Still having fun here...follow the bouncing ball...

Ok. I'm gonna stir this up.
2. and the Commutative Rule says: "The order of factors does not matter".

To this point, which is correct, given three factor a, b, c we can therefore write:

abc = (ab)c = a(bc)

Right? Now, your saying that division is just the same as multiplication right? So we can go ahead and write:

a/bc = (a/b)c = a/(bc) ... ooops, problem here. Still with me?

(a/b)c is not = a/(bc)

Are you guy's forgetting that multiplication is associative and division is not? You cannot just toss divisive factors around like multiplicative factors

So, when you mean c*a/b, you do not write it a/bc, or even a/b*c.

c*a/b is invariant under association. No ambiguity. a/bc is not.

a/bc or 48/2(9+3) are just <snip>. Nothing more.

 

Don't forget that basically we only work with multiplication when talking about the commutative rule:

\(48 \cdot 2^{-1} \cdot (9+3)=48 \cdot (2^{-1} \cdot (9+3))=(48 \cdot 2^{-1}) \cdot (9+3)= (2^{-1} \cdot 48) \cdot (9+3)\)

or in any other way you want to write it.

 

Ah, but your changing the game the way you are writing it Geo.

I'm contending that 48/2(9+3) is horribly ambiguous at best. That 2 adjacent to the (9+3) begs for an implied multiplication between them, not between the 48/2 and the (9+3), which would put it in the denominator.

The way you're writing it,


\(48\cdot 2^{-1}\cdot(9+3)\)

it's just fine.

 

Yet you both wrote the EXACT same thing.

 

@BillO
I know. As someone before me wrote, when in doubt, use C4. Wait - no.
It was like this: when in doubt, go back to basic operations and always cross-check results from different orders of operations.

 

Yet you both wrote the EXACT same thing.

Are you saying that:

48/2(9+3)

and:

\(48\cdot 2^{-1}\cdot(9+3)\)

are exactly the same thing?

 

when in doubt, use C4.

That might just do it...

 

\( \frac{48}{2} (9+3) = 48\frac{1}{2}(9+3)\), so yes

 

Neither of those are 48/2(9+3) and if you can't see that, then sorry, there is little I can do to help.

 

Old school way to write this problem...

48
2(9+3)

Simple and unambiguous, but the need to program it as a single line screwed it up, which is why multiplication came first.

It is the computer format that is the problem, and it is why MDAS was created.

 

I really like how the old school, manual users cling to their conception about math with their teeth.

Believe what you want, in a few years it won't matter anymore, we 'll have taken over.

 

Old school way to write this problem...

48
2(9+3)

As I think I mentioned before, in order to get the (9+3) into the denominator would require it's reciprocal, which was not in the equation. What you have written here is the same as (48/2) x (1/(9+3)), which is not the original problem.

 

Interesting.

AB can only be evaluated as an abbreviation of A*B. There is nothing else it can be. AB has no value on its own, it is not a single element. It is a shorthand way of saying there are 2 elements and they are multiplied together.

So since (9+3) must be evaluated into an element first, there are three elements existing in the equation and the (very poorly written I agree BillO) equation;
48/2(9+3)
can only ever be
48 / 2 * (9+3)
and there are 3 elements and only multiply and divide operations so any further order of precedence is irrelevant.

I think the confusion comes from the terrible practice of writing 2 multiplied numeric elements without using the * symbol.

You would not allow 212 or 2 12 to be a valid way to write 2*12, so therefore you should not allow 2(9+3) in any form but an abbreviation of writing 2 elements 2 * (9+3).

The days of math being done in shorthand on blackboards in chalk is seriously over. Math is done using * and / symbols and good precedence handling with () and the computer can do the rest.

Putting numbers on top of other numbers is dumb, computers have text in horizontal lines, with procedures executed vertically. Every one of us in this thread is communicating with keyboards with letters, numbers and symbols like * and /. Time for the math guys to leave the 1700's behind.

 

Neither of those are 48/2(9+3) and if you can't see that, then sorry, there is little I can do to help.

yes they are, they both are, they must teach things differently, but this is how things are always applied in school, especially in chemistry for conversion factors. Division signs (/) are simply not used, when they are you just flip them.
By the way, I haven't seen that line with two dots since elementary...

 

@THE_RB

Your are correct, thanks. It's refreshing to have someone that can explain this and I think you did great job of it.


@magnet18

Wow. Not since kindergarten eh? Well, dots are a valid way to show products in mathematics. Not just when the Jurassic was fresh and young, but today. When you finally graduate to vector mathematics you might realize.

48/2(9+1) has ambiguous interpretation at best. Get over it kid. It is just not the right way to express this.

Let me ask you, which do you feel is better, 48/2(9+1) or (9+1)48/2? (I think I know what you will say...)

Your lack of understanding of mathematics is a little depressing. Just flip'em, eh? Did you even read what I wrote about the associative properties of division and multiplication?

sigh!

 

By the way, for anyone who thinks that the 2 should be multiplied by the (9+3) first simply because of implicit multiplication, I thought I had better mention this:
In order for implicit multiplication to take precedence over explicit multiplication and division (left-to-right), it must be specified IN THE PROBLEM that this is the case. Since it is not stated in the problem that implied multiplication is more important, the problem can only be solved as 48/2 * 12, or 288.

 

@THE_RB

Your are correct, thanks. It's refreshing to have someone that can explain this and I think you did great job of it.


@magnet18

Wow. Not since kindergarten eh? Well, dots are a valid way to show products in mathematics. Not just when the Jurassic was fresh and young, but today. When you finally graduate to vector mathematics you might realize.

48/2(9+1) has ambiguous interpretation at best. Get over it kid. It is just not the right way to express this.

Let me ask you, which do you feel is better, 48/2(9+1) or (9+1)48/2? (I think I know what you will say...)

Your lack of understanding of mathematics is a little depressing. Just flip'em, eh? Did you even read what I wrote about the associative properties of division and multiplication?

sigh!

I meant the division sign, the line with two dots, the one that looks almost identical to a percent sign...

and honestly, neither, the 48/2 should really be in parentheses.
Having grown up with a single-line entry calculator I've gotten used to using excessive parentheses.

 

Okay, since the word of someone with a degree in math (me) carries no weight around here, maybe you will take the word of the American Mathematical Society.

Look here http://replay.waybackmachine.org/20011201061315/www.ams.org/authors/guide-reviewers.html

Under heading "Manuscripts and style elements", sub-heading "Formulas"

So, the answer is, as I had originally stated, 2.



Edit: Link should be fixed now....sorry

 

Look here http://replay.waybackmachine.org/20011201061315/www.ams.org/authors/guide-reviewers.html

Is this link working for anyone? I keep getting an "Error 404 Not Found"

EDIT: I finally got it to work--I had to delete "http://forum.allaboutcircuits.com/view-source:" from the beginning of the url.
Anyway, I wouldn't necessarily consider that as proof, BillO. I can understand your point of view, but the info on this site is simply about how something is programmed. There are hundreds, if not thousands, of sites with programs saying multiplication by juxtaposition DOESN'T take precedence over the order of operations, as well as hundreds or thousands that do. To be honest, I am actually surprised this thread has not been locked yet--I suppose there is no correct answer, or rather, they are both correct. We all know we will just keep arguing without coming to a unanimous vote. You have your opinion, I have mine, and there is no way anyone will convince me otherwise. I am sure it is the same with you. This problem is designed to create controversy, and it is serving its purpose well. I suppose this thread has no real point, so I would expect the moderators to close it soon.

Der Strom

NOTE TO MODERATORS: I though I should mention that I'm not trying to tell you what to do

 

I think by now we have found our true troll: "thatoneguy"

You should be ashamed of depriving AAC members of their precious free time.

(Just kidding of course)