48÷2(9+3) = ????

[KarlCarrera]

288

Follow order of operations correctly. Multiplication and division have the same priority so go left to right after you simplify what is in parentheses.

48/2(9+3)=
48/2(12)=
24(12)=
288

Karl
88 Targa

[island911]

Originally Posted by svandamme

They are not points of view, they are mathematical rules.
They are not opinions
They are not guesses
They are not open for interpretation...

and

there is a rule that says when operations are at the same precedence level, do left to right.

Yeah, and there is a rule that says when writing a sentence we start with a the first letter capitalized. --bfd.

Seriously we all -get- that there are rules (damn-it)

Now I certainly appreciate the 'rules' thought, but sorry, the OP eqn is a classic example of math notation ambiguity. (mixing 3rd grade symboligy ÷ w/ more advanced notation grouping) ...Now had the eqn been 48 ÷ 2 x (9+3) ...then yeah, the L/R-rule-nazis^* would have an easy 288 win.

. . .And for you rules-nazis; consider that if mathematical notation/syntax is so perfect then why are there SO MANY different symbols for say, multiplication? ( x * (dot) implies multiplication against a bracket.)

Again, math notation is just that - notation. ...a tool to an end.

Like it or not, math notation is not some fixed, unmoving set of logical perfection. It has a history. It has evolved. It does evolve. (shocking, I know)

To the current.. people use brackets, braces and grouping extensively, because the whole L/R rule is simply not a reasonable convention when solving large eqn's.

Again, the OP eqn was intentionally set to pit a third-grade math rule against a (math-working) grouping method. How about 1/ 2X .. 1÷2X ... what about -3² ...is that 9? ...or -9? Oh what did the writer mean?

*just to add a dash of thread-kill.

[DARISC]

It takes a man to admit he's wrong Island911.
You fail at that too.
So just pay attention to your Timex kiosk or it'll fail also.
That would make you a three time loser.
I'm being kind; some would say you're already at 3 to a higher power.

[72doug2,2S]

Darsie, With each post you make, I'm loosing the will to care. I've occasionally enjoyed a good riddle, but you are causing me to rethink that position.

[artplumber]

Originally Posted by DARISC

Depends on wind and which way Peter pointin' peter. Tha's why you be all wet.

No prostate probs, my stream is made with the power of the Force. (I've done it in a tornado. Goes where I point it.)

I fart in your general direction. Your mother was a hamster, and your father smells of elderberry.

[svandamme]

Originally Posted by island911

and

Yeah, and there is a rule that says when writing a sentence we start with a the first letter capitalized. --bfd.

Seriously we all -get- that there are rules (damn-it)

Now I certainly appreciate the 'rules' thought, but sorry, the OP eqn is a classic example of math notation ambiguity. (mixing 3rd grade symboligy ÷ w/ more advanced notation grouping) ...Now had the eqn been 48 ÷ 2 x (9+3) ...then yeah, the L/R-rule-nazis^* would have an easy 288 win.

. . .And for you rules-nazis; consider that if mathematical notation/syntax is so perfect then why are there SO MANY different symbols for say, multiplication? ( x * (dot) implies multiplication against a bracket.)

Again, math notation is just that - notation. ...a tool to an end.

Like it or not, math notation is not some fixed, unmoving set of logical perfection. It has a history. It has evolved. It does evolve. (shocking, I know)

To the current.. people use brackets, braces and grouping extensively, because the whole L/R rule is simply not a reasonable convention when solving large eqn's.

Again, the OP eqn was intentionally set to pit a third-grade math rule against a (math-working) grouping method. How about 1/ 2X .. 1÷2X ... what about -3² ...is that 9? ...or -9? Oh what did the writer mean?

*just to add a dash of thread-kill.

There's zero ambiguity to those who know the rules.. Math can't be ambigious, either it's right, or it's not... The equation in this thread, is right, it can be solved, it has been solved, and there's nothing ambigious about that.

Btw, pretty sad to pick on a single capital letter that was left out... big deal Grammar is not Math... The meaning of the sentence did not change one single bit because of the missing letter. It wan't ambigious...

[Esel Mann]

Originally Posted by island911

and

. . .And for you rules-nazis; consider that if mathematical notation/syntax is so perfect then why are there SO MANY different symbols for say, multiplication? ( x * (dot) implies multiplication against a bracket.)

I don't think anyone here or anyone anywhere else will state that mathematical notation/syntax is perfect.

To answer your comment/question, the reason for the differing ways to represent multiplication as well as division has to do with (A) what can be easily printed with the available means, (B) short-hand to permit more equation per inch or to permit an equation to be more quickly written.

Nevertheless, representation of an operator, does not fall under rules for handling mathematical operators. It falls under representation of a mathematical operator.

It's saddening to see this post disintegrating like others (seems to be happening more and more) into more hate than honest debate.

[DARISC]

Originally Posted by 72doug2,2S

Darsie,

It's DARISC 72doug2,2s (and an impressive moniker yours is!)

With each post you make, I'm loosing the will to care.

OMFG doug! Quick! Tighten it up before you lose it!

I've occasionally enjoyed a good riddle,

I completely understand doug; math's a riddle to you. I can't say I understand why you occasionally find that enjoyable though.

but you are causing me to rethink that position.

That's a definite sign of progress doug! Rethinking is good! I'm happy for you that you're giving it a try.

..

[DARISC]

Originally Posted by Esel Mann

I don't think anyone here or anyone anywhere else will state that mathematical notation/syntax is perfect.

Mmmmm, I'm not clear on that Esel. Math notation seems to work perfectly satisfactorily, no? And, can an equation with imperfect syntax be valid?

To answer your comment/question, the reason for the differing ways to represent multiplication as well as division has to do with (A) what can be easily printed with the available means, (B) short-hand to permit more equation per inch or to permit an equation to be more quickly written.

Good - I don't think that that has been mentioned.

Nevertheless, representation of an operator, does not fall under rules for handling mathematical operators. It falls under representation of a mathematical operator.

It's saddening to see this post disintegrating like others (seems to be happening more and more) into more hate than honest debate.

Sad, but not surprising. The hate's coming from those who came up with the answer, 2 ...and just HATE being proved wrong and won't admit it.

I don't harbor any feelings of hatred myself; I think this thread is hilarious and I'm having a ball taunting the haters.

..

[scoe911]

We all have character flaws. The inability to acquiesce could be considered one such flaw. I think we all here can agree this debate has gone beyond the realms of both math and syntax. Now things really get deep...

[sammyg2]

I know it's hard to believe, but apparently there are THOUSANDS of intelligent people arguing about this math problem all over the internets. Yeah I know, huh.

[island911]

Originally Posted by Esel Mann

I don't think anyone here or anyone anywhere else will state that mathematical notation/syntax is perfect.

To answer your comment/question, the reason for the differing ways to represent multiplication as well as division has to do with (A) what can be easily printed with the available means, (B) short-hand to permit more equation per inch or to permit an equation to be more quickly written.

Nevertheless, representation of an operator, does not fall under rules for handling mathematical operators. It falls under representation of a mathematical operator.

It's saddening to see this post disintegrating like others (seems to be happening more and more) into more hate than honest debate.

Yeah, Dari is a goof that really goes for the person, or whatever he thinks will spin people up. (thus his clown-shoes)

So, back to my main point..(which has never been 2 or 288) if anyone thinks that the OP eqn wasn't intended to be ambiguous, please raise your hand.

I mean, really "48 ÷ 2(9+3) = ????" ...who the hell uses ÷ AND the implied (distributive) multiplication, but someone looking to be ambiguous? ...no brackets, and the selective use of one old operator symbol ÷ which happen to print very closely to the common + symbol (our keyboards even have that character. -no key for the ÷ -btw, a little history on that.(used for subtraction)

Anyway, if you raise your hand, please read Mathematical Notation: Past and Future -it's very readable. (more math history.)

oh, and Ambiguity - Wikipedia, the free encyclopedia

[scoe911]

I think everyone here is clear on what ambiguity is however perception of what is ambiguous is debatable.

[m21sniper]

11 pages and i'm the first person to say "who cares?"

Amazing.

You guys will argue over literally anything.

[Bill Verburg]

Originally Posted by sammyg2

I know it's hard to believe, but apparently there are THOUSANDS of intelligent people arguing about this math problem all over the internets. Yeah I know, huh.

yes, and anyone that follows your thinking will be wrong

yes, there is a rule that says to perform all possible operation inside the parenthesis


It is actually not necessary to perform all the operations inside the parenthesis as there are rules for handling situations where it is not possible or desireable for one reason or another.

It is just usually a best practice to do so,

the next rule to follow is to perform any unary operations on the parentheses, the most common unary operation is exponent, in this case the exponent on the parenthesis is 1 and so does not change the value inside the parenthesis and so it says to do nothing

and yes, you correctly mention that the parenthesis stays, the only thing that every removes a parenthesis is when something out side the parenthesis multiplies it.

Here is where your understanding of mathematics is faulty. There is no rule that says you are to perform the multiplication on the parenthesis. You have confused and bastardized the rule you used above to try to use it in a situation where it does not apply.

once again the rule is perform all possible operation inside the parenthesis followed by perform any unary operations on the parentheses

multiplication is a binary operation it requires 2 arguments in this case 2 & (12)



in the absence of the division operation to it's left, yes, you would perform the multiplication, but we have that other pesky rule perform all operations which are at the same precedence level from Left to right. Since multiplication and division are at the same precedence level the division is performed first followed by the multiplication


Perhaps evaluating the expression(it is not an equation and so cannot be solved) in a different ways(I'm an optimist) will show you the error of your ways

for the sake of demonstration lets suppose that we don't wish to perform the addition first, it is entirely reasonable though not usually done this way. In fact lets just substitute some other value which is equivalent to the parenthesis. You remember substitution rule? =s may be substituted for ='s

lets say for the moment that 9+3 = a
can we agree that this does not violate anyones understanding?
48/2(9+3)
48/2(a)

Now it should be obvious that there are 2 operations of equal precedence, division and multiplication which need to be performed left to right
24(a)
resubstitute
24(9+3)
add
24(12)
288

or to prove a statement I made above, you do not have to add first, use the distributive property of multiplication over addition
24*9 + 24*3
now since there are no parenthesis to confuse anyone, multiply
216 + 72
add
288

[Bill Verburg]

Originally Posted by island911

Yeah, Dari is a goof that really goes for the person, or whatever he thinks will spin people up. (thus his clown-shoes)

So, back to my main point..(which has never been 2 or 288) if anyone thinks that the OP eqn wasn't intended to be ambiguous, please raise your hand.

I mean, really "48 ÷ 2(9+3) = ????" ...who the hell uses ÷ AND the implied (distributive) multiplication, but someone looking to be ambiguous? ...no brackets, and the selective use of one old operator symbol ÷ which happen to print very closely to the common + symbol (our keyboards even have that character. -no key for the ÷ -btw, a little history on that.(used for subtraction)

Anyway, if you raise your hand, please read Mathematical Notation: Past and Future -it's very readable. (more math history.)

oh, and Ambiguity - Wikipedia, the free encyclopedia

It was intended to test the mathematical understanding of the readers, it has amply done that by exposing the confused understanding on the part of all too many

It may not be common or best practice to mix notations but these sorts of devices are commonly used on standardized tests to separate the wheat from the chaff. which it has certainly done here. No matter what varying notation is used the expression should be able to be evaluated correctly

[Bill Verburg]

Originally Posted by Bill Verburg

y.....
48/2(a)

...

Since I've received a number of PMs objecting to performing the division first because there are some that erroneously believe that the parenthesis somehow forces precedence(voodoo mathematics) lets multiply first as it does no harm

48/2a

so now it should be even more obvious that there are 2 operations division and multiplication which are done left to right
24a
resubstitute
24(9+3)
24(12)
288

[DARISC]

Originally Posted by island911

...The OP eqn is a classic example of math notation ambiguity.

I never took a course in Classical Math Notation Ambiguity. What's another classic example?

mixing 3rd grade symboligy

You claim to remember your 3rd grade "symbiology"? But you can't remember your 8th grade basic algebra. That's a statement, not a question island911. If it was a question it would be rhetorical.

...Now had the eqn been 48 ÷ 2 x (9+3)

It was. You just added 'x', which is superfluous...and doesn't change a thing. If you remembered/understood your 8th grade beginning algebra you'd know that.

...then yeah, the L/R-rule-nazis^* would have an easy 288 win.

You seem to have a nasty psychological quirk that impels you to call people Nazis - not nice island911 (especially since you 'claim' to own a Porsche).

"an easy 288 win" That's amusing; you see mathematics as competitive, eh? You and doug crack me up (doug apparently sees math as a riddle).

. . .And for you rules-nazis; consider that if mathematical notation/syntax is so perfect then why are there SO MANY different symbols for say, multiplication? ( x * (dot) implies multiplication against a bracket.)

Gee whiz island911, there ya go again (Reagan, dontcha love it?), calling people Nazis, just because ya get all confused and irate about "SO MANY different symbols". Are you going to quote GWBush now and say, "This is hard!"?

Again, math notation is just that - notation. ...a tool to an end.

Of course it is. Who's saying it isn't? Are you just stubbornly being...a tool to the end?

Like it or not, math notation is not some fixed, unmoving set of logical perfection. It has a history. It has evolved. It does evolve. (shocking, I know)

Math notation doesn't 'evolve'. That's a silly notion. Conventions regarding its use may differ from discipline to discipline and by preference, but the notation doesn't change meaning. Ask an 8th grade algebra teacher, or masraum or stign or Bill Verburg et al...unless you think you're smarter and more knowledgeable than they are. THAT would be funny.

To the current.. people use brackets, braces and grouping extensively, because the whole L/R rule is simply not a reasonable convention when solving large eqn's.

So...you just use the parts you feel like using? Thats how you came up with the answer '2', right?

Again, the OP eqn was intentionally set to pit a third-grade math rule against a (math-working) grouping method.

That's really goofy island911.

How about 1/ 2X .. 1÷2X

You think that they are not identical, right? Or they confuse you?

... what about -3² ...is that 9? ...or -9?

Anyone who has a grasp of 8th grade algebra knows it's -9. Does that confuse you too?

Oh what did the writer mean?

That's the crux of your problem island911; if you were 8th grade algebra proficient the goofy question "what does the writer mean?" wouldn't even enter your mind. You'd just solve the equation.

*just to add a dash of thread-kill. .

You've obviously failed at thread-kill also.

So, what now? Wait for you to come back and call me a Nazi in clown shoes?

..

[DARISC]

Gee Bill, again I'm painfully typing away, not seeing you post.

I was POSITIVE you were really outta here.

But I was WRONG!

It's easy island911. You really ought to learn to do it when it applies.

[DARISC]

Originally Posted by island911

Yeah, Dari is a goof...

Hi Chaff!

Did you read Bill Verburg's post #418 before you went off- line?

Or is that WHY you went off-line?