Maths Test! 2(1+2)2/(1+2)

[Thorgalaeg]

Dp..............

 

[Thorgalaeg]

Your point is of course valid, but frankly I would interpret it as a sign that the author has no idea how to properly use TeX

Yes, I would say that this discussion is indeed a computer related problem which makes no sense if you use paper and pencil.

 

[Mise]

Yeah I agree with Thorgalaeg; usually the / sign means that you treat anything on the left hand side separately to anything on the right hand side, unless there's a space. That's not following BODMAS, but it's nonetheless how people write things when typing. I know that's how I do it sometimes.

E.g. thorgalaeg's 3/2x vs 3x/2. Nobody would write 3/2x if they meant (3*x) / 2 -- they would write 3x/2 if they meant that. If they wrote 3/2x, they'd mean 3/(2*x)

3/2 * x, on the other hand, means (3/2)*x. Because there is a space between x/2 and *.

 

[NickyJ]

Order of operations (with irrelevant operations removed): Brackets -> Multiplication -> Division

The order of operations places multiplication and division on the same level, so you would start at the beginning of the problem and work to the right, which means you would divide first, then multiply.

in essence multiplication and division are same operations. so they have same priority.

Precisely.

Oh, please, don't get me worked up on this lame order of operations thing. It doesn't mean you can't distribute parentheses whenever you feel like it, you just have to do it right.

So of course 2(1+2) = 2+4 = 6 is just as valid as 2(1+2) = 2*3 = 6.

But if you have something like 6/2(1+2) and then distribute the parentheses you have to keep them for the result term, i.e. 6/(2+4). The original poster's "mistake" (which of course was an intentional joke) was that he didn't keep these parentheses, not that he made a 4 appear or violated the sacred rules of the order of operations

The order of operations is one of the founding principles of mathematics. And as it says, you should do the parenthesis first, then the multiplication/division. If you don't like it fine, but you cannot deny that it is the correct way that will give you correct results.

You seemed. But I wasn't sure, so I asked.

Well, just to be clear, I was not contesting it.

 

[Takhisis]

Well, this thread will die within a week or so and someone will think up a new number in time for Workers' Day to restart the cycle.

 

[NickyJ]

Nah, this will die within the week, but it'll be necro'd in about five years.

 

[Mise]

Nobody who actually does maths would interpret 3/2x as (3/2)*x. And nobody who actually does maths would write 3/2x to mean (3/2)*x. They would write 3x/2 instead. Thoralaeg is perfectly correct in what he's saying.

 

[Murky]

What's the point of this thread? 6 ≡ (2/3)

 

[Leoreth]

The order of operations is one of the founding principles of mathematics. And as it says, you should do the parenthesis first, then the multiplication/division. If you don't like it fine, but you cannot deny that it is the correct way that will give you correct results.

That will hardly help you when you have to solve algebraic equations, i.e. do actual mathematics.

 

[CKS]

Nobody who actually does maths would interpret 3/2x as (3/2)*x. And nobody who actually does maths would write 3/2x to mean (3/2)*x. They would write 3x/2 instead. Thoralaeg is perfectly correct in what he's saying.

Well, I'd write \frac{3}{2} x quite often. When restricted to plain text and students who wouldn't understand LaTeX notation, I might write 3/2 x, although I'd be more likely to write 1.5 x. It would be very unlikely that I'd write 3x/2, even though it is unlikely to be misinterpreted.

Perhaps I'm not someone who "actually does maths" though, as I primarily do physics.

 

[Antilogic]

Nah, this will die within the week, but it'll be necro'd in about five years.

I'm shocked there's over 100 posts here.

Also, I have written (3/2) x with that intended meaning in text, on paper I write 3/2 x with the intention of it being read as before, but it's more obvious based on how it is written that it isn't 3/2x. Might be an engineering thing, but I like to separate out coefficients from my variables.

 

[Takhisis]

But it's clearer if you write

 3 
--- x
 2

than if you write 3/2 x. (3/2) x is better.

 

[Antilogic]

But it's clearer if you write

 3 
--- x
 2

than if you write 3/2 x. (3/2) x is better.

That's more like how I write it on paper, but I didn't bother using the code box. I use tons of parentheses, though, so it's never ambiguous.

 

[muhtesem insan]

Let me try to explain this from begining.
1)For the question at hand there's only one correct answer and this is 9. It doesn't matter what method you use.
2)I would not raise an objection if anyone said fraction is more human readable so it's better to use it and that's why scientists and mathematicians mainly prefer it over division.
3) What I object is the reason proposed for fraction is ambiguity of division. That's not the case. In every example given (including 3/2x) there's only one correct way to interpret it. If you don't its only because of lack of knowledge (or lack of using it in this case) I agree I wouldn't write 3/2x if i wanted to write 3x/2 but still 3/2x is equals to 3x/2. If a scientist wants to write 3/(2x), he should write 3/(2x) or use a fraction. There's no other way.

 

[IdiotsOpposite]

Can we at least agree that the main problem here is that the notation used in the problem is terrible, and fraction notation would be greatly preferred?

 

[NickyJ]

That will hardly help you when you have to solve algebraic equations, i.e. do actual mathematics.

I've been doing algebraic equations for a while now, it's been holding up just fine.

 

[Antilogic]

Can we at least agree that the main problem here is that the notation used in the problem is terrible, and fraction notation would be greatly preferred?

I thought that should have been agreed on long ago, but I'm not sure what you mean in the second half. Do you mean it's easier for humans to read if it's written on multiple lines with a fraction bar?

If so, then yes.

 

[Thedrin]

Sorry, but first find me any self-respecting mathematician who even uses the division symbol at all. Even if there are strict rules that govern its behaviour it's simply too prone to human error and I've never seen it used outside of the restricted world of computational notations.

The usual algebraic definitions of addition and multiplication even omit the inverse operators completely, simply because they're not necessary. If you already have defined + and *, you can invert +a by adding the additive inverse of a, i.e. +(-a) [note that the "-" here is not the minus operator] and invert *a by multiplying with the multiplicative inverse of a, i.e. *(a^-1) or *(1/a) [the fraction 1 over a].

Thorgalaeg:
[Numerous posts]

Defiant47: (later in this thread]
Yes it does, although you could argue that this fact is more from a notational perspective. Especially when you do University-level math, you use implicit multiplication all the time, and it's always meant as one term (i.e. implicitly multiplied taking precedence over regular multipliation).

3/2x will always equal 3/(2x) because "2x" is meant as one term (its resolution comes before all other of its kind).

BEDMAS is very useful for elementary school level math, and is used a lot for younger children, and even in high school. But it's hardly comprehensive enough to cover all aspects of math, such as implicit multiplication encountered later on in one's mathematical career.

Thank you. This all helps explains why I'm at a loss in this thread.

 

[Boundless]

I find it hilarious the thread has got to this length.

[/successful]

 

[Thedrin]

NickyJ:
The order of operations is one of the founding principles of mathematics. And as it says, you should do the parenthesis first, then the multiplication/division. If you don't like it fine, but you cannot deny that it is the correct way that will give you correct results.

No, it's not one of the founding princiapls of mathematics. Maybe you could argue that it's one of the founding principals of the notation of mathematics. The relationship

x(y + z) = (xy + xz) [1]

is easily derivable from the axioms of natural numbers. The axioms of natural numbers are the assumptions used to derive all other rules of the natural numbers. The rules of natural numbers are sufficient to determine the value of

a/(b(c+d)) [2]

where a, b, c, and d are natural numbers (as they are in the OP).This relationship [1] means that it is acceptable to rewrite [2] in the following way

a/(b(c+d)) = a/(b*c+b*d)