Casio anomaly or gremlin or bug...

[John Cadick]

(09-06-2017 12:17 AM)toml_12953 Wrote:  

(09-05-2017 07:21 PM)John Cadick Wrote:  In some parts of the world (the US primarily) the whole sequence is PEMDAS. parentheses, exponentiation, multiplication, division, addition and subtraction.

Doing your example using PEMDAS the answer would be developed as:
6/2(1+2) => 6/2*3 => 6/6 = 1

IJohn

No, In the US, Multiplication and division have the same precedence so they're done left to right (as are addition and subtraction). Thus

6/2(1+2) Do the operation in parentheses first.

6/2(3) Of the remaining operators, division is the first, left to right so it is done in precedence over the multiplication.

3(3) There's only a multiplication left to do.

9

Implied multiplication has the same precedence as a multiply sign in most implementations.

This thread has blown up as most of such threads do. I was not saying how to do,it. I was simply showing that two methods that are being used give different answers.

I have also seen folks use the method of giving equal precedence to MD and AS. If that is the case, shouldn't the rule be written as PE(MD)(AS)?

As Joe says, different people have learned in different ways. Even the different calculators give different results. That is what confused Matt.

Anyway, I hope I haven't offended anyone.

John

[Matt Agajanian]

(09-06-2017 03:45 AM)Dan Wrote:  

(09-05-2017 09:39 PM)pier4r Wrote:  I think that the idea of mathematics as precise (and boring) comes from poor teachers.

Teachers are always blamed for all of society's ills! Mathematics is not popular with many people because it requires one to think. Teachers do the best they can with the curriculum they are required to teach and the limited time they have to prepare students for their examinations.

Thank you for supporting teachers, mathematics, and stressing how important it is to think and use the brain.

[Matt Agajanian]

(09-06-2017 04:14 AM)John Cadick Wrote:  

(09-06-2017 12:17 AM)toml_12953 Wrote:  No, In the US, Multiplication and division have the same precedence so they're done left to right (as are addition and subtraction). Thus

6/2(1+2) Do the operation in parentheses first.

6/2(3) Of the remaining operators, division is the first, left to right so it is done in precedence over the multiplication.

3(3) There's only a multiplication left to do.

9

Implied multiplication has the same precedence as a multiply sign in most implementations.

This thread has blown up as most of such threads do. I was not saying how to do,it. I was simply showing that two methods that are being used give different answers.

I have also seen folks use the method of giving equal precedence to MD and AS. If that is the case, shouldn't the rule be written as PE(MD)(AS)?

As Joe says, different people have learned in different ways. Even the different calculators give different results. That is what confused Matt.

Anyway, I hope I haven't offended anyone.

John

Thank you. Yes, you understand where my confusion was/is coming from.

[Joe Horn]

(09-06-2017 04:14 AM)John Cadick Wrote:  I have also seen folks use the method of giving equal precedence to MD and AS. If that is the case, shouldn't the rule be written as PE(MD)(AS)?

As the Wikipedia page cited above says, "To emphasize that addition and subtraction have the same precedence (and multiplication and division have the same precedence) the mnemonic is sometimes written P E MD AS; or, simply as PEMA".

[pier4r]

(09-06-2017 03:45 AM)Dan Wrote:  Teachers are always blamed for all of society's ills! Mathematics is not popular with many people because it requires one to think. Teachers do the best they can with the curriculum they are required to teach and the limited time they have to prepare students for their examinations.

That is true. In my anecdotal experience I had both cases. Pupils unwilling to think and teachers unwilling to think (and therefore teaching poorly).

I also had wonderful math teachers that nevertheless had in the class people unwilling to think.

(09-06-2017 04:14 AM)John Cadick Wrote:  Anyway, I hope I haven't offended anyone.

Serious question: does the order of operation offend someone? I wanted to clarify about Europe because I perceived the sentence like "In Europe sometimes they use funny rules" while the mainstream rules - I guess - are the same almost everywhere.

[John Cadick]

"Serious question: does the order of operation offend someone? I wanted to clarify about Europe because I perceived the sentence like "In Europe sometimes they use funny rules" while the mainstream rules - I guess - are the same almost everywhere."


I did not mean to disparage anyone's or any place's rules. I only meant to express my belief that there are so many different precedence rules being used, that I am not sure which rules are mainstream.

Because of the many different rules, I personally never use any of them. If there is any anbiguity, I use parentheses, brackets, or curly braces.

John

[Matt Agajanian]

This dichitomy between variations begs a concern. When it comes to the sciences and colleagues with both varieties of PEDMAS/BODMAS rules work together, how can a consensus of math rules be agreed upon? Hypothetically, let's say American & British engineers are working on a project for NASA/JPL. Which Order of Operations rules would they follow in designing their fornulas and equations?

[klesl]

This example, at least for me, is undefined since two or more conventions can be used. Such examples should be expressed exactly.
According to the UG for 115 es - section "Calculation Priority Sequence" (page E-8)
the multiplication with omitted sign has higher priority than multiplication or division or remainder. Personally I prefer this behavior.
h/2Pi is h/(2Pi) and not (h/2)*Pi

[Massimo Gnerucci]

(09-06-2017 10:36 AM)klesl Wrote:  This example, at least for me, is undefined since two or more conventions can be used. Such examples should be expressed exactly.
According to the UG for 115 es - section "Calculation Priority Sequence" (page E-8)
the multiplication with omitted sign has higher priority than multiplication or division or remainder. Personally I prefer this behavior.
h/2Pi is h/(2Pi) and not (h/2)*Pi

No: \(\frac{h}{2\pi }\) and \(\frac{h}{2}{\pi}\) are unambiguous; h/2Pi is not

[Didier Lachieze]

(09-06-2017 08:44 AM)Matt Agajanian Wrote:  Hypothetically, let's say American & British engineers are working on a project for NASA/JPL. Which Order of Operations rules would they follow in designing their fornulas and equations?

I would expect that they use Latex or equivalent to write: \(\frac{6}{2(1+2)}\) or \(\frac{6}{2}(1+2)\) depending on what they want the formula to be, to avoid the ambiguity of writing \(6/2(1+2)\)

[ijabbott]

(09-06-2017 11:35 AM)Massimo Gnerucci Wrote:  No: \(\frac{h}{2\pi }\) and \(\frac{h}{2}{\pi}\) are unambiguous; h/2Pi is not

\(\frac{h}{2}{\pi}\) could be ambiguous if it is treated as a mixed fraction (albeit a somewhat bizarre mixed fraction — it reminds me of a certain TI-36X Pro (or TI-30X Pro MultiView) bug!).

[Matt Agajanian]

(09-06-2017 11:42 AM)Didier Lachieze Wrote:  

(09-06-2017 08:44 AM)Matt Agajanian Wrote:  Hypothetically, let's say American & British engineers are working on a project for NASA/JPL. Which Order of Operations rules would they follow in designing their fornulas and equations?

I would expect that they use Latex or equivalent to write: \(\frac{6}{2(1+2)}\) or \(\frac{6}{2}(1+2)\) depending on what they want the formula to be, to avoid the ambiguity of writing \(6/2(1+2)\)

Dieter, thank you. I appreciate that.

[ijabbott]

(09-05-2017 05:19 PM)ijabbott Wrote:  

(09-05-2017 02:26 AM)Joe Horn Wrote:  Bottom line: this notation is ambiguous. Therefore it should simply be avoided, which is why HP's RPL and Prime's CAS don't allow it.

At least the Casio PRIZM series (or at least the fx-CG50 I have) disambiguates it for you. If you enter 6÷2(1+2), it rewrites it as 6÷(2(1+2)) and gives the answer 1.

And the CLASSWIZ does the same, inserting the extra parentheses.

[Matt Agajanian]

Thank you, MoHPC folks. I appreciate the plenteous amounts of explanations and analyses given here. They have helped me learn so many essential mathematical concepts and rules. I am appreciative of the intense efforts all of you have put into this somewhat rudimentary question.

[Thomas Radtke]

I think Punkt vor Strich (M, D before A, S) is a global convention much like the expression -x=0-x. I doubt, however, that implicit multiplication or similar concepts are accepted as a convention by the scientific community. There is ambiguity, and it's not caused by insufficient rules but by improper notation. If one insists on writing a division of 1 by 2 as 1/2, then he should point out what that means or use parenthesis. I always do when programming since editors force me to use that notation and I refuse to study lex-files.

[Eddie W. Shore]

This may fall under the same category of squaring negative numbers on algebraic calculators: where on some:

-3^2 returns -9. The calculator treats squaring as priority over negation - prevalent in TI graphing calculators.


For the record:

TI-84 Plus CE:
6/2(1+2) returns 9

HP Prime:
6/2(1+2) returns 9

The HP48GX doesn't allow implied multiplication. I tend to agree with this; in practice I inserting multiplication signs.

I think in this case, I would side with caution and put an additional set of parenthesis if you meant 6/(2(1+2)) or a multiplication sign if you meant 6/2*(1+2).

Which brings up a question, should implied multiplication on calculators be allowed at all?

[Matt Agajanian]

(09-09-2017 03:23 PM)Eddie W. Shore Wrote:  This may fall under the same category of squaring negative numbers on algebraic calculators: where on some:

-3^2 returns -9. The calculator treats squaring as priority over negation - prevalent in TI graphing calculators.


For the record:

TI-84 Plus CE:
6/2(1+2) returns 9

HP Prime:
6/2(1+2) returns 9

The HP48GX doesn't allow implied multiplication. I tend to agree with this; in practice I inserting multiplication signs.

I think in this case, I would side with caution and put an additional set of parenthesis if you meant 6/(2(1+2)) or a multiplication sign if you meant 6/2*(1+2).

Which brings up a question, should implied multiplication on calculators be allowed at all?

Eddie, you bring up a valid point which does bring up perplexing shakeups of convention. For instance, while implied multiplication may (strengthened by a long-standing convention in print) be accepted in non-electronic setting, yes, textbooks, tables, print media, etc. should be tools that require thought processes rather than simply plug-and-play (yes, a play on the 90s interface jargon) data entry. So yes, just like AOS, Direct Formula Entry, and pre 2000 data entry methods from Sharp, Casio,TI, etc., implied multiplication on calculators should be disallowed as this thread had demonstrated in the ambiguities introduced in such usage.