OK, so how about 3*2÷6*4?

I could see a math teacher having fun with these kinds of problems.

 

OK, so how about 3*2÷6*4?

I could see a math teacher having fun with these kinds of problems.

Bill, the answer is 4.

 

That is assuming you don't do multiplication first, which was the point. I don't necessarily agree with your point of view. If you read the previous 13 pages multiplication and division don't necessarily have equal precedence.

I also agree with BillO that it is a sloppy way to write it out.

Me, I think the answer is ¼. It is the way I was taught way back when.

 

Borland C++ compiler says 3*2/6*4 = 4

although the compiler does not have that funny little ÷ symbol which is not even a legal ASCII character...

 

÷

Hmm, I have no problem with it.

÷÷÷÷


X = *

Welcome to old school.

3 X 2 ÷ 6 X 4

Stirring can be fun!

Take that BASIC and C++!!!

 

Well speaking of stirring, it does raise another issue of "intent".

A formula written on a blackboard may be considered as a "whole", something to be analysed, transposed around, the formula has value in its own right. So the *intent* may be to work with the formula as opposed to needing to resolve it to a numerical answer. And the conventional rules as such give that a high priority.

Where as with the C compiler, the *intent* is always to perform a sequence of calculations and arrive at a numerical answer. So the compiler would never expect you be entering fractions with numbers on top of each other to allow you to think about it, and transpose stuff around. The compiler only expects that you enter individual tasks to be executed in sequence, and of course there is a precedence character () to force the sequence ANY time that the sequence is important.

So in the argument of *intent*, if this 48/2(9+3) was written on a board with the intent to study it then it may be considered as an answer of 2.

So if this was passed on with the *intent* that the reciever (person or machine) was to resolve your commands as a *sequence of executions* then the answer is 288. If the originator wished to get an answer of 2 the originator was responsible to specify when they issued the sequence of executions. They should have issued; 48/(2(9+3)) because this sequence of executions; 48/2(9+3) results in 288.

 

If you go back to the beginning of this thread it was acknowledged that parenthesis are your friends. The meat of this discussion is the standards are changing, to the point a lot of people don't even recognize there used to be a different way of doing things. Computers help with math, but they don't really make math yet, but they have definitely had an influence that seems to be unrecognized.

 

I agree totally! Computers have had a strong influence on the order of many things in life that the offical "Math Societies" seem to be failing to recognise.

To me the crux of this argument is that it is not a pure math issue. It's easy to see "48/2(9+3)" as math. Especially for someone from a math background. But it is not just math, it is also a data communication, and a command sequence.

Here's an analogy that removes the math and highlights the basic issue;

Courtroom to establish blame;
PersonA instructed PersonB;
"We're going on a trip, go get in the car, and make sure that you take a leak"

PersonB received a clearly defined command sequence of 2 commands;
"get in the car and take a leak"
command1; get in the car
command2; relieve yourself

Who's to blame?
The two commands were very clearly issued in sequence. However there is a traditional "rule" that "everyone should know" that you always take a leak BEFORE you get in the car. But that is NOT what was commanded.

So you have a valid enough analogy that the sequence (as was given) commands one thing, but the traditional rule requires you not to perform it in the sequence commanded, but in a DIFFERENT sequence to that which was commanded because "the rule says so".

 

Anyone who has ever had kids knows this.

Including, unfortunately, the part about taking a leak after you get in the car.

 

Anyone who has ever had kids knows this.

Including, unfortunately, the part about taking a leak after you get in the car.

That would be the Order of Urinations

 

That would be the Order of Urinations

QFT and hilarity.

And to state the obvious, no C compiler does math.

C does calculations to the ANSI standard, with deviations of whatever the compiler designer chose. These deviations are typically commented somewhere, and best of luck finding them.

Math is what the human does when defining equations to preform some task. It is then up to the human to translate the math into calculations that the compiler understands.

Math ≠ Calculation

 

I'm in complete agreement ErnieM.

Especially with;

...
Math is what the human does when defining equations to preform some task. It is then up to the human to translate the math into calculations that the compiler understands. ...

Which brings me back to the OP's post #1. The context of the entire discussion was in relation to the operation 48/2(9+3) as sequentially entered into a pocket calculator, and what the answer should be.

Pocket calculators have always traditionally required the human operator to enter data and commands in sequence. All early calculators that set this standard performed any calculation everytime you pressed a +-*/= key.

So A/B*C was ALWAYS performed in the sequence entered by the human operator.

This set a very strong precedence for a "standard" for what to expect with data and commands entered over time into a calculator. It's only recently that calculators have tried to be more sophisticated and attempting to force precedence themselves rather than what the user sequentially entered.

So taken in the context of the original question your words;

... It is then up to the human to translate the math into calculations that the compiler (calculator) understands. ...

side with the correct result on the calculator should be as it always has been on pocket calculators where 48/2(9+3) = 288.

My good TI scientific calculator says 288 and actually I would be a bit ticked off if it said 2.

 

The contention here is not the way a calculator executes commands as entered, but whether A/B*C should interpreted the same as A/BC.

BTW, the original expression does NOT always calculate to 288 on a pocket calculator. Not even on almost identical models from the same manufacturer. See post #1.

 

Which brings me back to the OP's post #1. The context of the entire discussion was in relation to the operation 48/2(9+3) as sequentially entered into a pocket calculator, and what the answer should be.

Well, it's been a long long time since post #1, so here is a reminder:

Post #1

This has been around on the net, I'm interested in how Math people interpret this:

48/2(9+3) = ?

It says "people." Me is a people. I use a calculator or a computer to do calculations. I use a pencil and paper to do math.

Math still ≠ Calculation

 

BTW, the original expression does NOT always calculate to 288 on a pocket calculator. Not even on almost identical models from the same manufacturer. See post #1.

I can get the Windows calculator to tell me it is 4. Same with my TI-30Xa.

4 is just such a lovely answer, I don't know why it doesn't get the love.

 

...
BTW, the original expression does NOT always calculate to 288 on a pocket calculator. Not even on almost identical models from the same manufacturer. See post #1.

I did say "as it always has been" which was a past-tense reference to the early tradition of calculators. Sorry it was a poor choice of words. "As the traditional standard set by early calculators" would have communicated my intent better.

... (Originally Posted by thatoneguy
This has been around on the net, I'm interested in how Math people interpret this:
48/2(9+3) = ?

I see, you inferred a more literal meaning of what he asked, and you are probably right about his meaning! I inferred he was asking what "math people" thought about why the 2 calculators gave different answers. Communications issues again.

 

I can get the Windows calculator to tell me it is 4. Same with my TI-30Xa.

So it does! It just seems to drop the two altogether.

 

So it does! It just seems to drop the two altogether.

Yeah , i stopped reading after 7... but the AMS thing was convincing. But it was a cached site. And if you keep looking it was updated in September 2005 and the whole juxtaposition was removed. As it has in the most recent http://www.ams.org/mresubs/guide-reviewers.html . I think they just got tired of arguing the point and just gave up. That's around the same time Texas Instrument removed implied multiplication from their newer calculators. So who knows... maybe math is degenerating uncontrollably.

I mean i'm not even 30 yet and i remember going from pemdas to pe(md)(as)... as in multiplication came before division... So who knows what's correct.

And windows 7 calculator gives me "ERROR!" when submiting it as is.

 

I just bought a used TI 82 graphing calculator for $8, it is also old school on the order of operations, and states it in the manual.

 

Yeah , i stopped reading after 7... but the AMS thing was convincing. But it was a cached site. And if you keep looking it was updated in September 2005 and the whole juxtaposition was removed. As it has in the most recent http://www.ams.org/mresubs/guide-reviewers.html . I think they just got tired of arguing the point and just gave up. That's around the same time Texas Instrument removed implied multiplication from their newer calculators. So who knows... maybe math is degenerating uncontrollably.
...

Very interesting! Thanks for that info. I think "degenerating" may be too derogatory a term. "Evolving" seems more accurate and less judgemental, as evolution often includes general simplifications and improvements where some less-used things are lost. You wouldn't say ships have "degenerated" to using GPS nav instead of a sextant, even though there may be a loss of some of the older skills.

...
And windows 7 calculator gives me "ERROR!" when submiting it as is.

That's pretty much exactly what a compiler would do to the math. Either autoinsert the missing * operator or signal an error because of the missing * operator. Windows 7 may use a javascript component for the math which will be almost identical to the C compiler math.

I just bought a used TI 82 graphing calculator for $8, it is also old school on the order of operations, and states it in the manual.

Interesting that you bought a calc that gives you the answer that you prefer and i bought one that gives me the answer I prefer... Nobody wants an argumentative servant!

May I ask what year the calculator is and what the exact wording is in the manual? I'm interested in trying to narrow down the year where the precedence went from being "mathematically correct precedence" to "traditional math precedence".

I'm sure TI whose reputation is based in a big part on their calculators have some real smart math PHDs that have not taken this issue lightly. Wouldn't it be great if we get one of them to post here?