Many calculators not following math rules?

[Davros]

Nope the calculator is correct
remember your bodmas

do the sum in brackets first
9+3 = 12
divide and multiply have equal precedence so you evaluate left to right
48/2 = 24
that leaves you with
24(12) = 288

B Brackets first
O Orders (ie Powers and Square Roots, etc.)
DM Division and Multiplication (left-to-right)
AS Addition and Subtraction (left-to-right)

Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)

http://www.mathsisfun.com/operation-order-bodmas.html

 

[Mize]

I think most people who have taken calculus would get 2 as their answer. In math and science textbooks they often stretch out long arithmetic expressions for example:

n=PV/RT (T is often written as a sum)

99% of the time the ideal gas law is written that way which could be incorrect if entered into a calculator with T being a sum of two numbers. So for the equation in the OP, 2 is the wrong answer but a lot of people are just used to that form by now.

Blah. Nobody writes it that way and if you had to type it you'd right PV=nRT since that's the standard form.
The only time you'd write it on a single line is when coding an if you coded it:

n = P*V/R*T all would be well

in the example in this thread, if you coded

n = 48/2*(9+3) again all would be well

So if you really wanted

n = 48/(2*(9+3)) then that's what you should have written.

 

[Davros]

just to be clear mize how are you evaluating 48/(2*(9+3)) same way as me ?

im confused because
n = 48/2*(9+3)
n = 48/(2*(9+3))

are not the same

 

[Bludd]

just to be clear mize how are you evaluating 48/(2*(9+3)) same way as me ?

im confused because
n = 48/2*(9+3)
n = 48/(2*(9+3))

are not the same

And Mize said that they are not the same. Oh, poor Davros forgot how to read again.

 

[Mize]

LOL.

Davros, all I'm saying is that the only time you would write an equation like that on a line is for coding and to get the one results (2*(9+3)) requires parens in any coding application. i.e. I was agreeing with you.

 

[Davros]

. i.e. I was agreeing with you.

I never realised this before but you are a genius

 

[Mintmaster]

The problem is that "/" and "÷" aren't real math operators. They're short for the long horizontal line that clearly describes what you are dividing. We use them on calculators and in primary school for convenience, but mixing this shorthand notation with the implied multiplication (a number next to parentheses, which is only used when you are familiar with the long division sign) is just asking for ambiguity.

 

[RudeCurve]

When rewritten with a good old fashioned pencil and paper it looks like this.


48
______
2 (9+3)



so the answer is 2...

 

[Kaotik]

When rewritten with a good old fashioned pencil and paper it looks like this.


48
______
2 (9+3)



so the answer is 2...

You've written it wrong, the correct way is this:
48
---- (9+3)
2

If the one you wrote would be correct, the "one row syntax" would be 48/(2(9+3))

 

[RudeCurve]

Well then that means half of the calculators in the wrold are wrong too...lol.

 

[RudeCurve]

....

 

[Mintmaster]

You've written it wrong

How can you say one is wrong? They're two different expressions.

In mathematics, if you're going to use numbers adjacent to parentheses, then you should use proper notation for division. You'll never find any math paper using "/" and "÷" for anything but the simplest expression. The order of ops you described in the original post which does include "/" and "÷" has no concept of numbers right next to parentheses.

Programming languages don't allow the input you described. For the longest time calculators didn't either, but through market demand they allowed implicit multiplication. It's a bastardization of primary school math (which doesn't use numbers next to parentheses) and higher level math (which doesn't use "/" or "÷").

Personally, I would prefer my calculator to interpret "48/2(9+3)" the way you call incorrect, as it saves me from entering some parentheses for the common case of a number scaling a variable in the denominator (e.g. '2a'). If I wanted 48/2*(9+3), I would enter "48(9+3)/2".

 

[DarthShader]

The problem is that "/" and "÷" aren't real math operators. They're short for the long horizontal line that clearly describes what you are dividing. We use them on calculators and in primary school for convenience, but mixing this shorthand notation with the implied multiplication (a number next to parentheses, which is only used when you are familiar with the long division sign) is just asking for ambiguity.

100% agree with Mintmaster.

There is no "left to right" rule in mathematics. Multiplication and division happen at the same time. It's up to the person writing down the expression to avoid ambiguity by using correct mathematical notation. Calculators cannot do expressions at the same time, so they use a convention. From left to right or right to left, both are mathematicaly correct. If that created ambiguity and not the result the user intended, it's not the calculator's fault, but ther user's.

 

[Davros]

Calculators cannot do expressions at the same time,

I doubt people can, I cant do a multiplication and a division simultaneously

 

[Silent_Buddha]

Anyone have PowerCalc from Windows XP Powertoys? The calculator in Win 7 doesn't really handle inputting this equation.

Win7 calculator has no problems inputing this equation. But it forces the user to use proper syntax as many in this thread have pointed out.

The correct way to put it in as a one line item is...

48 / 2 * (9+3) if you want 288. 48 / (2 * (9+3)) would be correct if you wanted an answer of 2.

The calculator is basicly correct in forcing users to avoid lazy and ambiguous equation writing.

48 / 2 (9+3) as has been mentioned could result in either 2 or 288 and be correct in both cases due to the abiguity of the shorthand used.

Hence, all calculators are correct when using that ambigous notation. It's the users fault if they don't get the answer they expected, not the calculators.

Regards,
SB

 

[Mize]

I thought we had more programmers here.

 

[Kaotik]

100% agree with Mintmaster.

There is no "left to right" rule in mathematics. Multiplication and division happen at the same time. It's up to the person writing down the expression to avoid ambiguity by using correct mathematical notation. Calculators cannot do expressions at the same time, so they use a convention. From left to right or right to left, both are mathematicaly correct. If that created ambiguity and not the result the user intended, it's not the calculator's fault, but ther user's.

Wait.. what? Algebra completely new thing to you?
It has clear rules on order of operations, which include left to right rule.

Mintmaster, it's wrong when talking about the (extremely) simple equation this thread was about

 

[Silent_Buddha]

Wait.. what? Algebra completely new thing to you?
It has clear rules on order of operations, which include left to right rule.

Mintmaster, it's wrong when talking about the (extremely) simple equation this thread was about

Even in algebra there is no rule that you have to go from left to right for multiplication and division. It's a convention that is taught, but it really doesn't matter if you go right to left or left to right you'll get the same answer regardless assuming you use correct equation writing notations. Otherwise, it only matters with addition and subtraction.

The only time it becomes an issue is with the use of the / shorthand.

48
__ * (9+3)
2

Will result in the same answer either way. Well, except here since we're using correct notation writing you can obviously see why.

4
______
2 * (9+3)

Also results in the same answer either way. But again correct notation makes things clear in a way that isn't when using shortcuts.

It's only when we start using shorthand that it becomes an issue. And that's where you have the convention of left to right.

But that has nothing to do with algebra itself. Only with writing it using shortcut notation, as Mintmaster noted above, which is inherently imprecise.

Regards,
SB

 

[Kaotik]

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)

 

[DarthShader]

Wait.. what? Algebra completely new thing to you?
It has clear rules on order of operations, which include left to right rule.

Actualy, I had a semester of abstract algebra at Uni. Hated it. But I learned a few things. Like the fact that the real numbers we use every day and sometimes commonly refer to as "algebra", is in fact a field. Oversimplifying it a bit, it's two two abelian (where the order of operands doesn't matter) groups over the same set of real numbers, whose operators: addition and multiplication are connected together by the equation a * (b + c) = a*b + a*c. Oh, and division by 0 is prohibited. Notice, there is no operator "division". That is because what we refer to as division, is in fact multiplication by the inverse of the given element. And the axiom of associativity says ( A * B ) * C = A * ( B * C ). There's nothing that says "left to right" here. I am entitled to interpret A * B * C as I wish and swap around the order, since the end result will be the same.

So why are kids in primary school tought to do it from left to right, like your links show. I can think of four trivial reasons:
1. Because it's not wrong. (see above)
2. Because in european and related cultures we read from left to right. And kids usualy learn basic algebra at a roughly similar time they learn to read. (might not hold for other cultures, no idea how it's done there) 3. Not to overload their young heads with abstract things.
4. Consequently, to avoid some of the young creative ones doing 9 - 4 + 5 = 0.