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48÷2(9+3) = ????

Débuté par Bjelseth , avril 08 2011 02:02

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#126
Wicked 702
Posté 08 avril 2011 - 11:30

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AwesomeName wrote...

Bjelseth wrote...

Poll added

http://social.biowar...79/polls/18184/


So, which is it?  (48÷2)(9+3) or 48÷(2(9+3))?

I think that's the main issue really...


It's neither. You can't just add parenthesis to suit a purpose. While the first setup will yield the correct answer, it's not the way the question was presented. Refer back to the forum poster (sorry, too lazy to look back on who this was) who split the question up into three fractions.

It's really 48/1 * 1/2 * (9+3)/1

Edit: You know what...I'm not really sure. Maybe it is ok to add parenthesis here. If it is, then the first term (48/2)(9+3) is correct. Either way, the answer is 288.

Second Edit: I stand by my original point (until told otherwise). Math used to be mah thing. Gettin' old. The fractions way is the best way to look at this. Used to use that method a lot.

Modifié par Wicked 702, 08 avril 2011 - 11:39 .

#127
Guest_AwesomeName_*
Posté 08 avril 2011 - 11:34

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Wicked 702 wrote...

AwesomeName wrote...

Bjelseth wrote...

Poll added

http://social.biowar...79/polls/18184/


So, which is it?  (48÷2)(9+3) or 48÷(2(9+3))?

I think that's the main issue really...


It's neither. You can't just add parenthesis to suit a purpose. While the first setup will yield the correct answer, it's not the way the question was presented. Refer back to the forum poster (sorry, too lazy to look back on who this was) who split the question up into three fractions.

It's really 48/1 * 1/2 * (9+3)/1


AH.  Thanks - that makes perfect sense, and doesn't assume anything extra in the question.  PLUS, this explanation at gives me an understanding of the maths rather than just, "do step 1, then 2, etc." :)

Modifié par AwesomeName, 08 avril 2011 - 11:35 .

#128
Volus Warlord
Posté 08 avril 2011 - 11:35

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Wow. Just wow.

#129
Guest_AwesomeName_*
Posté 08 avril 2011 - 11:37

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Wicked 702 wrote...

Edit: You know what...I'm not really sure. Maybe it is ok to add parenthesis here. If it is, then the first term (48/2)(9+3) is correct. Either way, the answer is 288.


What you said:  48/1 * 1/2 * (9+3)  seems to be the most solid because it doesn't seem to assume anything extra and seems to be based on a solid understanding of the mathematics rather than just blindly following a series of steps...  If that makes sense?

EDIT: and yes, adding the parenthesis like that IS correct, BASED  on ^said deeper understanding^ of the maths problem presented...

EDIT 2: I THINK..... (lmao...)

EDIT 3: sneaky edit...

Modifié par AwesomeName, 08 avril 2011 - 11:53 .

#130
Godak
Posté 08 avril 2011 - 11:40

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AwesomeName wrote...

a solid understanding of the mathematics rather than just blindly following a series of steps


Well, that solid understanding of mathematics usually involves following said steps. :lol:

#131
Wicked 702
Posté 08 avril 2011 - 11:40

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AwesomeName wrote...

Wicked 702 wrote...

Edit: You know what...I'm not really sure. Maybe it is ok to add parenthesis here. If it is, then the first term (48/2)(9+3) is correct. Either way, the answer is 288.


What you said:  48/1 * 2/1 * (9+3)  seems to be the most solid because it doesn't seem to assume anything extra and seems to be based on a solid understanding of the mathematics rather than just blindly following a series of steps...  If that makes sense?

EDIT: and yes, adding the parenthesis like that IS correct, BASED  on ^said deeper understanding^ of the maths problem presented...

EDIT 2: I THINK..... (lmao...)


HAHAHA! I know. Brain hurts. Let's both agree to stick to the fractions!

#132
Guest_AwesomeName_*
Posté 08 avril 2011 - 11:48

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Godak wrote...

AwesomeName wrote...

a solid understanding of the mathematics rather than just blindly following a series of steps


Well, that solid understanding of mathematics usually involves following said steps. :lol:


Indeed!  But it's exactly for situations like this when you realise how important it is to understand the "why" of those rules!  I bet the maths students of the thread are laughing at most of us - I mean, you know how it usually is between them and, well... all the other science students (and most other people, I suppose).  The maths students usually understand why the steps are the way they are, whereas the rest of us usually just follow them without caring how any of it works.  :P  >.<

Modifié par AwesomeName, 08 avril 2011 - 11:48 .

#133
Shirosaki17
Posté 09 avril 2011 - 01:22

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AwesomeName wrote...

Godak wrote...

AwesomeName wrote...

a solid understanding of the mathematics rather than just blindly following a series of steps


Well, that solid understanding of mathematics usually involves following said steps. :lol:


Indeed!  But it's exactly for situations like this when you realise how important it is to understand the "why" of those rules!  I bet the maths students of the thread are laughing at most of us - I mean, you know how it usually is between them and, well... all the other science students (and most other people, I suppose).  The maths students usually understand why the steps are the way they are, whereas the rest of us usually just follow them without caring how any of it works.  :P  >.<

Don't worry you don't have to be a math student to laugh at people who don't get this. It's all about order of operations. If multiplication always came before division then the answer would be 2. It's quite simple really. Wicked changing it to multiplication and fractions doesn't really change that, even though it came out to the right answer.

Everyone is suppose to be 18+ on these forums. Very odd.

Modifié par Shirosaki17, 09 avril 2011 - 01:22 .

#134
Guest_Nyoka_*
Posté 09 avril 2011 - 02:07

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Can't believe this is 6 pages long now =]

The parentheses are clear enough. The problem comes in 48 / 2 * 12, right? Now, both * and / have the same priority, but / is left-associative, which means you must do the division first.

If somebody doesn't get why the multiplication shouldn't be made first, you can get rid of it by transforming it into 48 / 2 / (1/12). There, all divisions now. Do it left to right :) Or if you're more into multiplications, you can turn it into 28 * (1/2) * 12 and do it in any order you want, since * is associative from both sides.

Modifié par Nyoka, 09 avril 2011 - 03:02 .

#135
mousestalker
Posté 09 avril 2011 - 02:18

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Maths are srs bzns. Rly.

#136
Maria Caliban
Posté 09 avril 2011 - 02:22

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BeljoraDien wrote...

Based on this, I just thought of something... Imagine a scenario where you're on a gameshow with 2 players and 3 boxes. Player 1 gets to pick a box first, but then must wait as player 2 lifts up his/her box from the two remaining choices. If player 2 doesn't lift up the box with cash, player 1 is then allowed to switch boxes. Would you want to be player 1 or player 2? And, if player 1, would you still want to switch boxes?

Player 1. Switch boxes.

Hasn't that question been around forever now?

#137
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Posté 09 avril 2011 - 02:24

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Shirosaki17 wrote...

Don't worry you don't have to be a math student to laugh at people who don't get this. It's all about order of operations. If multiplication always came before division then the answer would be 2. It's quite simple really. Wicked changing it to multiplication and fractions doesn't really change that, even though it came out to the right answer.

Everyone is suppose to be 18+ on these forums. Very odd.


I wouldn't say it was all about order of operations.  In this instance, there's a REASON why the order of operations is correct, beyond simply saying, "it just is".  The reason you do it left-to-right and not right-to-left is demonstrated by changing the operators to be the same - so the order in which you multiply the numbers together no longer matters, since the answer always comes out the same, no matter what.  From that, you can prove that working left to right is true, since the answer matches.  As far as I can tell, that's  what it's really about.  Both come up with the same answer, but the latter gives a deeper understanding and proves the order of operations.  I think that was the point you were missing - no one was saying it was more correct (they both are) - the point was that the latter actually shows  it. 

Basically, understanding the maths is more useful than simply remembering a bunch of steps.

p.s. Erm, I wasn't implying that it's okay to laugh at people who don't get this, if that's what you were suggesting??

#138
Shirosaki17
Posté 09 avril 2011 - 02:31

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I didn't miss the point you did.

I was implying that you don't have to be good at math to laugh at people who don't get this because it's pretty basic.

#139
ejoslin
Posté 09 avril 2011 - 02:44

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Wicked 702 wrote...

AwesomeName wrote...

Bjelseth wrote...

Poll added

http://social.biowar...79/polls/18184/


So, which is it?  (48÷2)(9+3) or 48÷(2(9+3))?

I think that's the main issue really...


It's neither. You can't just add parenthesis to suit a purpose. While the first setup will yield the correct answer, it's not the way the question was presented. Refer back to the forum poster (sorry, too lazy to look back on who this was) who split the question up into three fractions.

It's really 48/1 * 1/2 * (9+3)/1

Edit: You know what...I'm not really sure. Maybe it is ok to add parenthesis here. If it is, then the first term (48/2)(9+3) is correct. Either way, the answer is 288.

Second Edit: I stand by my original point (until told otherwise). Math used to be mah thing. Gettin' old. The fractions way is the best way to look at this. Used to use that method a lot.


That would be me.  I really have nothing more to add to this whole thing, but I wanted to take my little bow anyway ;)

I wouldn't add the paretheses here -- the equation is not at all ambiguous, though it's a bit confusing if you don't think of the order of operations.  I blame beginning algebra for much of the confusion. 

#140
Shirosaki17
Posté 09 avril 2011 - 02:47

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ejoslin wrote...

Wicked 702 wrote...

AwesomeName wrote...

Bjelseth wrote...

Poll added

http://social.biowar...79/polls/18184/


So, which is it?  (48÷2)(9+3) or 48÷(2(9+3))?

I think that's the main issue really...


It's neither. You can't just add parenthesis to suit a purpose. While the first setup will yield the correct answer, it's not the way the question was presented. Refer back to the forum poster (sorry, too lazy to look back on who this was) who split the question up into three fractions.

It's really 48/1 * 1/2 * (9+3)/1

Edit: You know what...I'm not really sure. Maybe it is ok to add parenthesis here. If it is, then the first term (48/2)(9+3) is correct. Either way, the answer is 288.

Second Edit: I stand by my original point (until told otherwise). Math used to be mah thing. Gettin' old. The fractions way is the best way to look at this. Used to use that method a lot.


That would be me.  I really have nothing more to add to this whole thing, but I wanted to take my little bow anyway ;)

I wouldn't add the paretheses here -- the equation is not at all ambiguous, though it's a bit confusing if you don't think of the order of operations.  I blame beginning algebra for much of the confusion. 

I think the education system probably failed a lot of these people. hahaha.

#141
Guest_Nyoka_*
Posté 09 avril 2011 - 02:59

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Funny thing is people gets confused by * and /, but everybody understands perfectly + and -! :huh:

If I said hey people, what is the answer to 48 - 2 + 12? Nobody would get that one wrong, even though the supposed difficulty here is exactly the same, because -, same as /, is left-associative, while +, like *, is associative from both sides.

By the way, it's not a coincidence that + and * on one hand and / and - on the other hand share the same associativity. It's because multiplication is just abbreviated addition, and division is simply abbreviated substraction.

Modifié par Nyoka, 09 avril 2011 - 03:11 .

#142
BeljoraDien
Posté 09 avril 2011 - 04:09

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Maria Caliban wrote...

BeljoraDien wrote...

Based on this, I just thought of something... Imagine a scenario where you're on a gameshow with 2 players and 3 boxes. Player 1 gets to pick a box first, but then must wait as player 2 lifts up his/her box from the two remaining choices. If player 2 doesn't lift up the box with cash, player 1 is then allowed to switch boxes. Would you want to be player 1 or player 2? And, if player 1, would you still want to switch boxes?

Player 1. Switch boxes.

Hasn't that question been around forever now?


Well, I heard Creature 1's version a long time ago... and so did everyone else, I would guess based on how quickly they all jumped on the answer. I was just trying to throw a little twist in it to see if people would think it through instead of repeating what they heard long ago (Including myself... I had to think how those percentages worked out as you can see in one of my posts). 'My' version may very well have already been out there, but I honestly did just come up with that based on how Creature 1 phrased the first problem. It hasn't seemed to stump anyone severly though...

#143
Timon44
Posté 09 avril 2011 - 08:37

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Shirosaki17 wrote...

I didn't miss the point you did.

I was implying that you don't have to be good at math to laugh at people who don't get this because it's pretty basic.

Laughing is unnecessary either way. You are arguing about applying a mathematic RULE. Not about mathematic intelligence in general.

#144
v_ware
Posté 09 avril 2011 - 08:56

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2

#145
BeljoraDien
Posté 09 avril 2011 - 09:42

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v_ware wrote...

2


Image IPB

#146
Kronner
Posté 09 avril 2011 - 01:11

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48 / 2 * (9+3) = 48 / 2 * 12 = 24 * 12 = 288
No way you can get 2, unless it was 48 / ( 2 * (9+3)), which it is not.
I know this for sure. Between * and /, whatever is the leftmost has the preference (barring any brackets of course). This is elementary school stuff. I am surprised to see how many people do not know this basic stuff.

Modifié par Kronner, 09 avril 2011 - 01:15 .

#147
Guest_AwesomeName_*
Posté 09 avril 2011 - 01:31

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Kronner wrote...

48 / 2 * (9+3) = 48 / 2 * 12 = 24 * 12 = 288
No way you can get 2, unless it was 48 / ( 2 * (9+3)), which it is not.
I know this for sure. Between * and /, whatever is the leftmost has the preference (barring any brackets of course). This is elementary school stuff. I am surprised to see how many people do not know this basic stuff.


To be fair, barely anyone is explaining WHY you do the leftmost one (beyond just stating the name of a convention (order of operations)).  I've only seen, like, 4 people in this entire thread try to explain WHY starting left actually works. :P

#148
Kronner
Posté 09 avril 2011 - 01:38

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Why? Because it had to be decided. It is a simple rule, a convention. Just like * and / has preference over + and -. It's just stuff everyone is supposed to know.

Modifié par Kronner, 09 avril 2011 - 01:39 .

#149
Guest_Nyoka_*
Posté 09 avril 2011 - 01:42

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It really is just a convention. / is left-associative because - is left-associative, but you can define a new substraction operator that is right-associative and give it another symbol, like # or whatever. That's all you need.

10 - 5 - 2 = (10 - 5) - 2 = 3

10 # 5 # 2 = 10 - (5 - 2) = 7

There.

There's no special reason why - should be left-associative. It's just part of its definition.

Modifié par Nyoka, 09 avril 2011 - 01:43 .

#150
Guest_AwesomeName_*
Posté 09 avril 2011 - 02:22

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Well, you can actually prove and show why starting from the left in this case gives the right answer.

/ is done first because the answer you get in the end, 288, matches up with the following when you make all the operators the same:

48 * 0.5 * 12 = 288
0.5 * 12 * 48 = 288
etc.. regardless of the order you do it in..

To me, that shows very solidly why starting left-to-right is correct. Starting right-to-left doesn't match up with the above answer. However, for whatever accident, starting left-to-right happens to match. So I think that shows a deeper understanding than just blindly following a procedure without knowing why it's true. *shrugs*
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