48÷2(9+3) = ????

[DARISC]

Originally Posted by island911

I just trudged thru this thread, and...

...and you should have trudged right back out.

Don't give up your lease on your Timex kiosk at the mall island; you'd never make it as an engineer.

Remember this thread, where you struggled so hard trying to solve the problem between changing watchbands?

And came up with the wrong answer then too?







And then you got pissed when I posted the right answer. HAHAHAHA!
What expletive did you decide to delete from the parentheses?




Got any good deals on cheap calculator watches goin' on island?

[sammyg2]

Originally Posted by NotaBRG

With your math skilz I assume you voted 2. 172 to 94 is not 2 to 1.

It's sitting 64.66% in favor of "2" right now, that's close enough to 66 2/3% to be called 2 to 1.
I'm intelligent enough to know how and when it's appropriate to round off.
I was gonna use the term "common sense" instead of "intelligent" but common sense ain't that common in this thread

[DARISC]

Originally Posted by sammyg2

It's sitting 64.66% in favor of "2" right now, that's close enough to 66 2/3% to be called 2 to 1.
I'm intelligent enough to know how and when it's appropriate to round off.
I was gonna use the term "common sense" instead of "intelligent" but common sense ain't that common in this thread

So...your answer is 2 sammyg2?

[Bill Verburg]

Originally Posted by island911

I just trudged thru this thread, and it does have some redeeming value - now we know the stiffies who will demand that the eqn. as written, is w/o ambiguity because " third-grade rules always dictate mathematical syntax! . . .damnit! "

btw, Dari (you strange old fart) I did plug the eqn in to both my HP calc and into Mathcad (both eqn writers) and both gave 2. --the mult next to the bracket forces priority multiplication in the denominator.

This pic shows the isse w/ using technology to get answeres rather than knowing the rules of math


if the person that wrote the calculator code doesn't know the rules he will get the wrong answer

2/3 and 2÷3 are identical

2(3) and 2x3 and 2 • 3 are identical too(I know it looks like a dot product which is something else but it was either that or use a *, I chose the lesser of 2 evils)

2x3(4) is still 2 multiplications that by rule are done left to right unless another rule allows something different(there is no rule that says that 3(4) takes precedence over 2x3)

6(4)
24

in this case the commutative property of real #s under the multiplication operation allows the transposition of 3 & (4) & 2
(4)3 x 2 or (4)2 x 3 are the same as 2x3(4)


apparently everyone remembers that a parenthesis alters the operator precedence, but only for operations that occur inside the parenthesis and have no operator on the outside of the parenthesis so there is no debate as to the first operation here. Some would be confused if there was an exponent on the parentheses, but if it is remembered that the exponent is a unary operator that only operates on the inside of the parentheses no issues will result. note that multiplication is a binary operation whether it is implicit 2(3) or explicit 2x(3), and if it is paired w/ another operation 2+2(3) 2(3) is done first because multiplication takes precedence over addition, if it was 2÷2(3) the division takes precedence because when 2 binary operations are at the same precedence level the left to right rule is in effect

48÷2(9+3)

48÷2(12)

we are now left w/ an expression that has 2 hierarchically identical operators, division and multiplication which must be done left to right by rule

24(12)

now there is only 1 operation, multiplication which removes the parenthesis
288

here are the rules
1) perform all grouping operations, Grouping Symbols:
Perform operations inside first.
( ), [ ], { }, square root, fraction, absolute value (yes, square root and fraction are grouped operations)

2) multiplication and division from left to right

3) addition and subtraction from left to right

commutative, associative and distributive properties when properly applied can alter the precedence.

the issue as I see it is that some people that don't know the rules as well as they should seem to be applying an associative property incorrectly

they want to make this
48÷2(9+3) into this 48÷(2(9+3)) the only rule that allows the addition of a grouping symbol is the associative property of addition or the associative property of multiplication which says that 2x3x4 is the same as 2x(3x4) or 2+3+4 is the same as 2+(3+4)

the associative property does not work for division or subtraction and so the addition of the explicit grouping is not allowed for 8÷2(9+3)

8÷2(9+3) does not equal 8÷(2(9+3)) because the associative property only works w/ pure multiplication or pure addition

[island911]

Originally Posted by Bill Verburg

...

if the person that wrote the calculator code doesn't know the rules he will get the wrong answer...

Yeah, those idiots who programed those HP calc's. ...and to think that NASA was so stupid to use those devices for alt landing program for the space shuttles.

I should point-out that both the HP and Mathcad eqn writers give a graphical (non-ambiguous) representation of the entry.

Originally Posted by Bill Verburg

...
2(3) and 2x3 and 2 • 3 are identical too..
...

No. They MAY be identical. ...but when it comes to writing logical mathematical groupings they are not.

If you want to stamp your feet and demand that everything anyone needs to know about math operations, they learned in the third grade, then so be it. ...but the OP eqn is intentionally ambiguous. And,this inconsistency in notation is nothing new. ...just as is the eqn 1/2x (read: is that .5*X ? ...or 1/(2x)

Demanding that "left to right" always takes precedence is simply short-sighted. (unless one is in the third grade)

Again, engineers and math geeks often use notation beyond the third grade rules. Sure, you can claim they are "not right" to do so, but we also don't speak the Queens English, now do we?

...this will lead Dari to spazz-about with the story idea of "Rebel Nerds . . . on Planes .. with snakes."

[DARISC]

Originally Posted by island911

Yeah, those idiots blah blah bluster blah blah bluster bluster"Rebel Nerds . . . on Planes .. with snakes."

HAHAHAHAHA! Can't win and don't know how to lose, eh island911?

Back to your Timex kiosk with you boy!

[Bill Verburg]

Originally Posted by island911

Yeah, those idiots who programed those HP calc's. ...and to think that NASA was so stupid to use those devices for alt landing program for the space shuttles.

the proof is right before your eyes, and you still try to deny it,
one of these is wrong

Originally Posted by island911

I should point-out that both the HP and Mathcad eqn writers give a graphical (non-ambiguous) representation of the entry.

and yet one of the above is wrong

Originally Posted by island911

No. They MAY be identical. ...but when it comes to writing logical mathematical groupings they are not.

In what classroom did you learn that little tidbit? It must have been the same one where you learned that in 48÷2(9+3) multiplication by 2 comes before the division by 2,

again there is no rule that tells you to do the binary multiplication on the parenthesis first,
there is a rule that says when operations are at the same precedence level, do left to right.
There is a rule that says perform all operations inside the parenthesis first.
There is a rule that says that unary operations like exponent on a parentheses are done first.

To reiterate, there is no rule that says to multiply by a parenthesis comes first, if you think there is find it in a credible source and post a link to it, I double dog dare you


adding the laws of logic to the laws or arithmetic and algebra to evaluate the expression does not change the result as there are no logical operators present in the given expression, merely the binary arithmetic operators and a parenthesis
2(3) and 2x3 and 2 • 3 are identical because they all simplify to the same result and they are the same as 3(2) and 3x2 and 3 • 2 because of the commutative law and are the same as 3^2 - 3 and 3^2 -(-2-1) etc.

Originally Posted by island911

If you want to stamp your feet and demand that everything anyone needs to know about math operations, they learned in the third grade, then so be it. ...but the OP eqn is intentionally ambiguous. And,this inconsistency in notation is nothing new. ...just as is the eqn 1/2x (read: is that .5*X ? ...or 1/(2x)

If they were taught correctly and learned correctly, yes. It's obvious that math was either incorrectly taught or learned by a lot of folks. There is nothing inconsistent or ambiguous about the notation, there is a lot of fuzzy headed understanding of the rules of arithmetic and algebra. There is no ambiguity in 1/2x either it is 1 divided by 2 times x and must be done left to right because multiplication and division are at the same hierarchical level, if it was other than that the explicit use of a parenthesis is necessary. If you do not understand that, then you do not have a good grasp of elementary math. I know that it is difficult to accept that but it is true

Originally Posted by island911

Demanding that "left to right" always takes precedence is simply short-sighted. (unless one is in the third grade)

the rules of arithmetic and algebra are independent of time or location. You do not get to make up rules that suit you own view and then claim others that do follow the rules correctly are wrong. I did not make up any of the rules nor did any of the posters that got the correct result, we simply followed the correct set of rules in the correct order. Many times you or others follow your muse and still get the correct answer, that does not mean that the rules you followed are correct, It merely means that in that particular case they worked. Following the correct set of rules in the correct order is the only way to always get the correct answer.

here is an example that I used to give my grad students,
64/16 = 4, the easy way(though incorrect to do in all cases) to get the correct answer is of course to cancel the 6 's in the division. then divide by 1 to get 4

It's obvious(though incorrect) that this must be correct because in (6x4)/(3x6) we can (correctly) cancel the 6s and get the result 4/3. This is correctly done only because of a quirk of algebra and is a valuable trick to know.

Originally Posted by island911

Again, engineers and math geeks often use notation beyond the third grade rules. Sure, you can claim they are "not right" to do so, but we also don't speak the Queens English, now do we?

I don't know about 'the Queens English' but I do know a thing or two about Math, using the rules correctly gives the simplified result 288 any other result comes from the misapplication of the rules,

if the rules were correctly taught then they are applicable to any one, at any time, there are not different rules for different folks when it comes to math, each level is a super set of the preceding level. There is obviously a different level of comprehension among the various respondents that has been exposed by this thread.

[scoe911]

The inability to acquiesce is much worse than deficient math skills.

[DARISC]

"There is obviously a different level of comprehension among the various respondents that has been exposed by this thread."

Mr./Prof./Dr. (correct me if not all apply) /Bill Verburg,

You are an excellent teacher and have been extraordinarily patient with the woefully recalcitrant posters on this thread, affirming others explanations in detail as well as painstakingly, even tediously, amplifying at great length, theirs with yours.

I am dumbfounded that all of your and a number of other's efforts have apparently been for naught, leaving only one possible, and I don't hesitate to say, tragic, conclusion, your quote above.

And, caring nil that some will say I am being melodramatic, this does not bode well for the future of our country,

On a positive note, you build stunningly beautiful boats.

David

[artplumber]

Isn't the answer truly dependent on how one visualizes the division sign? If one envisions it as a vinculum, then it is easy to see how this equation might be interpreted as two arguments, the convention of which is to solve the arguments above and below the vinculum before performing the fraction/division. OTOH the linear operands POV is also possible. The ambiguity really is there, and that's why this has been 20pages long. It is why the two different calculators got different answers and not equivalent to the issue of 64/16 that Bill has suggested is equivalent.

[svandamme]

the sign means just the same as / ... ÷=/

If you write the equation as this 48/2(9+3)

then that part of the discussion is binned.

[DARISC]

Originally Posted by artplumber

Isn't the answer truly dependent on...

Peter, read and digest Bill Verburg's posts in particular.

[artplumber]

Originally Posted by DARISC

Peter, read and digest Bill Verburg's posts in particular.

I did, that's why I wrote what I did (Please read my post again). One can easily interpret as:

48
2(9+3)

Hence answer 2. Let's be a little less dogmatic guys.

[Bill Verburg]

Originally Posted by artplumber

I did, that's why I wrote what I did (Please read my post again). One can easily interpret as:

48
2(9+3)

Hence answer 2. Let's be a little less dogmatic guys.

The problem is that Math is all rules that must be followed, you are not following the rules correctly
48/2(9+3) is the same as 48÷2(9+3) but not the same as 48/(2(9+3))

there are only 2 properties of the real #s that allow you to add a grouping symbol to this expression
1) associative property of addition which allows 3+4+5 to become 3+(4+5), this only applies when there are only additions involved
2) associative property of multiplication which allows 3x4x5 to become 3x(4x5) this only applies when there are only multiplications involved

it does not allow 48÷2(9+3) to become 48÷(2(9+3)) because there is a ÷

you can change 48÷2(9+3) to 48 X 1/2 x (9+3) by using the reciprocal equivalence property then you can add the grouping but it would look like this 48/1 x(1/2 x (9+3)/1) or (48/1 x 1/2) x (9+3)/1 multiplying numerator by numerator and denominator by denominator gives 48/1 x (9+3)/1 or (48/2) x (9+3)/1 which in turn gives
24/1 x (12)/1 or (24) x(12) which gives 24 x 12 which is 288

you can follow any rule you want in any order you want but you must follow the rules, you can't make stuff up and get the correct result all the time.

Pretty hard to do if you weren't paying attention in HS algebra

[DARISC]

Peter,

First, add the 9+3 in the parentheses to get 12 (indulge me and keep the parentheses around the 12 for now).

Now, perform the first operation, beginning at the left, i.e.,

Divide 48 by 2 to get 24

Now you're looking at the number 24 next to the number 12 in parentheses.

That says to you, Multiply 24 times 12 to get 2.

Do NOT multiply 2 times 24 because it will give you the same answer.

There are other 'interpretations' of course (), but none of them are 'correct'.

To paraphrase the little old lady in that old hamburger ad, WHERE'S THE DOGMA?!

Oops - You posted while I was typing Bill.

I'm surprised; was pretty sure you were outta here!

[artplumber]

Originally Posted by Bill Verburg

The problem is that.....
....
....
....
....

(Not so rhetorical a question)Does anybody read around here? I wrote, I can understand both points of view. I don't need the 20 pages repeated.

Oy. Really. Oy.

[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

They are fixed and not open for discussion.

Everybody who knows em, knows that the answer is 288.
Only somebody who doesn't know em, can answer 2.

[artplumber]

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

They are fixed and not open for discussion.

Everybody who knows em, knows that the answer is 288.
Only somebody who doesn't know em, can answer 2.

Stijn, my pee goes farther than anybody else's pee.. So there...

I submit to the Borg! Wait maybe it's we have been assimilated! sumthin lak dat

[DARISC]

Peter,

Did you even bother to read post #397?!!!

[DARISC]

Originally Posted by artplumber

Stijn, my pee goes farther than anybody else's pee.. So there...

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