6÷2(1+2) (A math topic)

Hypothetically, object-oriented notation as practiced in C++ or Java should come most natural to SVO-speakers, right? "subject.do(object)" Actually, that rings true to me. And, coming back to maths, infix notation. As much as I despise it for it's disgusting, self-deprecating need for parentheses, it's still the most natural to me. See what they done to me at school? They made an infix zombie out of me!!! /rage ;-)

edited 1st May '11 7:00:47 AM by vijeno

^You might like Design Principles Behind Smalltalk. Also, multimethod dispatch systems don't associate methods with objects like that, so it's more like VSO order. Or really, Verb and then a bunch of objects.

But it's not interesting. You're arguing over very much arbitrary rules. This situation wouldn't even arise in real life. I don't understand.

edited 1st May '11 9:08:55 AM by Tzetze

I'm interested inasmuch as this thread has thusfar left me very confused as to what the standard practice would be for a mathematician confronted with 6÷2(1+2).

To ask the person to rewrite it in a more clear manner. This is supposedly understood.

Ah.

Then yes, this does seem a bit silly.

Well, okay, to be more realistic, it might be that they interpret it as one or nine, and if this gets them a nonsensical result they go back and ask for it to be clearer, and if it doesn't then they continue on their merry way.

Though I'm still not sure where it would come up. Using the whole fraction division thing seems to be the norm nowadays.

edited 1st May '11 9:18:00 AM by Tzetze

Well if you're given no clarification you'd just go ahead blindly with BEDMAS rules. So you'd evaluate left to right, except where parentheses are concerned.

So you'd go...

6÷2(1+2)

Then go with

6÷2(3)

This is the sticky point here because 2(3) is short-hand for 2*3 but the parenthesis increase the priority as well. In essence I wrote something that doesn't even look right. If I were a compiler I'd just tell you that your code had a syntax error. Or I'd do something at random.

edited 1st May '11 9:18:58 AM by breadloaf

No wait, I got this figured out, 2 is a function.

Thus, this entire dealy is 6 divided by a function 2 of 3.

f(x) -> 2(3)

Problem solved.

Parenthesis indicate priority for what's INSIDE them. Once you've evaluated the inside, it's not parenthesis anymore, it's multiplication. (3) is just 3, there's no operations inside the parenthesis to be solved.

...Right?

If you replace the 2 with an X you get 6/X(1+2). You can get that to 6/3X, substitute 2 for X, and get 1.

If you replace the 1 with an X, you get 6/2(X+2) which is starting to look more like a real equation. Typically you distribute: 6/(2X+4), then you're stuck until you substitute: 6/(2+4). 6/6, 1.

This leads me to believe that the answer ought to be one.

Replacing the second 2 with an X gets you the same: 6/(2+2X), 6/(2+4), 6/6, 1.

Replacing the six gets you X/2(1+2), X/2(3), X/6, 6/6, 1.

If you replace the (1+2) with its sum, 3, and a proper multiplication sign, as I was led to believe is what basically happens when you finish with the P in PEMDAS and move on to the EMDAS, you get: 6/2*3, which is 3*3, which is 9.

Hrm. This freaks me out.

edited 1st May '11 9:24:43 AM by Yamikuronue

Presumably you mean f(x) -> 2(x)? f : Ø -> {6} isn't particularly useful.

The question seems to boil down to whether or not the (1+2) is actually being divided.

edited 1st May '11 9:26:31 AM by Yej

Which is why I said 9 at the beginning. For what I learned and I presume it is quite international, BEDMAS rules, the 2(3) is multiplication, so you'd follow left to right.

I was presuming that there's some kind of strange rule system some of you were following here for the 2(3) but maybe I shouldn't presume and just say that the rest of you are wrong because this is math and if the international BEDMAS system weren't international nobody could transmit math to one another with any hope that the other guy would understand.

Nope, we just have some funky notion where instead of using a letter, someone used a number as the function. There's probably some specific output if you input three in function two, but there's not enough information given to find out what that is. Six is just an outside operation that will effect how the entire equation looks (like say, multiply everything by 5, but in this, divide 6 by everything).

My thought is that 2(3) == 2*3. But then I thought of the distributive property where 2(X+Y) = (2X+2Y) and that muddled things up for me. And then I got lost.

I don't think 2(3) is higher priority than 2*3 however.

Joking aside, enjoy this.

That confirms my thought that parenthesis only elevates what's inside, not what's adjacent. Yay! Now the distributive thing - I'm tempted to say that's me not understanding math properly, but what bugs me is that replacing some known quantity with a variable ought to produce the same result when you re-substitute later, but in this case it doesn't.

Shouldn't really matter, you just combine what's inside the parenthesis and then go from left to right. As. Stated. In. The. Linked. Article.

Wikipedia for God, 2012.

2(3+0)==(2*3+2*0)==(6+0)?

edited 1st May '11 9:40:10 AM by Yej

@118 yes?

2(3+0)==(2*3+2*0)==(6+0) == 6.

2(3+0) == 2(3) == 6.

I don't see where there's a problem?

I don't know, this question totally confuses me @.@

edited 1st May '11 9:42:26 AM by Yamikuronue

Yes. Now I'm confused about where you're getting confused, since 2(X+Y)=(2X+2Y) does give the right result if you substitute in appropriately.

edited 1st May '11 9:46:02 AM by Yej

I found the problem!

Replace (1+2) by X. Thenyou have a two-equation system:

• X= 1+2
• 6/2X

we can all agree X=3 is a valid step here I presume. But.

6/2X

Does that mean six halves times X, which is (6/2)X = 3X = 9?

Or does it mean six over two ex, which is 6/(2X) = 6/6 = 1.

The parenthesis just confuse the issue further and throw me off the scent. Order of Operations would say without parenthesis, 6/2X = (6/2)X = 9.However, using the division sign instead of the slash symbol, the natural sentence read aloud is "Six divided by two X" and we tend to treat 2X as a unit, a single variable, rather than 2*X, so it starts to look like 1 when it should be 9.

Okay, now where did I go wrong with my earlier variable substitutions? Specifically

I think.... does distributing break out of the parentheses? Such that I should have written 6/2X+4, which is (6/2X)+4 = (3X)+4 = holy crap I got seven. Bad Yami.

ETA:

edited 1st May '11 10:00:04 AM by Yamikuronue

The final answer is nine because you go from left to right and that's the standard.

6/2(3) = 6/2*3 = 3*3 = 9

I swear, I'll get my friend who's a math major in here and have him confirm it, it's 9.

A lot of people in this thread have been majors in mathematics and related fields, you know.

I believe you, but I was more concerned with why what I wrote was wrong so I can know not to do that again on more complicated equations. Which I've now solved with help from Red ^_^

The key to my issues is you can't distribute if the coefficient is involved in other, higher-priority actions than the multiplication. Since I tend to jump to the distributive property when I'm lost as to what else to do, that explains several, several failed tests. Nobody ever pointed that out to up, up through Calculus I (which I barely passed).

edited 1st May '11 10:08:00 AM by Yamikuronue

Yeah I was about to say that your distributive property isn't a concern here. The only thing that matters is that you evaluate (I keep typing elevate for some reason) from left to right, instead of right to left like Tom did.