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

[Hehehe]

Guys, we've already had this discussion. Don't tell me you already forgot 48/2(9+3) ?

http://forums.civfanatics.com/showthread.php?t=418981

I'll just post here what I posted in that thread:

As written, your expression

ax/by

should be evaluated left to right: a times x, divided by b, times y.
The multiplication is not done before the division, but both are done
in the order they appear. Your first solution is right.

Some texts make a rule, as in your second solution, that
multiplication without a symbol ("implied multiplication") should be
done before any other operations in an expression, including "explicit
multiplication" using a symbol. Following this rule, you would
multiply a by x, then multiply b and y, then divide one by the other.
Some (probably most) texts don't mention such a rule - but some of
those may use it without saying so, which is far worse.

I don't know of a general rule among mathematicians that implied
multiplication should be done before explicit multiplication. As far
as I'm concerned, all multiplications fit in the same place in the
order of operations. It's not an unreasonable rule, though, since it
does seem that implied multiplication ties the operands together more
tightly, at least visually; but the idea of Order of Operations (or
precedence, as it is called in the computer world) is supposed to be
to ensure that everyone will interpret an otherwise ambiguous
expression the same way - so if some texts change the rules, or if
people do what feels natural, the purpose has been lost.

The problem here is that the expression looks as if it were meant to
be

ax
----
by

In the Dr. Math FAQ about writing math in e-mail, one of our
recommendations is to use parentheses wherever possible to avoid
ambiguity, even where the rules should make it clear, because it can
be easy to forget them in some situations:

http://mathforum.org/dr.math/faq/faq.typing.math.html

(click on the Fractions link).

So in e-mail we would write it like this:

ax/(by) or (ax/b)*y

depending on what is intended.

There's no rule that implicit multiplication is given higher priority, but that convention is nevertheless sometimes used, as a result, the equation in the OP can be interpreted both ways.

 

[IdiotsOpposite]

Gawd, this thread again. The internet problem so problematic that my other forum banned it.

There is no answer - there can't be when you're that ambiguous.

 

[muhtesem insan]

Gawd, this thread again. The internet problem so problematic that my other forum banned it.

There is no answer - there can't be when you're that ambiguous.

Actually there isn't any ambiguity. There's lack of knowledge.

 

[Arwon]

Maybe we should have a thread about Monty Hall instead.

It could tear this board apart.

 

[Mise]

It's pretty easy to demonstrate the optimum Monty Hall strategy via reductio ad absurdum, even if you don't understand statistics.

 

[Yeekim]

Maybe we should have a thread about Monty Hall instead.

It could tear this board apart.

This is one messed up puzzle!

 

[Leoreth]

That's where he said it.

Also, where do you get 2x1 + 2x2 from? When following the order of operations, you do the parenthesis first, which gives you (3). Then, you go from left to right, so you do 6/2, which equals 3. 3 times (3) equals 9.

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

 

[muhtesem insan]

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

You did it wrong btw. It would be (6/2 + 12/2)

 

[Thorgalaeg]

The problem comes from the original noatation being ambiguous and we dont know if the (1+2) is in the denominator or numerator:

             6               6  
6/2(1+2) =   ---------- or  -----(1 + 2)  ??
                  2(1+2)            2

The real and only solution is not losing time discussing about it, but to write more parentheses: 6/[2(1+2)] or (6/2)(1+2)

 

[muhtesem insan]

The problem comes from the original noatation being ambiguous and we dont know if the (1+2) is in the denominator or numerator:

             6               6  
6/2(1+2) =   ---------- or  -----(1 + 2)  ??
                  2(1+2)            2

The real and only solution is not losing time discussing about it, but to write more parentheses: 6/[2(1+2)] or (6/2)(1+2)

This is not a fraction. This is division.

 

[Leoreth]

This is not a fraction. This is division.

You can't say that with any meaningful amount of certainty. Which is why fractions (also known as the unambiguous way to denote division, and not something inherently different from division) are usually preferred.

 

[muhtesem insan]

You can't say that with any meaningful amount of certainty. Which is why fractions (also known as the unambiguous way to denote division, and not something inherently different from division) are usually preferred.

you can use fraction to represent division. And in this case 2nd fraction you draw can represent this division not the first one. There no ambigiuty on this, for anyone with basic mathematics knowledge.

 

[Thorgalaeg]

Tell me a case where you cant use a fraction to "represent" a division.

 

[Leoreth]

you can use fraction to represent division. And in this case 2nd fraction you draw can represent this division not the first one. There no ambigiuty on this, for anyone with basic mathematics knowledge.

But apparently there is one for people with advanced mathematic knowledge

Fractions are nothing else but a way to denote division, and have the advantage to be unambiguous in the order of operations without the use of parentheses.

 

[Thorgalaeg]

I totally agree. Divisions are used by people with basic mathematic knowledge (children at school, economists and such), scientists use fractions and dont lose time discussing silly notation problems.

 

[muhtesem insan]

I totally agree. Divisions are used by people with basic mathematic knowledge (children at school, economists and such), scientists use fractions and dont lose time discussing silly notation problems.

As a computer engineer i disagree. In computing we can't use fractions.

 

[Thorgalaeg]

That is a computer related problem. Which for me is a complex world with different computer languages that use different conventions. Some read from left to right some right to left, etc...

But i can tell you as a chemist that if i used such ambiguous notation in class instead of fractions some proffesors would have launched the chalkboard eraser to my head a second after.

 

[muhtesem insan]

That is a computer related problem. Which for me is a complex world with different computer languages that use different conventions. Some read from left to right some right to left, etc...

But i can tell you as a chemist that if i used such ambiguous notation in class instead of fractions some proffesors would have launched the chalkboard eraser to my head a second after.

But mathematically this not ambiguous. Rules about operations are clear and if you follow them there's only one right solution. If you want to represent this as a fraction also there's only one right solution.

 

[Terxpahseyton]

Who is contesting that?

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

Actually, discussion of this issue almost always tends to look like evidence the other way, though there are likely confounding factors. The proportion of Americans who incorrectly repeatedly assert that the worse interpretation is better (in this case that's answering 9) is at least no higher than that proportion in other countries. Anecdotally, it seems to be significantly lower compared to some certain nationalities.

Well that wasn't at all what I was getting at, but without numbers I'll won't put much stock in this observation of yours (not saying it isn't possible).

 

[Thorgalaeg]

But mathematically this not ambiguous. Rules about operations are clear and if you follow them there's only one right solution. If you want to represent this as a fraction also there's only one right solution.

I think that something is unambiguous only when everyody agrees on it which is not the case here obviously.

In chemistry there is the IUPAC who has the international authority to say what notation is correct or not and to publicate the rules, dont know if there is a similar authority for mathematics with rules for this case (if so they have not been very successful it seems).