Order of operations - what is 6÷2(1+2) ?

[pier4r]

I think we had this already but I cannot find the thread

I tried to find it with. site:hpmuseum.org/forum order operations

[SlideRule]

Might I suggest Ambiguous PEMDAS as a mutual & agreeable point of reference? If not, a very interesting read, at the least.

BEST!
SlideRule

[smp]

(12-07-2018 01:41 PM)Dave Britten Wrote:  If any calculator has the nerve to say that 6÷2(1+2)=1, but then turn around and say that -2^2=-4, then it can just go straight in the bin.

Both of those are exactly what my Prime does when I key these into my Home screen...

8-)

smp

[Paul Berger (Canada)]

I just tried the 6/2(1+2) on my prime which was in textbook mode and it entered this as a fraction with with 6 on the top and 2(1+2) on the bottom so naturally the answer it get is 1, I then changed the entry mode to algebraic and it entered as 6/2(1+2) and gave me 9 as the answer.

[StephenG1CMZ]

And in CAS it gives the answer 3, after a warning message!

[Sukiari]

If it’s anything other than 1 you break centuries of established math.

[franz.b]

It is wrong to write an ambiguous expression, it is like writing a sentence without punctuation. The fraction line and parentheses were invented, they must be used. In any case, that calculation will have a physical meaning, once the problem is known, the ambiguity is clarified.

[toml_12953]

(12-11-2020 07:50 AM)Sukiari Wrote:  If it’s anything other than 1 you break centuries of established math.

If you do PEMDAS, then you get

(1+2) = 3

6/2 = 3

3*3 = 9

There is no standard that calls for the implied multiplication to be of higher priority than a multiplication sign.
Multiplication is the same priority as division and is done left to right. The division comes before the multiplication on the line and so is done before the multiplication.

[Massimo Gnerucci]

(12-11-2020 11:15 PM)toml_12953 Wrote:  

(12-11-2020 07:50 AM)Sukiari Wrote:  If it’s anything other than 1 you break centuries of established math.

If you do PEMDAS, then you get

(1+2) = 3

6/2 = 3

3*3 = 9

There is no standard that calls for the implied multiplication to be of higher priority than a multiplication sign.
Multiplication is the same priority as division and is done left to right. The division comes before the multiplication on the line and so is done before the multiplication.

So when you write x/2y what you really mean is (x*y)/2?
Luckily we have PEJMDAS!

Turns out that PEMDAS is quite a novelty and that its core fans are North American teachers...





:)

[toml_12953]

(12-12-2020 12:32 AM)Massimo Gnerucci Wrote:  So when you write x/2y what you really mean is (x*y)/2?
Luckily we have PEJMDAS!

Turns out that PEMDAS is quite a novelty and that its core fans are North American teachers...

Yes, to most programmers I know it means (x/2)*y.

Let x=4, y=7
if you use a computer to print the result, you get 14. Most computer languages don't allow implied multiplication so in order to write it as it's written without introducing parentheses, we'd write it as

x/2*y

We have no juxtaposition. Mathematicians might but us computer programmers don't.

[Hlib]

The calculator manual always specifies the priority of operations, so we can use private rules to get rid of ambiguous interpretation.
Implied multiplication and division has a higher priority than normal multiplication and division. Operations with the same priority are performed sequentially from left to right. And that`s where all the arguments end.
6◢2(1+2)=(6÷2)×(1+2)=9 (CASIO)
6÷2(1+2)=6÷(2×(1+2))=1 (CASIO, TI-85,86)
6÷2×(1+2)=(6÷2)×(1+2)=9 (CASIO, TI-83,85,86,89, HP-50G)

[Massimo Gnerucci]

(12-12-2020 04:58 AM)toml_12953 Wrote:  

(12-12-2020 12:32 AM)Massimo Gnerucci Wrote:  So when you write x/2y what you really mean is (x*y)/2?
Luckily we have PEJMDAS!

Turns out that PEMDAS is quite a novelty and that its core fans are North American teachers...

Yes, to most programmers I know it means (x/2)*y.

Let x=4, y=7
if you use a computer to print the result, you get 14. Most computer languages don't allow implied multiplication so in order to write it as it's written without introducing parentheses, we'd write it as

x/2*y

We have no juxtaposition. Mathematicians might but us computer programmers don't.

We are talking about math, not about computer programmed to sort it out.
Do you think like a computer when you read a formula on a textbook?

You have to write it down in such a way that other humans should be able to decode it as you meant, after that they could even program a computer in order to solve that formula.

And you are not the only programmer hereabout. ;)

[rprosperi]

(12-12-2020 09:46 AM)Hlib Wrote:  The calculator manual always specifies the priority of operations, so we can use private rules to get rid of ambiguous interpretation.
Implied multiplication and division has a higher priority than normal multiplication and division. Operations with the same priority are performed sequentially from left to right. And that`s where all the arguments end.
6◢2(1+2)=(6÷2)×(1+2)=9 (CASIO)
6÷2(1+2)=6÷(2×(1+2))=1 (CASIO, TI-85,86)
6÷2×(1+2)=(6÷2)×(1+2)=9 (CASIO, TI-83,85,86,89, HP-50G)

I've seen people claim this priority, but have never seen this is in any mathematics book, nor ever found a mathematician or teacher that agrees. Do you recall where you learned this or have any reference?

[ijabbott]

(12-12-2020 04:58 AM)toml_12953 Wrote:  

(12-12-2020 12:32 AM)Massimo Gnerucci Wrote:  So when you write x/2y what you really mean is (x*y)/2?
Luckily we have PEJMDAS!

Turns out that PEMDAS is quite a novelty and that its core fans are North American teachers...

Yes, to most programmers I know it means (x/2)*y.

Programmers, perhaps, but what about programming languages? Most would treat x/2y as a syntax error, and x/y2 as division of two variables x and y2 (except those primitive languages that only allow single letter variable names).

[Massimo Gnerucci]

(12-12-2020 01:48 PM)rprosperi Wrote:  I've seen people claim this priority, but have never seen this is in any mathematics book, nor ever found a mathematician or teacher that agrees. Do you recall where you learned this or have any reference?

Bob, have a look at the video I linked above.

[toml_12953]

(12-12-2020 01:30 PM)Massimo Gnerucci Wrote:  Do you think like a computer when you read a formula on a textbook?

Actually, I do! Whenever I see a formula, I think in terms of BASIC or Python.

[rprosperi]

(12-12-2020 02:11 PM)Massimo Gnerucci Wrote:  

(12-12-2020 01:48 PM)rprosperi Wrote:  I've seen people claim this priority, but have never seen this is in any mathematics book, nor ever found a mathematician or teacher that agrees. Do you recall where you learned this or have any reference?

Bob, have a look at the video I linked above.

Wow, really good video, thanks for the link Massimo!

Seems one conclusion is Algebraic calculators are inconsistent and potentially confusing if you just type in an equation as given.

I'll consider sticking with RPN/RPL machines, which require some thought to use. So I can decide on PEMDAS or even PEJMDAS, based on which math teachers I'm trying to appease, but at least I can expect consistent results.

Does anyone here recall being taught PEJMDAS, even if that acronym wasn't used?

[DavidM]

(12-12-2020 07:59 PM)rprosperi Wrote:  Does anyone here recall being taught PEJMDAS, even if that acronym wasn't used?

I honestly don't recall any conversation about these topics in any math class, but that could just be my memory failing me.

It seems to me that expressions were always written in such a way that the groupings were obvious, usually involving alterations of element size, length of division bars, and parentheses where appropriate to emphasize relationships of operations.

As a computer science major in the early '80s, I distinctly remember being taught to use parentheses liberally in source code expressions, even when we thought they wouldn't be needed. This was specifically to avoid potential problems resulting from differences in implementation. I remember feeling at the time that it was an overly-cautious practice, but age has taught me to appreciate the value of specificity in source code for things like that.

[rprosperi]

(12-12-2020 08:53 PM)DavidM Wrote:  

(12-12-2020 07:59 PM)rprosperi Wrote:  Does anyone here recall being taught PEJMDAS, even if that acronym wasn't used?

I honestly don't recall any conversation about these topics in any math class, but that could just be my memory failing me.

I'm the same. I was taught that if you write it unambiguously, then it would be... well, unambiguous. I recall being taught that various people are taught differently, and could make different assumptions, so don't leave any opportunity requiring people to guess what you meant. There were no acronyms or memory aides, simply 'make it clear'. Which could be why I took so well to RPN.

[toml_12953]

(12-12-2020 07:59 PM)rprosperi Wrote:  

(12-12-2020 02:11 PM)Massimo Gnerucci Wrote:  Bob, have a look at the video I linked above.

Wow, really good video, thanks for the link Massimo!

Seems one conclusion is Algebraic calculators are inconsistent and potentially confusing if you just type in an equation as given.

I'll consider sticking with RPN/RPL machines, which require some thought to use. So I can decide on PEMDAS or even PEJMDAS, based on which math teachers I'm trying to appease, but at least I can expect consistent results.

Does anyone here recall being taught PEJMDAS, even if that acronym wasn't used?

We were always taught that a missing multiplication sign should be treated the same as if the sign was there. It had no priority over regular multiplication or division.