always ask your teacher...

I already explained to you that the note at the bottom of the page lets you know that calculators don't do these functions correctly, and that some people have qualms with excluding the brackets for clarity's sake. It IN NO WAY states that people do these types of problems differently. I'll give you the benefit of the doubt seeing as English is your second language.

 

[Taerdin]

Honostly...

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.

Source:
http://www.purplemath.com/modules/orderops2.htm
(bottem half of page)

The fact that you where NOT taught this in basic algebra and that i have to go to 'purplemath' to prove you wrong hurts my brain...

there is a complex reason involving distribution, coeffecents and terms that are probably beyond your comperhension as to WHY you calculate numbers against brackets First... but i'll leave it at just Basic Algebra level for you...

You can't spell honestly... so your criticism of my academic prowess is pretty moot.

For the purposes of my education and my industry (computer programming) I do math like computers do math, so in my world 288 is the correct answer. Enjoy being right in your own world, and please stop coming into mine purely to insult me.

When you distribute the forty eight over two fraction into the brackets, you get 288 too by the way... so even your website agrees with me on my distribution method.

 

[mps4li3n]

I already explained to you that the note at the bottom of the page lets you know that calculators don't do these functions correctly, and that some people have qualms with excluding the brackets for clarity's sake. It IN NO WAY states that people do these types of problems differently. I'll give you the benefit of the doubt seeing as English is your second language.

You must have missed this part:

""and sometimes teachers view things differently. If in doubt, ask!""

My fault for quoting too much really.

 

[Joseph Webb]

Honostly...

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.

Source:
http://www.purplemath.com/modules/orderops2.htm
(bottem half of page)

The fact that you where NOT taught this in basic algebra and that i have to go to 'purplemath' to prove you wrong hurts my brain...

there is a complex reason involving distribution, coeffecents and terms that are probably beyond your comperhension as to WHY you calculate numbers against brackets First... but i'll leave it at just Basic Algebra level for you...

You can't spell honestly... so your criticism of my academic prowess is pretty moot.

For the purposes of my education and my industry (computer programming) I do math like computers do math, so in my world 288 is the correct answer. Enjoy being right in your own world, and please stop coming into mine purely to insult me.

Are you aware that they've fixed this problem in more recent editions of Texas Instruments calculators? If you're thinking like a computer, why aren't you think like the new calculators? Like I've said, old calculators are flawed in that they don't distribute properly. If you are thinking like these old computers, you aren't doing the problem correctly. It doesn't matter how you look at it, from a mathematical perspective, you are wrong. When it comes to a mathematical equation, the only perspective that matters is the mathematical one. Pro tip - If you were really thinking like a computer, you would have altered the equation in your mind to solve it correctly 48/[2(9+3)] Oh, and yeah, you are allowed to insert the brackets, because they're implied in the equation. Stop acting like you're right, because you're not.

 

[Taerdin]

You can't spell honestly... so your criticism of my academic prowess is pretty moot.

For the purposes of my education and my industry (computer programming) I do math like computers do math, so in my world 288 is the correct answer. Enjoy being right in your own world, and please stop coming into mine purely to insult me.

Are you aware that they've fixed this problem in more recent editions of Texas Instruments calculators? If you're thinking like a computer, why aren't you think like the new calculators? Like I've said, old calculators are flawed in that they don't distribute properly. If you are thinking like these old computers, you aren't doing the problem correctly. It doesn't matter how you look at it, from a mathematical perspective, you are wrong. When it comes to a mathematical equation, the only perspective that matters is the mathematical one. Pro tip - If you were really thinking like a computer, you would have altered the equation in your mind to solve it correctly 48/[2(9+3)] Oh, and yeah, you are allowed to insert the brackets, because they're implied in the equation. Stop acting like you're right, because you're not.

When you distribute the forty eight over two fraction into the brackets, you get 288 too by the way... so even your website agrees with me on my distribution method.

 

[Joseph Webb]

I already explained to you that the note at the bottom of the page lets you know that calculators don't do these functions correctly, and that some people have qualms with excluding the brackets for clarity's sake. It IN NO WAY states that people do these types of problems differently. I'll give you the benefit of the doubt seeing as English is your second language.

You must have missed this part:

""and sometimes teachers view things differently. If in doubt, ask!""

My fault for quoting too much really.

If a teacher tells you to solve that equation any other way, they should have their teaching license revoked. I'm sure that statement is to cover the ambiguities involved in the strict method of going at this problem (you could simply add the 9 and 3, and THEN multiply by two - slightly different order of operations, same result). However, that is not how math works. Math has be around A LOT longer than modern day computers. These rules have existed before the teachers that think they can change them have. You CAN NOT change the way these rules work unless you have irrefutable proof that the current rules are wrong. That's how math works. Computers have not shown a flaw in the current system, lazy programmers have. Lazy teachers have. Lazy students have.

 

[yeel]

according to you (and i say this without being condescending) the sign / implies a fraction. But not everything following it is part of that fraction. In honestly didn't know that and apparantly i really don't understand mathematical notation as well as you do.

Well notation is not set in stone and never was... a lot of people seem to think that because math is so must mathematical notations...

It's silly really... it's not like everyone who understood that putting 1 and 1 stick together makes 2 sticks used + in between them all of a sudden, or used the same symbol even if they where thousands of miles away, using totally different languages etc.

Maybe it would be better if this was somehow mentioned when people first learn these math rules just to create some patience and undertanding for these kind of situations. But i do understand why especially mathematicians might be a little bit more touchy on this stuff.

So just to help Joseph Webb out a bit here

mps4li3n offered a nice link (http://www.purplemath.com/modules/orderops2.htm) [EDIT correction this link was actually offered by Joseph Webb]

In it the following is mentioned:

"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."

This seems to be what Joseph Webb is referring to in his earlier arguments.
And according to this system, which seems to be pretty official, the answer would indeed be 2.

(But i still like the system which says it's 288)

 

[Joseph Webb]

You can't spell honestly... so your criticism of my academic prowess is pretty moot.

For the purposes of my education and my industry (computer programming) I do math like computers do math, so in my world 288 is the correct answer. Enjoy being right in your own world, and please stop coming into mine purely to insult me.

Are you aware that they've fixed this problem in more recent editions of Texas Instruments calculators? If you're thinking like a computer, why aren't you think like the new calculators? Like I've said, old calculators are flawed in that they don't distribute properly. If you are thinking like these old computers, you aren't doing the problem correctly. It doesn't matter how you look at it, from a mathematical perspective, you are wrong. When it comes to a mathematical equation, the only perspective that matters is the mathematical one. Pro tip - If you were really thinking like a computer, you would have altered the equation in your mind to solve it correctly 48/[2(9+3)] Oh, and yeah, you are allowed to insert the brackets, because they're implied in the equation. Stop acting like you're right, because you're not.

When you distribute the forty eight over two fraction into the brackets, you get 288 too by the way... so even your website agrees with me on my distribution method.

Are you stupid? Seriously. There is no way that can possibly come out to 288 unless you are typing it in wrong. Want me to take pictures of me typing it in? I'll do that for you buddy.
http://www.google.com/search?rlz=1C1SKPH_enUS384&aq=f&sourceid=chrome&ie=UTF-8&q=48%2F(2(9%2B3))
There it is in the google calculator. Is that wrong?

 

[mps4li3n]

For the purposes of my education and my industry (computer programming) I do math like computers do math, so in my world 288 is the correct answer. Enjoy being right in your own world, and please stop coming into mine purely to insult me.

And there lies the problem, people seem to think that different notation systems can't exist side by side because math is the same everywhere...

The reason why we have the same notations for math is one of convenience, so you can share more easily math proof and other stuff... if a computer system uses another type of notation it's not wrong math because if it was the computer wouldn't work, it's simply a different way to write the same thing, and sometimes the same symbol can be used for different things in different systems...

In the end whichever system is more popular will win out, or the losing system will be reserved for a niche of the population...

Having giant arguments about which system of notations is the only correct one is pointless because what you're arguing about is temporary...

Math on the other hand will be the same no matter id 2(x) means what either of you says it does or if it means 2-x a thousand years from now. It's just a symbol that's can depict anything as long as the person reading it and the one it's meant for understand it the same...

 

[Taerdin]

Are you stupid? Seriously. There is no way that can possibly come out to 288 unless you are typing it in wrong. Want me to take pictures of me typing it in? I'll do that for you buddy.
http://www.google.com/search?rlz=1C1SKPH_enUS384&aq=f&sourceid=chrome&ie=UTF-8&q=48%2F(2(9%2B3))
There it is in the google calculator. Is that wrong?

Patronise me all you want. (48/2)*9 + (48/2)*3 = 288, following the distribution of purple math. Do the multiplication implied by the brackets before the division, means you must distribute the fraction into the expression before simplifying it.

 

[mps4li3n]

If a teacher tells you to solve that equation any other way, they should have their teaching license revoked. I'm sure that statement is to cover the ambiguities involved in the strict method of going at this problem (you could simply add the 9 and 3, and THEN multiply by two - slightly different order of operations, same result). However, that is not how math works. Math has be around A LOT longer than modern day computers. These rules have existed before the teachers that think they can change them have. You CAN NOT change the way these rules work unless you have irrefutable proof that the current rules are wrong. That's how math works. Computers have not shown a flaw in the current system, lazy programmers have. Lazy teachers have. Lazy students have.

Pretty sure an 8th grade teacher that told a student to do the equation in the OP like you describe would be overstepping his curriculum...

AND IT'S NOT THE MATH RULES THAT PEOPLE ARE GETTING WRONG, IT'S THE SYMBOLS USED TO REPRESENT THEM.

JUST BECAUSE THE SYMBOL IS A FULL EQUATION LIKE 2(X+Y) DOES NOT MAKE THEM ANYTHING ELSE BUT SYMBOLS...

NOT UNDERSTANDING THAT NUANCE MAKES YOU LITTLE BETTER THEN THOSE COMPUTERS YOU SAY ARE DOING MATH WRONG (WHEN IT'S IMPOSIBLE FOR THEM TO WITHOUT FREEZING IN AN ERROR, THEY JUST AREN'T INTERPRETING THE SYMBOLS LIKE YOU AND THE MAJORITY OF THE MATHEMATICIANS APPARENTLY ARE).

 

[RonHiler]

Well, I have a build compiling, so I thought I'd drop in on this thread and see how it's going. Glad I did, I learned something new.

Precisely, so if one country uses the lack of the symbol * to mean something while another uses it just as if it's the same as using an * it in no way changes math...

The only problem would be people from the two countries not understanding what the other people are trying to say to them with the formula that uses the lack of an *.

This is what's happening here, except that we don't have any well defined borders.

This hits the nail on the head, I think.

Pyro, thanks for pointing out that 2(9 + 3) isn't equivalent to 2*(9+3) in some circles. That's interesting, and something I was never taught (and before you go off, Joseph, yes I did pass all my math classes, I'll be happy to compare advanced degrees with you any time you like. I have two of them).

It seems like that's the crux of our disagreement. It all depends on which of these forms you agree with:
2(9 + 3) == 2*(9+3)
2(9 + 3) != 2*(9+3)

Clearly, as pointed out by the very web site that Joseph linked to (and has been quoted several times), there is no true consensus on that, even teachers view it differently (obviously, since mine never said anything about them being different). So I suppose either answer is right, depending on your methodology. Good stuff.

Since I work with computers, I'll stick with the definition I know (and the one the computer knows). As far as I'm concerned, that one is right. However, I allow that others who were taught differently have a different perspective.

I wonder, however, if that second form [2(9 + 3) != 2*(9+3)] might not be falling out of favor with the advent of computers (which don't calculate it that way), and may evolve out of mathematics altogether. Interesting thought.

 

[Joseph Webb]

Are you stupid? Seriously. There is no way that can possibly come out to 288 unless you are typing it in wrong. Want me to take pictures of me typing it in? I'll do that for you buddy.
http://www.google.com/search?rlz=1C1SKPH_enUS384&aq=f&sourceid=chrome&ie=UTF-8&q=48%2F(2(9%2B3))
There it is in the google calculator. Is that wrong?

Patronise me all you want. (48/2)*9 + (48/2)*3 = 288, following the distribution of purple math. Do the multiplication implied by the brackets before the division, means you must distribute the fraction into the expression before simplifying it.

I will patronize you, because you can't do basic math functions. The FRACTION isn't the coefficient, JUST the 2 is. if the WHOLE fraction was the coefficient, it would be written as (48/2)(9+3). Did you even look at the example on purple math? It's the same situation. If you were to do the problem on purple math the way you're trying to solve it, it would look something like this. 16/2[8 ? 3(4 ? 2)] + 1 = 16/2(8-6)+1 = 16(8)/2-16(6)/2+1 = 128/2-96/2+1 = 64-48+1 = 16+1 = 17, which is NOT the right answer. If you can't see why, then I'm done trying to explain it to you. I'm not a math tutor.

 

[mps4li3n]

This hits the nail on the head, I think.

And i've been saying it for only about 10 pages...

But Crippling Overspecialisation is very hard to overcome:http://tvtropes.org/pmwiki/pmwiki.php/Main/CripplingOverspecialization

I wonder, however, if that second form [2(9 + 3) != 2*(9+3)] might not be falling out of favor with the advent of computers (which don't calculate it that way), and may evolve out of mathematics altogether. Interesting thought.

"Lol" is in teh official dictionary now, so that seems likely, even if it will take longer then language, which was always at the mercy of the masses, and only recently actually became formalized (well compared to math).

Did you even look at the example on purple math?

You know, it's funny how you rely on purplemath so much and yet dismissed the fact that they didn't say those teachers should be fired so easily... think they might have a reason for that?

 

[Joseph Webb]

If a teacher tells you to solve that equation any other way, they should have their teaching license revoked. I'm sure that statement is to cover the ambiguities involved in the strict method of going at this problem (you could simply add the 9 and 3, and THEN multiply by two - slightly different order of operations, same result). However, that is not how math works. Math has be around A LOT longer than modern day computers. These rules have existed before the teachers that think they can change them have. You CAN NOT change the way these rules work unless you have irrefutable proof that the current rules are wrong. That's how math works. Computers have not shown a flaw in the current system, lazy programmers have. Lazy teachers have. Lazy students have.

Pretty sure an 8th grade teacher that told a student to do the equation in the OP like you describe would be overstepping his curriculum...

AND IT'S NOT THE MATH RULES THAT PEOPLE ARE GETTING WRONG, IT'S THE SYMBOLS USED TO REPRESENT THEM.

JUST BECAUSE THE SYMBOL IS A FULL EQUATION LIKE 2(X+Y) DOES NOT MAKE THEM ANYTHING ELSE BUT SYMBOLS...

NOT UNDERSTANDING THAT NUANCE MAKES YOU LITTLE BETTER THEN THOSE COMPUTERS YOU SAY ARE DOING MATH WRONG (WHEN IT'S IMPOSIBLE FOR THEM TO WITHOUT FREEZING IN AN ERROR, THEY JUST AREN'T INTERPRETING THE SYMBOLS LIKE YOU AND THE MAJORITY OF THE MATHEMATICIANS APPARENTLY ARE).

No, It's the math rules they're getting wrong. NOTHING DENOTES A COEFFICIENT ASIDE FROM THE FACT THAT IT STANDS DIRECTLY NEXT TO ITS TERM. There is no symbol for it. It just is. Get over it dude, you and your symbols are wrong. Learning the order of operations is pre-algebra, I took pre-algebra in 7th grade. An 8th grade math teacher shouldn't even NEED to go over the order of operations to let you know how to distribute properly.

Well, I have a build compiling, so I thought I'd drop in on this thread and see how it's going. Glad I did, I learned something new.

Precisely, so if one country uses the lack of the symbol * to mean something while another uses it just as if it's the same as using an * it in no way changes math...

The only problem would be people from the two countries not understanding what the other people are trying to say to them with the formula that uses the lack of an *.

This is what's happening here, except that we don't have any well defined borders.

This hits the nail on the head, I think.

Pyro, thanks for pointing out that 2(9 + 3) isn't equivalent to 2*(9+3) in some circles. That's interesting, and something I was never taught (and before you go off, Joseph, yes I did pass all my math classes, I'll be happy to compare advanced degrees with you any time you like. I have two of them).

It seems like that's the crux of our disagreement. It all depends on which of these forms you agree with:
2(9 + 3) == 2*(9+3)
2(9 + 3) != 2*(9+3)

Clearly, as pointed out by the very web site that Joseph linked to (and has been quoted several times), there is no true consensus on that, even teachers view it differently (obviously, since mine never said anything about them being different). So I suppose either answer is right, depending on your methodology. Good stuff.

I wonder, however, if that second form [2(9 + 3) != 2*(9+3)] might not be falling out of favor with the advent of computers (which don't calculate it that way), and may evolve out of mathematics altogether. Interesting thought.

But that's exactly it. 2(9+3) =/= 2*(9+3), they are saying different things, and that's what you guys aren't understanding. In the equation 2(9+3), 2 is acting as the coefficient, which means that it is tied to the numbers (9 and 3 individually, at the same time) inside of the parentheses. In the equation 2*(9+3), 2 is tied to the sum of 9+3, and not to the numbers 9 and 3 individually. In the case that the 2 is tied to the numbers inside of the parenthesis (ex: 2(9+3)) the numbers in the parentheses will follow the 2 WHERE EVER it goes, meaning it will follow it into the denominator. Please tell me you're beginning to understand.

 

[Taerdin]

Are you stupid? Seriously. There is no way that can possibly come out to 288 unless you are typing it in wrong. Want me to take pictures of me typing it in? I'll do that for you buddy.
http://www.google.com/search?rlz=1C1SKPH_enUS384&aq=f&sourceid=chrome&ie=UTF-8&q=48%2F(2(9%2B3))
There it is in the google calculator. Is that wrong?

I think you typed the equation wrong

http://www.google.com/search?rlz=1C1SKPH_enUS384&aq=f&sourceid=chrome&ie=UTF-8&q=48%2F%282%289%2B3%29%29#sclient=psy&hl=en&rlz=1C1SKPH_enUS384&q=48%2F2%289%2B3%29&aq=f&aqi=&aql=&oq=&pbx=1&bav=on.2,or.r_gc.r_pw.&fp=c875dd2b8adea15a

As you can see the answer is 288. No need to call me stupid over getting frustrated that you were wrong, really uncalled for.