Maths Q

[DerStrom8]

Unfortunately, questions such as these are a waste of time because they cause people to argue over precedence. So the correct answer is "state the precedence rules you want to use first -- then it's easy to calculate the answer.

I wouldn't say that. This particular problem definitely has an exact answer. PEMDAS or BODMAS is a universal rule, meaning that regardless of where you are, it still holds true. Unfortunately, this rule wasn't taught to some of the members here, which causes the problem. But, regardless of how you look at this one, the answer is still definitely B.

 

[Sceadwian]

PEMDAS or BODMAS is a universal rule

This is however not exactly the case....
There is no rule, just commonly accepted convention.
I'm having difficulty finding standards based definition of order of operations recognized by any standards issuing body.

I would love some links if there are any to such standards.

 

[DerStrom8]

According to site:

The nearly universal mathematical convention dictates the following order of operations (in order of which operators should be evaluated first):

Factorial.
Exponentiation.
Multiplication.
Division.
Addition.
Any parenthesized expressions are automatically higher ``priority'' than anything on the above list.

I'm not sure why it is only "nearly" universal. If it wasn't, then problems like these would cause major issues in engineering. Perhaps it is simply not being taught everywhere, though it really should. It is the standard, though I'm constantly surprised how many people have never heard of it. Hmm, this is worth looking further into....

 

[KeepItSimpleStupid]

Then there is this one: -2^2

Is it 4 or -4?

 

[DerStrom8]

Then there is this one: -2^2

Is it 4 or -4?

According to the order of operations, exponents would come first, before subtraction. Therefore, it would equal -4. For it to be 4, it'd have to be (-2)^2. Most scientific calculators will give you an answer of -4 if you have -2^2.

 

[Sceadwian]

It is the standard, though I'm constantly surprised how many people have never heard of it.

It's not a standard, it's a convention, like I said I'm really curious if there are an standards organization that reference these conventions. Otherwise the standards you know to be true are nothing more than figments of imagination, they have to be ratified by an organization like the one that came up with and continues to evolve the set of SI units.

Hmm, this is worth looking further into....

Definitely!!

According to the order of operations, exponents would come first, before subtraction. Therefore, it would equal -4. For it to be 4, it'd have to be (-2)^2. Most scientific calculators will give you an answer of -4 if you have -2^2.

I have a problem with this; the negative is a sign indicator not an operation. It would in fact be 4.

Again.... not so easy when you try to work out the details =)

 

[KeepItSimpleStupid]

Yep, unary minus comes first. Got at least one of ya.

 

[DerStrom8]

I have a problem with this; the negative is a sign indicator not an operation. It would in fact be 4.

A negative sign simply stands in for 0-x. Therefore, a negative is the same as subtraction. For example, let's say you're adding 2X and -X. You simply say 2X MINUS X, which equals 1X.

 

[DerStrom8]

Yep, unary minus comes first. Got at least one of ya.

I'd like to see the convention or rule that says this. I disagree with this statement 100%. -2^2 is the same as 0-2^2, and according to the order of operations, the 2^2 must come first.

Sorry guys, I'm completely bent on using the order of operations. It is what I've been taught since I was a kid, and it was taught to me as a universal rule. I challenge you to find where a generally accepted rule states that the minus comes first in that equation.

 

[Sceadwian]

A negative sign simply stands in for 0-x. Therefore, a negative is the same as subtraction. For example, let's say you're adding 2X and -X. You simply say 2X MINUS X, which equals 1X.

Could you state the standards you used to derive this information?
The positive square of ANY number positive or negative is always positive, This is one of the reasons RMS is so useful, sign goes out the window.

 

[DerStrom8]

Could you state the standards you used to derive this information?

It is simple mathematics. 0-x always equals the opposite of x. Therefore, the opposite of x equals 0-x. It's like saying x=x. It doesn't matter what direction you look at it from. if the first is equal to the second, than the second is equal to the first. Period.

The positive square of ANY number positive or negative is always positive, This is one of the reasons RMS is so useful, sign goes out the window.

If you're squaring a negative number, than yes, I agree--it will always be positive. However, squaring a negative number means that you have the negative number first, and raise it to the second power. That would look like (-2)^2. -2^2 is completely different.

 

[Mikebits]

I wouldn't say that. This particular problem definitely has an exact answer. PEMDAS or BODMAS is a universal rule, meaning that regardless of where you are, it still holds true. Unfortunately, this rule wasn't taught to some of the members here, which causes the problem. But, regardless of how you look at this one, the answer is still definitely B.

Well now I feel like a dummy, good thing I went into fire/rescue. I will be the guy saving your butt in the next disaster

 

[MrAl]

I wouldn't say that. This particular problem definitely has an exact answer. PEMDAS or BODMAS is a universal rule, meaning that regardless of where you are, it still holds true. Unfortunately, this rule wasn't taught to some of the members here, which causes the problem. But, regardless of how you look at this one, the answer is still definitely B.

Hi,

I agree mostly so the correct answer is 41, but there are exceptions.
For example:
"In the following example we will use left to right order of calculations ignoring the normal rules of algebra:"
"40+40*0+1=1"

In this case what are we to do, contact the author and tell him that he got it wrong, or accept his rule for doing calculations?
What if we cant find him/her? Do we throw the book in the garbage?

Luckily this doesnt happen often in modern books or even older ones, but in hand calculators it does. Some of the cheaper ones dont want to have to keep track of multiplications and additions and whatever so they just spit out the answer after each new entry. Is it wrong? Yes it is, but if you know this in advance you can still use the calculator for many tasks anyway.

In the lack of any other context however i'd always assume multiplication and division before addition and subtraction even without parens, unless the author gave examples where it was clear he/she was using simple left to right calculation order.

I guess what i am trying to say is that we might run into both kinds of rules so we do have to be prepared just in case.

 

[DerStrom8]

Hi,

I agree mostly so the correct answer is 41, but there are exceptions.
For example:
"In the following example we will use left to right order of calculations ignoring the normal rules of algebra:"
"40+40*0+1=1"

In this case what are we to do, contact the author and tell him that he got it wrong, or accept his rule for doing calculations?
What if we cant find him/her? Do we throw the book in the garbage?

Luckily this doesnt happen often in modern books or even older ones, but in hand calculators it does. Some of the cheaper ones dont want to have to keep track of multiplications and additions and whatever so they just spit out the answer after each new entry. Is it wrong? Yes it is, but if you know this in advance you can still use the calculator for many tasks anyway.

In the lack of any other context however i'd always assume multiplication and division before addition and subtraction even without parens, unless the author gave examples where it was clear he/she was using simple left to right calculation order.

I guess what i am trying to say is that we might run into both kinds of rules so we do have to be prepared just in case.

Okay, I will agree with that. I suppose it really depends on when the book was written. I guess they didn't start teaching the order of operations in a majority of the schools until recently. The only operations I was told to carry out from left to write were multiplication/division, and addition/subtraction. However, these operations still have their place in PEMDAS. I have actually met several people, both online and in my personal life, who were never taught the order of operations. Nowadays, I don't think the example you gave would stand up. It is frowned upon and considered downright wrong by most mathematicians today. If you know any, I suggest you ask them, saying something like "how would you solve this equation?" I am curious as to how many use the order of operations, and how many don't. Perhaps a poll wouldn't be a bad idea--have everyone ask a mathematician and post their answer.

Does anyone here know how to set up such a poll?

Regards,
Der Strom

 

[Sceadwian]

If you're squaring a negative number, than yes, I agree--it will always be positive. However, squaring a negative number means that you have the negative number first, and raise it to the second power. That would look like (-2)^2. -2^2 is completely different.

You're inferring something with no standards based proof...
It is an opinion, and idea, a concept, not a standard.

A poll wouldn't help anyone.


No one is allowed to infer the methodology of the definition of the length of a meter. Or the amount of mass that makes up a kilogram. It is defined and absolute.

Such is not the case in this respect.

 

[DerStrom8]

First of all, Scead, why are you arguing? I thought you were one of the people that agreed with me

Wow, I guess ARandomOwl was right in post #4. I thought this question was a very simple one with only a single definite answer. I'm surprised at how many people disagree. I guess this is just another one of those threads that will go on and on without solving anything....

 

[Sceadwian]

DerStrom... I am unable to find a standard for mathematical operations, only a convention, if this doesn't fundamentally bother you.... I don't agree or disagree with anyone; I share my thoughts as I see them.

What you know as absolute fact is not what everyone else does.. This is why standards exists in the first place! Which is why I'm surprised I haven't found any in regards to order of operations.

 

[DerStrom8]

DerStrom... I am unable to find a standard for mathematical operations, only a convention, if this doesn't fundamentally bother you.... I don't agree or disagree with anyone; I share my thoughts as I see them.

What you know as absolute fact is not what everyone else does.. This is why standards exists in the first place! Which is why I'm surprised I haven't found any in regards to order of operations.

I understand where the confusion comes from. Depending on when and where you went to school, you may or may not have learned the order of operations. I am saying that nowadays, I firmly believe that PEMDAS/BODMAS has become a standard, not just a convention. I am almost 100% sure it is now taught in most schools, though I don't have proof. That is why I asked for a poll. It could give us a basic understanding of what is being taught these days.

 

[Sceadwian]

If it's a standard what is the organization that declares or stands by the standard? Doesn't matter how many schools teach a thing it doesn't make it standard, until a group that everyone declares as a leading authority says it is one.

 

[duffy]

A negative sign simply stands in for 0-x. Therefore,

No, it's a negative number. Numbers can also be imaginary, or transcendental. In the same manner, "negative" is a quality intrinsic to the number itself, not an operation performed on it. What, do you think a transcendental number is secretly an integer before someone attaches a long tail of decimals to it during evaluation?