help me with math!

[Deleted]

I like how you guys really answer these...

[Tarantism]

In certain problems, the outcome changes depending on which you prioritize over the other. On of which is actually a common thread-starter here for people trying to illicite angering responses.

I feel like there is some sort of miscommunication here. Or I am really missing something. Multiplication and division are of the same priority in the sense that, assuming the operations are contained in the same parenthesis, You operate from left to right in order of doing multiplication and division. Yes, there are examples in which different prioritization of multiplication and division lead to different results, but all of them would require different parenthetical positioning for the different prioritization to be legitimate. Otherwise multiplication couldn't be well-defined on R (since division is just multiplication by the inverse), and that would be a rather big problem.

But as I said maybe I am missing something.

[Deleted]

In certain problems, the outcome changes depending on which you prioritize over the other. On of which is actually a common thread-starter here for people trying to illicite angering responses.

No, it does not.

[Badpaladin]

Sure it does, plug 48/2(9+3) in different calculators. You'll likely get different answers because of implied multiplication taking precedence in the program, which isn't ecessarily incorrect, just not agreed upon. You could write this with the 48 on top, simplify to 24/(9+3) and get 2. It's clear why something like this can cause people to get riled up. I still agree that M and D hold equal precedence(else I wouldn't have written they do earlier).

[haxartus]

The whole "Order of Operations" thing makes absolutely no sense and it's technically wrong. It gives a correct answer but it doesn't mean you have to repeat it and follow it like it's a general rule of mathematics or something like it.

[Deleted]

Sure it does, plug 48/2(9+3) in different calculators. You'll likely get different answers because of implied multiplication taking precedence in the program, which isn't ecessarily incorrect, just not agreed upon. You could write this with the 48 on top, simplify to 24/(9+3) and get 2. It's clear why something like this can cause people to get riled up. I still agree that M and D hold equal precedence(else I wouldn't have written they do earlier).

Wait... you are talking about calculators? As in having some piece of junk doing the job for you?

[Tarantism]

The whole "Order of Operations" thing makes absolutely no sense and it's technically wrong. It gives a correct answer but it doesn't mean you have to repeat it and follow it like it's a general rule of mathematics or something like it.

It is a general rule of mathematics for operations on any set of numbers contained by C and standard operations? We have the notation we do for a reason. Unless you want to explain how it is technically wrong.

And Badpaladin, your example of simplifying to 24 then dividing by 12 only works with brackets around [2(9+3)]. If you do write it with 48 in the numerator of a fraction and 2(9+3) in the denominator, there are implied brackets around 2(9+3).

[Deleted]

48/2(9+3) = 24*1/12 = 2
48/2(9+3) = 48/2*12 = 48/24 = 2
48/2(9+3) = 48/18+6 = 48/24 = 2

[haxartus]

There is no "order of operations" in a properly written equation (not in a single line). You can calculate it the way you like it. The only thing you have to know is what is a valid or an invalid operation.
Limiting in any way the creativity of the students by teaching them a standard algorithm for solving problems like the "Order of Operations", and then criticizing them for not following it is wrong.

[Tarantism]

There is no "order of operations" in a properly written equation (not in a single line). You can calculate it the way you like it. The only thing you have to know is what is a valid or an invalid operation.
Limiting in any way the creativity of the students by teaching them a standard algorithm for solving problems like the "Order of Operations", and then criticizing them for not following it is wrong.

If you could please give an example. As far as I am concerned, order of operations is rather necessary to prevent people from solving things incorrectly as Ichiago has done. 48/2(9+3)= 24*(9+3). That is just how the notation works. You can't say 3+5^9= (3+5)^9 because then functions written in that form would not be well defined. Its not limiting creativity by teaching them a single algorithm, it is teaching them the rules of a language.

[Gwiez]

@OP
It would only be 13 if it was written "(9 + (-n)^2)=?"
I know it's the same symbol for minus and for negative number, but unless there's something to indicate that it's supposed to be a negative, you assume it's a minus sign. Like others have said, when you follow PEMDAS, you do exponents before you do add/subtract, so you do 2^2 before you do the subtraction (or negative).

[Deleted]

There is no "order of operations" in a properly written equation (not in a single line). You can calculate it the way you like it. The only thing you have to know is what is a valid or an invalid operation.
Limiting in any way the creativity of the students by teaching them a standard algorithm for solving problems like the "Order of Operations", and then criticizing them for not following it is wrong.

What you are saying is that 3*2+2*2= 16

[Knuffelbert]

Yes, there are examples in which different prioritization of multiplication and division lead to different results

Could you give an example? Because I can't think of one, multiplication before division should have exactly the same result as the other way around (left to right does not matter (once you "draw" the syntax tree of an equation it becomes apparent why this is)


To haxartus, yes the times before addition rule (and similar) are not in the sense a law of physics, however it is universally agreed upon. 3*2+2*2 is easy to see that it's 10, because we all have practice following the (arbitrary) BEDMAS (or similar) rule, otherwise it will be 16 if you follow the (arbitrary) rule of left to right. The way physical, stochastic and similar equations are written make it convenient to just make the exponents-before-multiplications-before-addition rule (with parenthesis as an override function so to speak) otherwise everything would be ambiguous without loads of parenthesis.

Teaching them to "do it how they like" will not translate the intent of the equation correctly and would thus be wrong. The BEDMAS (and similar) rules are pretty much always assumed by the author, if the student fails to follow them then it IS wrong.

[haxartus]

You can't say 3+5^9= (3+5)^9 because then functions written in that form would not be well defined.

Exactly. Adding integers with different exponents is an invalid operation. If I have (5+6)^2 the order of operations tells me that I have to sum 5+6 and then calculate 11^2. But I don't have to. I can solve the exponent first by writing it as (5+6)(5+6) or in a thousand other ways and still get the right answer.

What you are saying is that 3*2+2*2= 16

I'm saying that 3*2+2*2=5*2 or (2+3)*2

[Tarantism]

You do realize that you are still following order of operations in any of those situations right?

Edit: Knuffelbert, what I meant by different prioritization would be how you place parenthesis. For example (4*4)/(4/4)= 16, but 4*4/4/4 = (((4*4)/4)/4)= 1

[haxartus]

You do realize that you are still following order of operations in any of those situations right?

Parentheses outrank exponents, didn't they ?

[Deleted]

Parentheses outrank exponents, didn't they ?

Huh? When?

[haxartus]

Huh? When?

According to the famous "order of operations".

[Myrlae]

maybe he thought the minus would be an algebraic sign.
In that scenario it'd be -2^2=4

[Tarantism]

Parentheses outrank exponents, didn't they ?

You haven't really done anything other than apply the definition of exponents. When people say parenthesis first, they do mean (5+6)^2 =/= 5+6^2. You still maintained the parentheses as illustrated by the fact that all your terms are still in parentheses. I suppose that depending on how you use the language that could be seen as a counter example but I don't think so.

More over, you initially said order of operations was technically wrong. Well it is never wrong. Besides I hardly feel that it limits creativity. I don't think being able to solve a simple algebraic equation in multiple ways is creative at all. Its just application of definitions of operations and then properties like distributive or commutative. Its more that you don't really understand simple algebra if you can't do that.

Sure there is creativity in math, but I don't think you see any of it till you get to proofs.