Many calculators not following math rules?

[Silent_Buddha]

http://www.math.com/school/subject2/lessons/S2U1L2GL.html
"Working from left to right, do all multiplication and division."

http://www.algebrahelp.com/lessons/simplifying/oops/
"Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right. "

http://www.themathlab.com/Pre-Algebra/order of operations/orderof.htm
"These operations are done in the order they appear from left to right. They are done together because they have the SAME IMPORTANCE."

http://www.studygs.net/pemdas/
"Then multiplication and division, from left to right"

http://en.wikibooks.org/wiki/Algebra/Order_of_Operations
"Multiplication and/or division from left to right"

First results from google search "algebra order of operations" - if it was just "commonly taught" why would it be mentioned in every single iteration of algebra order of operations rules?
(not to mention, if such rule would exists, any equation with multiple divisions and multiplications without parenthesis telling you specificly which order to do them in) couldn't have correct answer)

Again, it's all rules in order to make imprecise notation work.

If you take

A             E         A + B
_  * (C+D) *  _  * Q *  _____
B             A         C + D

It doesn't matter one bit if you go from left to right or right to left due to correct equation writing notation.

It only becomes a problem when you use shorthand notation to write it on one line using "/" notation...

A / B * (C+D) * E / A * (A+B) / (C+D)

That would obviously result in a different answer depending on how you evaluate it because in this case it isn't obvious that the division operations are their own entity.

In the first case it's obvious that it's basically

S * T * U * V * W

The second equation is exactly the same, but since it's written in shorthand it's not so obvious and unless you follow correct order of operations for shorthand writing then you'll get it wrong. Something that you absolutely cannot mess up if you write it correctly.

But that is entirely due to using shorthand to write the equation and absolutely NOTHING to do with Algebra or math.

When written correctly the order doesn't matter as you can immediately see at a glance how one should evaluate the equation. It's only when you use shorthand that order becomes important because the equation would be ambiguous otherwise.

BTW - calling it shorthand probably isn't the correct terminology, but either way that method that requires an order of operation only requires that due to the imprecise method of representing the equation. Hence, why it's only relevant in low order math classes and not relevant for higher orders of math where you should always write equations correctly to avoid that ambiguity.

Regards,
SB

 

[Arwin]

I thought we had more programmers here.

As a programmer, I learnt to use brackets early and often to make sure there is no room for misinterpretation.

My wife's old CASIA fx-82SX, which I think I've owned as well, gives me 4 as a result if I input this with an implicit multiplier. But I think that implicit multiplier is simply not something that was ever explicitly given a meaning, so I have trouble counting any result wrong.

Intuitively, I would say that writing 2(9+3) should be treated the same as 2x as discussed by someone before, and therefore 48/2(9+3) should in fact be 2, like as if you were resolving something like:

surface of the front garden of a house is twice the size of the pool and the fountain combined

front garden surface y = 2 * (size of the pool x + size of the fountain z)

As a programmer, that would be the formula I program in where the input variables would then be the size of the pool and the size of the fountain, say. Of course, again as a programmer I would write something like 48/2(9+3) as (48/2) * (9+3) if that's how I meant it to be calculated, or 48 / (2 * (9+3)) if that was what I meant.

Incidentally, I wrote my own expression parser / mini-programming language to use xml exclusively, which is also the way you insert logic into configuration, and for a calculation as above ends up something like:

<Multiply>
   <Divide>
      <Value>48</Value>
      <Value>2</Value>
    </Divide>
    <Add>
      <Value>9</Value>
      <Value>3</Value>
    </Add>
</Multiply>

Of course the values here would more likely be XPaths to values in an xml input dataset. And note that for Divide it still implies reading from left to right / top to bottom.

 

[chavvdarrr]

And it's a damn simple equation too:
48 / 2 ( 9 + 3 )

Who says that 24(12) is 24*12 and not 24/12 ?

 

[Kaotik]

Who says that 24(12) is 24*12 and not 24/12 ?

At least last time I was taught any maths, number/letter-parenthesis combo without any multiplication/division/add/substract symbol is always multiplication

 

[Mintmaster]

http://www.math.com/school/subject2/lessons/S2U1L2GL.html
"Working from left to right, do all multiplication and division."

http://www.algebrahelp.com/lessons/simplifying/oops/
"Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right. "

http://www.themathlab.com/Pre-Algebra/order of operations/orderof.htm
"These operations are done in the order they appear from left to right. They are done together because they have the SAME IMPORTANCE."

http://www.studygs.net/pemdas/
"Then multiplication and division, from left to right"

http://en.wikibooks.org/wiki/Algebra/Order_of_Operations
"Multiplication and/or division from left to right"

Notice how none of your examples use numbers next to parentheses.

At least last time I was taught any maths, number/letter-parenthesis combo without any multiplication/division/add/substract symbol is always multiplication

Yes, and when you were taught that, you learned what the real division operator looks like.

You are mixing up two different notations. Calculators can do whatever they want in this situation because it's undefined. As I mentioned above, programming languages don't even allow the bastardized notion that you are so obsessed with. Older calculators didn't either. Newer ones do only due to market demand, and the free market does whatever it feels like.

 

[Blazkowicz]

I've tried bc, python and gnome's calculator, all give 288 from 42/2*(9+3) and all refuse 42/2(9+3)

well, python is a programming language but you can just type arithmetic at it
bc is an interactive command line calculator, comes with ubuntu, debian or any GNU based system.
dc is similar, but RPN! I've tried it, it's old horseshit. you have to type "p" to display the top of the stack. can't really do the operation on it, I end up with 0

 

[Kaotik]

Notice how none of your examples use numbers next to parentheses.
Yes, and when you were taught that, you learned what the real division operator looks like.

You are mixing up two different notations. Calculators can do whatever they want in this situation because it's undefined. As I mentioned above, programming languages don't even allow the bastardized notion that you are so obsessed with. Older calculators didn't either. Newer ones do only due to market demand, and the free market does whatever it feels like.

I know what real division operator looks like, but sadly that simply isn't available when you're writing on single row, in which case depending probably a bit on teaching methods either ":" or "/" is typically used.
They act as if they were the real symbol, meaning that
3
--
4

is same as 3/4 (or 3:4) - in case you have more than one component divider, you need to use parenthesis, example:

3
--
4-2

Doesn't turn to 3/4-2, but to 3/(4-2)

 

[aaronspink]

I know what real division operator looks like, but sadly that simply isn't available when you're writing on single row, in which case depending probably a bit on teaching methods either ":" or "/" is typically used.
They act as if they were the real symbol, meaning that

Um, using elementary anecdotes on math for real math is like using barney as an example of a dinosaur.

It is quite simple really. You are running into a combination of incorrect/imprecise notation and ignorance of instructions.

So if you are writing on a single row, be precise. Simple, easy. /thread

 

[hoom]

Its ambiguous as written.
Absence of ambiguity is why you should use clear notation.

48
----- * (9+3)
2

or

48
-----
2(9+3)


I'm inclined to interpret this as = 2.

The absence of explicit multiplier indicates that 2(9+3) is grouped & should be evaluated before the divide ie 2nd version above.

If you wanted 288 you should write in the multiplier explicitly: 48/2 * (9+3) or (48/2)*(9+3) or as first version above

You wouldn't ever write it as

48
-----(9+3)
2

 

[Bludd]

You wouldn't ever write it as

48
-----(9+3)
2

Of course you would. Fractions in front of parentheses is not unusual notation.

 

[Cheezdoodles]

I find it strange that you find this "bug" strange at all.

Your notation is also not exactly free for misinterpretation.

48/2 (9+3)

Is it above or below the / ? The way you wrote it, its not really clear. Is the (9+3) to be multiplied by 2? Or not? Without a multiplier it looks to me like its below.

Had you written it like (48/2)(9+3) the whole thing would be correct every time, on every calculator.

 

[green.pixel]

 

[hoom]

Of course you would. Fractions in front of parentheses is not unusual notation.

OK true now that I look at it.

But the point remains that (9+3) being next to the divide part makes clear that it is to be evaluated separately from the divide by 2 so is still clear notation.
If the (9+3) is written on same line as the 2 it would get ambiguous again.

42
---
 2 (9+3)