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View Poll Results: 6÷2(1+2) = ?
9 94 54.34%
1 77 44.51%
7 2 1.16%
Voters: 173. You may not vote on this poll

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Old May 3rd, 2011, 03:26 AM   #151 (permalink)
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Oh I'm not trolling... Just trying to figure out how you guys are separating it out.

Using that logic, that means 6÷2(x+y) = 3(x+y)?

Don't know - I wasnt taught that way. I was taught that:

6÷2(x+y)

is

6
---
2(x+y)

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Old May 3rd, 2011, 03:33 AM   #152 (permalink)
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From a previous wiki reference -



Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x).


Substitute (1+2) for x and it's case closed.

The division sign was covered by the mathematician.

You were taught that 3x is the same as 3*x, focus on that.
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Old May 3rd, 2011, 03:40 AM   #153 (permalink)
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Quote:
Originally Posted by EarlyMon View Post
From a previous wiki reference -



Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x).


Substitute (1+2) for x and it's case closed.
That one I can follow.

6/2(x+y) being equal to 3(x+y) I have trouble following.

substituting (1+2) for x in that example is still not the same, as you only have the multiplier.

So you can follow my logic, I was taught 6/2(x+y)
is
6
---
2(x+y)

which is same as

6
---
2x +2y

Sounds like something to send to school with my son, and see what answer his algebra IV professor sends back


EDIT: never mind - I see your reference . almost 5am here.
1/2x = 1/2(x), 6/2x = 6/2(x).

Still curious as to what his prof will say
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Old May 3rd, 2011, 05:02 AM   #154 (permalink)
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Quote:
Originally Posted by EarlyMon View Post
It was settled long ago.

Wanting a thing does not make it so.
Whoo Hoo!!! Another objectivist. EarlyMon solves the equation A=A. Nice to find a kindred spirit.
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Old May 3rd, 2011, 09:36 AM   #155 (permalink)
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Quote:
Originally Posted by Sharkonwheels View Post

So you can follow my logic, I was taught 6/2(x+y)
is
6
---
2(x+y)

That's the part that's incorrect.


6/2(x+y)

is

6
--- (x+y)
2

See the difference? You can't put just the 2 in the parenthesis, the way you're doing it, you're supposed to multiply the entire "six halves" against x and y.

The 6/2 part doesnt need a parenthesis to go before the 2 * (3) part since it's equal in order of operations and leftmost.
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Old May 3rd, 2011, 10:31 AM   #156 (permalink)
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Order of operations - Wikipedia, the free encyclopedia

Scroll down to "Gaps in the Standard."

What this section states (or implies) is that if you try to interpret 6÷2(1+2) strictly by the HUMAN-MADE order of operations, it is ambiguous. The system is not perfect. There are gaps where additional parens are needed to remove ambiguity. But as long as ambiguity exists, it can go multiple ways.

Of course the problem is, most people don't believe that it's ambiguous; they think there must be a correct answer and that their interpretation of PEDMAS is absolutely correct. And in both directions, it's a correct interpretation. That is the definition of ambiguous. That's the reason people are split 50/50 no matter where this question is posed.

It doesn't matter how many PhDs you have and in what field. I'm sure there are super-intellects on both camps. The right answer is: don't expect a consensus until you add parentheses to the original problem to make it unambiguous. The problem was designed to exploit the gap in the order of operations.
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Old May 3rd, 2011, 11:49 AM   #157 (permalink)
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Oh, don't worry guys - it was a MAJOR facepalm moment when the light turned on

His example, fyi, if you were to ask me what 1/2(1+2) was, I could literally read it out as "one half times one plus two". so, 6/2, 1/2, makes no difference. Call it "six halves times one plus two" and the result is 9.

Guess that's why it's a math problem. I assume it's the 6/2 throwing folks off, I dunno. I think if you were to ask what 1/2(1+2), most people would probably get it right

And to answer n0ct3m, yes, it's settled, and the answer is 9.

And, sadly, the Atrix bootloader is still locked

Oh, and I'd like to apologize to my teachers, because there is NO WAY they taught me that 6/2(1+2) = 1
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Old May 3rd, 2011, 12:07 PM   #158 (permalink)
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Quote:
Originally Posted by novox77 View Post
Order of operations - Wikipedia, the free encyclopedia

Scroll down to "Gaps in the Standard."

What this section states (or implies) is that if you try to interpret 6÷2(1+2) strictly by the HUMAN-MADE order of operations, it is ambiguous. The system is not perfect. There are gaps where additional parens are needed to remove ambiguity. But as long as ambiguity exists, it can go multiple ways.

Of course the problem is, most people don't believe that it's ambiguous; they think there must be a correct answer and that their interpretation of PEDMAS is absolutely correct. And in both directions, it's a correct interpretation. That is the definition of ambiguous. That's the reason people are split 50/50 no matter where this question is posed.

It doesn't matter how many PhDs you have and in what field. I'm sure there are super-intellects on both camps. The right answer is: don't expect a consensus until you add parentheses to the original problem to make it unambiguous. The problem was designed to exploit the gap in the order of operations.
I believe a distinction should be made; the problem can be written better, but the answer isn't ambiguous.

People in the 1 camp would still have to modify the problem by adding their own independent set of brackets to the equation, in order to arrive at 1, making it look like this: 6÷[2*(1+2)]. <-- In that specific case, you certainly would solve for the inner set of parenthesis/brackets, and then outward with the second set, multiplying the sum of 1+2 against 2.

As written, but simplified without making any additions or violating rules, (6)÷(2)(3) or (6)÷(2)*(3)= 9.

Anything else would mean we're placing priority on numbers outside of parenthesis, or working from right to left.
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Old May 3rd, 2011, 06:14 PM   #159 (permalink)
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I still maintain the answer is 42.
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Old May 3rd, 2011, 06:46 PM   #160 (permalink)
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Quote:
Originally Posted by alostpacket View Post
I still maintain the answer is 42.

I maintain that this thread is full of nerds. I don't think that puts me in a very good position now....
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Old May 3rd, 2011, 06:52 PM   #161 (permalink)
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The geeks like you, so it's all good.
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Old May 3rd, 2011, 06:57 PM   #162 (permalink)
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Only because we have too
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Old May 3rd, 2011, 07:06 PM   #163 (permalink)
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@EM, awww<3

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Only because we have too

Oh hush you
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Old May 3rd, 2011, 07:16 PM   #164 (permalink)
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back off.. or i will take your reecess cup
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Old May 3rd, 2011, 08:31 PM   #165 (permalink)
 
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9

I did that shit in my head....

The answer to the problem depends on how it's written and in this case...
6/2(1+2)
6 / 2 * 3
3*3
9

You always do math left to right, like reading a book, or this post. Always solve for whats in parentheses first. Then solve ops like square roots & powers. Then solve muliplication & division, left to right. Then addition & subtraction, left to right.

It's not phrased "6 / 2 + (1 + 2)" so how you get anything but "9" is beyond me.
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Old May 3rd, 2011, 08:41 PM   #166 (permalink)
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Quote:
Originally Posted by Roze View Post
I maintain that this thread is full of nerds. I don't think that puts me in a very good position now....

Actually:

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Old May 3rd, 2011, 08:48 PM   #167 (permalink)
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^^^ i am dan330 and i approve that message
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Old May 3rd, 2011, 10:27 PM   #168 (permalink)
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Quote:
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I still maintain the answer is 42.
No, no...It's 37.
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Old May 4th, 2011, 04:09 AM   #169 (permalink)
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This thread wins 'Nerdiest thread in all of Phandroid' hands down.
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Old May 4th, 2011, 10:13 AM   #170 (permalink)
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This thread wins 'Nerdiest thread in all of Phandroid' hands down.

I don't know... there the other one about.. traveling at near light speed
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Old May 4th, 2011, 12:08 PM   #171 (permalink)
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I don't know... there the other one about.. traveling at near light speed

link?
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Old May 4th, 2011, 12:29 PM   #172 (permalink)
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Hang on tight : Speed of LIGHT!

Here's another good one - 2012 2 suns

Ummm ... basically, the whole forum is kinda full of nerdy threads, really.
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Old May 4th, 2011, 12:31 PM   #173 (permalink)
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Quote:
Originally Posted by alostpacket View Post
link?
There you go ALP: Hang on tight : Speed of LIGHT!

Edit: -_-;;; Got ninja'd by the EM!!! Curse you and your ninjaing ways!
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Old May 4th, 2011, 12:37 PM   #174 (permalink)
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Ninjas are masters of time, too.
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Old May 4th, 2011, 12:41 PM   #175 (permalink)
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Ninjas are masters of time, too.

No.. just the shadows
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Old May 5th, 2011, 01:13 PM   #176 (permalink)
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i just wonder
let x=1, y=2
2x ÷ 3y
---> (2x) ÷ (3y) = 2 ÷ 6 = 1/3

or
(if u say by follow left-to-right rule)
---> 2*x÷3*y
= 2*(1)÷3*(2)
= 2 ÷3*(2)
= 0.6666667*(2) = 4/3

------------------------------------
6÷2(3)
let x=3
6÷2x, then means 6÷(2x)
and 6÷6=1
isn't it ?
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Old May 5th, 2011, 07:15 PM   #177 (permalink)
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Quote:
Originally Posted by bluetree View Post
i just wonder
let x=1, y=2
2x ÷ 3y
---> (2x) ÷ (3y) = 2 ÷ 6 = 1/3

or
(if u say by follow left-to-right rule)
---> 2*x÷3*y
= 2*(1)÷3*(2)
= 2 ÷3*(2)
= 0.6666667*(2) = 4/3

------------------------------------
6÷2(3)
let x=3
6÷2x, then means 6÷(2x)
and 6÷6=1
isn't it ?

Welcome to AF

I think a good thread where you can find the answer to your question is: here

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Old May 5th, 2011, 10:27 PM   #178 (permalink)
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Here is the answer: YouTube - 6÷2(1+2)=?
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Old May 5th, 2011, 10:41 PM   #179 (permalink)
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Here is my reply to that:



Read the thread if you haven't already for explanations. Welcome to the forums by the way!
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Old May 5th, 2011, 10:52 PM   #180 (permalink)
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I think I've brought a lot of people to Android Forums (whether they make an account or not) based off of this thread. lol I assume a lot of people typed it in Google and this site came up as a link.

... I should be paid. That's all.
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Old May 5th, 2011, 11:00 PM   #181 (permalink)
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Check's in the mail!
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Old May 5th, 2011, 11:43 PM   #182 (permalink)
 
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in math, whenever in doubt, the answer is always eleventeen.

thought everyone knew that.
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Old May 5th, 2011, 11:48 PM   #183 (permalink)
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Quote:
Originally Posted by Vihzel View Post
I think I've brought a lot of people to Android Forums (whether they make an account or not) based off of this thread. lol I assume a lot of people typed it in Google and this site came up as a link.

... I should be paid. That's all.
You're nowhere near Fex though :P I think he got a platoon to join AF, lol, just so they can post in his thread.
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Old May 5th, 2011, 11:55 PM   #184 (permalink)
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I brought in eleventeen.
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Old May 6th, 2011, 12:42 AM   #185 (permalink)
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is that before sexteen
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Old May 8th, 2011, 04:52 AM   #186 (permalink)
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‎6÷2(2+1)=?...some said 1 some said 9...
I said 6÷2(2+1)=6÷4+2=3/2 + 2= 7/2
and for
‎6÷2(1+2)=?...some said 1 some said 9...
the solution should be 6÷2(1+2)=6÷2+4=3+4=7
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Old May 8th, 2011, 07:04 AM   #187 (permalink)
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Quote:
Originally Posted by susanlai89 View Post

‎6÷2(2+1)=?...some said 1 some said 9...
I said 6÷2(2+1)=6÷4+2=3/2 + 2= 7/2
and for
‎6÷2(1+2)=?...some said 1 some said 9...
the solution should be 6÷2(1+2)=6÷2+4=3+4=7
In any form of math this answer is clearly wrong since the 6 is outside the brackets, it has to operate on everything within the brackets.

The simple answer is that order of operation dictates that;

terms inside parenthesis
exponents and roots
multiplication and division
addition and subtraction

This means that, step one

Add 1+2 = 3

Step 2 there are two ways to go here,

V1.0 if you subscribe to the rule that multiplication and division have no precedence then you operate from left to right.

6/2 = 3

3*3 = 9

V2.0 If you subscribe to the rule that PEMDAS = Parenthesis -> exponents > multiply -> divide -> add -> subtract

2*3 = 6
6/6 = 1

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Old May 9th, 2011, 07:35 AM   #188 (permalink)
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Originally Posted by novox77 View Post
Order of operations - Wikipedia, the free encyclopedia

Scroll down to "Gaps in the Standard."

What this section states (or implies) is that if you try to interpret 6÷2(1+2) strictly by the HUMAN-MADE order of operations, it is ambiguous. The system is not perfect. There are gaps where additional parens are needed to remove ambiguity. But as long as ambiguity exists, it can go multiple ways.

Of course the problem is, most people don't believe that it's ambiguous; they think there must be a correct answer and that their interpretation of PEDMAS is absolutely correct. And in both directions, it's a correct interpretation. That is the definition of ambiguous. That's the reason people are split 50/50 no matter where this question is posed.

It doesn't matter how many PhDs you have and in what field. I'm sure there are super-intellects on both camps. The right answer is: don't expect a consensus until you add parentheses to the original problem to make it unambiguous. The problem was designed to exploit the gap in the order of operations.
This. Definitely this.



I was going to write a massive reply to a whole bunch of posts, but novox has got it under wraps quite elegantly.

The only other thing I have to say on the matter is to correct those among you who think that left/right has any precedence. IT DOESN'T MATTER AT ALL.
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Old May 9th, 2011, 10:23 AM   #189 (permalink)
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The only other thing I have to say on the matter is to correct those among you who think that left/right has any precedence. IT DOESN'T MATTER AT ALL.
Glad you agreed with my previous post (even though I'm sure many people don't). But I'm not sure I agree with your above statement without some clarification. 6÷2x3 gives a different result depending on if you calculate it from left to right or vice versa. To me, left-to-right takes precedence, so 9 is the only correct answer.

I see two camps of people. I will call them strict and intent. Strict people use PEDMAS as law; no exceptions. Perfectly logical. Intent people look at the problem as written and try to infer what the person who created the equation meant while still trying to accommodate the order of operations. It's the difference between correct and truth. In that sense, this equation could act as a personality test.

I'll say that through the course of following this thread, I'm convinced that 9 is the correct answer, but the alternate answer, 1, has a lot of merit from a practical application of mathematics: engineering. I previously discussed the "gap in the standard" as described in the wiki. Engineers aren't always unambiguous, and as a team reaching a common engineering goal, it's more important to read the intent of the calculations/equations rather than get hung up over the technical correctness as written. For a simple brain teaser like the one in this thread, we can afford to take the hard stance and claim a superior correct answer. But that's not always the right approach in the real world.

Ideally people are always unambiguous in their mathematical statements, but that's not always the case. And the strict methodology isn't necessarily better than the intent methodology. And that probably explains why so many people can see "1" as the right answer. As written, there's a strong intent toward "1", even though technically, the answer is "9."
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Old May 9th, 2011, 10:25 AM   #190 (permalink)
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i feel like we are arguing which is better.. ios or android

the answer is : android and 9
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Old May 9th, 2011, 11:32 AM   #191 (permalink)
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I'm no longer at all interested in the original question, as it's an interpretation question: basically does the (x+y) term belong to the numerator or denominator. This is the difference between evaluating to 9 and to 1, respectively. The problem is it's missing a set of parentheses and left up to the reader to decide where they ought to fit.

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To me, left-to-right takes precedence, so 9 is the only correct answer.
I can assure you, left and right has absolutely no precedence because of the commutative property of addition and multiplication. Since subtracting term y from term x (seen as (x-y))is nothing more than the addition of the negative value of term y to term x (seen as (x+(-1)*y)), we can force subtraction to commutativity through addition. Similarly, division can be forced to commutativity through the use of fractions and multiplication (yes, this doesn't completely remove the need for division, but it does help me in what I'm looking to illustrate).

Once we have reached this, we can work through (useful iterations) of this type of problem from left to right, from right to left, or from the centre out if desired as long as we remember to give good respect to the order of operations (and though it has been stated a couple of times already, I think it merits repeating that multiplication and division are on an equal order, as are addition and subtraction (this is why we see several different flavours of PEMDAS)).
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Old May 9th, 2011, 01:22 PM   #192 (permalink)
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since we all agree (1+2) must be evaluated first, I'm going to sub in 3 in its place:

6÷2*3

I still don't see how order is irrelevant to the above equation. If I do 2*3 first, the final answer is 1. If I do 6÷2 first, the final answer is 9.

if I convert the division into multiplication, I have to first determine what the divisor is: 2 or the quantity 2*3. Order is irrelevant once everything is converted to multiplication and/or addition, but before that can be done, order IS affecting that conversion...
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Old May 9th, 2011, 03:45 PM   #193 (permalink)
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Eh, since the #3 post, I'm still waiting for the voting option "Both 9 and 1"...
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Old May 9th, 2011, 06:50 PM   #194 (permalink)
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Originally Posted by novox77 View Post
I have to first determine what the divisor is: 2 or the quantity 2*3.
And this is exactly why this poorly iterated problem is undergoing such a long debate. This numerator or denominator question is the ambiguous part you were alluding to earlier. It's an interpretation question. But remove the ambiguity by adding a set of parentheses around one term or another, and it's all good. This particular problem is written badly, but I still insist that left and right are no higher order than each other.

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Originally Posted by novox77 View Post
Order is irrelevant once everything is converted to multiplication and/or addition, but before that can be done, order IS affecting that conversion...
So it isn't a question of order, it's just that this problem is badly written and open to a couple of conflicting interpretations.
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Old May 9th, 2011, 07:14 PM   #195 (permalink)
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Originally Posted by Ichapp View Post
This particular problem is written badly, but I still insist that left and right are no higher order than each other.
You should use only multiplications, since divisions are a multiplication of the inverse. Just like subtraction is the addition of negative numbers. Also, the algorithm computers use is left to right.

Have you read the whole thread? There are good replies out there.
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Old May 9th, 2011, 10:17 PM   #196 (permalink)
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I did indeed read the thread. There were a small handful of replies with decent content; the rest was pretty much chaff.

The reason computer algorithms evaluate left to right is that they were coded that way. One could just as easily code them to evaluate right to left. Or using a different notation entirely, like RPN.

The rest of what you said I agree with and also mentioned a couple of posts up.
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Old May 9th, 2011, 11:01 PM   #197 (permalink)
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Quote:
Originally Posted by Ichapp View Post
I did indeed read the thread. There were a small handful of replies with decent content; the rest was pretty much chaff.

The reason computer algorithms evaluate left to right is that they were coded that way. One could just as easily code them to evaluate right to left. Or using a different notation entirely, like RPN.

The rest of what you said I agree with and also mentioned a couple of posts up.
Alright.

I know there are many notations, but the one used "by default" as a convention is usually left to right, that was the point I was trying to make.

Well, I think we're pretty much done with that topic then. What else is there to say?
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Old May 10th, 2011, 02:04 AM   #198 (permalink)
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Enough that this thread reaches 200 posts.
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Old May 10th, 2011, 08:00 AM   #199 (permalink)
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It seems to me that the answer is somewhat split between the simple folk and the math geeks. Ask anyone in the street and they will probably solve the question using left to right. where as ask anyone with some kind of higher education in math, and they will probably use the math parenthesis. Theres not a lot of point 'simplifying' the problem, the problem 'as is' done by a mathematician, using the common laws of math, will simply answer it as 1.

Who can tell me the highest number, that when written in the queens English, consists of only three words?

(IE 110 = one hundred and ten, 4 words)
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Old May 10th, 2011, 08:56 AM   #200 (permalink)
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Quote:
Originally Posted by Outlaw71 View Post
This thread wins 'Nerdiest thread in all of Phandroid' hands down.
Hush!!

Quote:
Originally Posted by novox77 View Post
Glad you agreed with my previous post (even though I'm sure many people don't). But I'm not sure I agree with your above statement without some clarification. 6÷2x3 gives a different result depending on if you calculate it from left to right or vice versa. To me, left-to-right takes precedence, so 9 is the only correct answer.

I see two camps of people. I will call them strict and intent. Strict people use PEDMAS as law; no exceptions. Perfectly logical. Intent people look at the problem as written and try to infer what the person who created the equation meant while still trying to accommodate the order of operations. It's the difference between correct and truth. In that sense, this equation could act as a personality test.

I'll say that through the course of following this thread, I'm convinced that 9 is the correct answer, but the alternate answer, 1, has a lot of merit from a practical application of mathematics: engineering. I previously discussed the "gap in the standard" as described in the wiki. Engineers aren't always unambiguous, and as a team reaching a common engineering goal, it's more important to read the intent of the calculations/equations rather than get hung up over the technical correctness as written. For a simple brain teaser like the one in this thread, we can afford to take the hard stance and claim a superior correct answer. But that's not always the right approach in the real world.

Ideally people are always unambiguous in their mathematical statements, but that's not always the case. And the strict methodology isn't necessarily better than the intent methodology. And that probably explains why so many people can see "1" as the right answer. As written, there's a strong intent toward "1", even though technically, the answer is "9."

Quote:
Originally Posted by XplosiV View Post
It seems to me that the answer is somewhat split between the simple folk and the math geeks. Ask anyone in the street and they will probably solve the question using left to right. where as ask anyone with some kind of higher education in math, and they will probably use the math parenthesis. Theres not a lot of point 'simplifying' the problem, the problem 'as is' done by a mathematician, using the common laws of math, will simply answer it as 1.

Who can tell me the highest number, that when written in the queens English, consists of only three words?

(IE 110 = one hundred and ten, 4 words)
These 2 answers are enough to help me sleep good at night about this thread.... I did go to college for engineering for a few semesters.
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