v_ware wrote...
2
...88.
That's what he meant.
LET IT GO!
EDIT: Do we still not know why this question was asked?
Modifié par Godak, 09 avril 2011 - 02:56 .
48÷2(9+3) = ????
Débuté par
Bjelseth
, avril 08 2011 02:02
#151
Posté 09 avril 2011 - 02:38
Godak
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...88.
That's what he meant.
LET IT GO!
EDIT: Do we still not know why this question was asked?
Retour en haut
#152
Posté 09 avril 2011 - 03:00
Kronner
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AwesomeName wrote...
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*
It's not an accident..it is the only correct solution, which is why there is the leftmost preference rule.
Modifié par Kronner, 09 avril 2011 - 03:06 .
#153
Posté 09 avril 2011 - 03:19
Elvis_Mazur
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Wow. Who would think that this topic would get 7 pages? I'm stunned.
#154
Guest_AwesomeName_*
Posté 09 avril 2011 - 03:27
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Kronner wrote...
AwesomeName wrote...
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*
It's not an accident..it is the only correct solution, which is why there is the leftmost preference rule.
Yes, that's precisely what I'm saying....(???) I think you might have a different interpretation than I over the use of the word "accident"?
#155
Posté 09 avril 2011 - 03:29
The Narrator
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2+2=4 man, no matter what the party says.
#157
Guest_Nyoka_*
Posté 09 avril 2011 - 03:40
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@AwesomeName, you still have product commutativity even if / were right-associative. You just have to do the transformations right to left, according to that new definition. For example, using the traditional division: 16 / 4 / 2 = 2.
Let's make division right-associative and let's use the sign \\ for it. Then, 16 \\ 4 \\ 2 = 16 / (4 / 2) = 8.
Now, let's transform that into a list of products. We may be tempted to do this: 16 \\ 4 \\ 2 = 16 * 0.25 * 0.5, but in fact that's not true! One side of the equality is 8, but the other side is 2. Does that mean our new operator is not really as valid as the traditional /? Not at all. All we've proved here is that transformation is wrong now, because it doesn't pay attention to the right-associativity of our new division. Instead, we must do it right to left:
16 \\ 4 \\ 2 = 16 * (1 \\ (4 \\ 2)) = 16 * (2 \\ 4) = 16 * 2 * 0.25.
That's it. Now you can change the order of the factors in that product, same as before. If I change the definition of an operator (or create a new, different convention with a new sign and all, like I've done here with '\\'), I must make sure my transformations are done accordingly with its new properties.
Let's make division right-associative and let's use the sign \\ for it. Then, 16 \\ 4 \\ 2 = 16 / (4 / 2) = 8.
Now, let's transform that into a list of products. We may be tempted to do this: 16 \\ 4 \\ 2 = 16 * 0.25 * 0.5, but in fact that's not true! One side of the equality is 8, but the other side is 2. Does that mean our new operator is not really as valid as the traditional /? Not at all. All we've proved here is that transformation is wrong now, because it doesn't pay attention to the right-associativity of our new division. Instead, we must do it right to left:
16 \\ 4 \\ 2 = 16 * (1 \\ (4 \\ 2)) = 16 * (2 \\ 4) = 16 * 2 * 0.25.
That's it. Now you can change the order of the factors in that product, same as before. If I change the definition of an operator (or create a new, different convention with a new sign and all, like I've done here with '\\'), I must make sure my transformations are done accordingly with its new properties.
Modifié par Nyoka, 09 avril 2011 - 03:58 .
#158
Posté 09 avril 2011 - 03:52
Chanegade
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I feel ashamed that I picked 2 since I went to a Japanese high school.
#159
Guest_AwesomeName_*
Posté 09 avril 2011 - 04:30
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Nyoka wrote...
@AwesomeName, you still have product commutativity even if / were right-associative. You just have to do the transformations right to left, according to that new definition. For example, using the traditional division: 16 / 4 / 2 = 2.
Let's make division right-associative and let's use the sign for it. Then, 16 4 2 = 16 / (4 / 2) = 8.
Now, let's transform that into a list of products. We may be tempted to do this: 16 4 2 = 16 * 0.25 * 0.5, but in fact that's not true! One side of the equality is 8, but the other side is 2. Does that mean our new operator is not really as valid as the traditional /? Not at all. All we've proved here is that transformation is wrong now, because it doesn't pay attention to the right-associativity of our new division. Instead, we must do it right to left:
16 4 2 = 16 * (1 (4 2)) = 16 * (2 4) = 16 * 2 * 0.25.
That's it. Now you can change the order of the factors in that product, same as before. If I change the definition of an operator, I must make sure my transformations are done accordingly with its new properties.
I don't really do maths much, but... why would we use right-associativity? My understanding is that right-associative is proven to be false because the product commutativity shows that it doesn't work... Hence we never use it (or do we for some situations?). I thought product commutativity was often used in mathematical proofs for the purpose of defining these things? But... really, I don't know! I'm no mathematician.
#160
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Posté 09 avril 2011 - 04:46
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But now you know product commutativity does work, regardless of what kind of division we use. We use left-associative division because it's easier to use, more intuitive, a more convenient convention 
formally, both are equally valid. However, for practical purposes, the traditional division is more useful.
formally, both are equally valid. However, for practical purposes, the traditional division is more useful.
Modifié par Nyoka, 09 avril 2011 - 05:01 .
#161
Guest_VanguardOfDestruction_*
Posté 09 avril 2011 - 05:08
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The answer is roughly 8.7.... or 8.666666666so-on-and-so-forth....
#162
Guest_AwesomeName_*
Posté 09 avril 2011 - 05:23
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Nyoka wrote...
But now you know product commutativity does work, regardless of what kind of division we use. We use left-associative division because it's easier to work with, more intuitive, a more convenient convention
Actually, we can even define new "from extremes to center" operators and vice versa, like this:
1 / 2 / 3 / 4 / 5 / 6 = ((1 / 2) / 3) / (4 / (5 / 6))
or
1 / 2 / 3 / 4 / 5 / 6 = 1 / (2 / (3 / 4) / 5) / 6
or whatever else you can imagine. But these would be terrible to work with!
But... I ALWAYS knew product commutativity worked? That is why I kept bringing it up to explain why the left-associative convention was correct and the right-associative wasn't. That's basically what I've been saying for ages now...
But, I'm confused with the way you're wording this (I suspect you just think on a different wavelength and do actually agree with me, and are just wording my argument differently) :/ Maybe I'm being stupid, but it seems that you're saying that left-associative is used only because it's easy to. Not because it's actually correct. Which, in my opinion it is, as product commutativity seems to verify it.
I'm not sure why 1/2/3/4/5/6 would be tricky even if we mysteriously forget the left-associative convention. If you were in doubt you would just... use product commutivity... and from that, I guess you'd rediscover the left-associative short-cut and know that no other rules you could come up with would be right.
BAH. I think we're just on a different wavelength in the way we think about this. Either way, we agree on the answer!
Modifié par AwesomeName, 09 avril 2011 - 05:26 .
#163
Guest_VanguardOfDestruction_*
Posté 09 avril 2011 - 05:27
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..so what is the answer?
#164
Guest_Luna Siwora_*
Posté 09 avril 2011 - 05:31
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VanguardOfDestruction wrote...
..so what is the answer?
48 : 2 = 24
24 x (9+3) = 24 x 9 + 24 x 3 = 0
24 x 9 = 216
24 x 3 = 72
216 + 72 = ???
216 + 72 = 288
#165
Posté 09 avril 2011 - 05:39
Godak
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PetrySilva wrote...
Wow. Who would think that this topic would get 7 pages? I'm stunned.
I...I don't know how it happened, but I'm scared. Hold me.
#166
Guest_Nyoka_*
Posté 09 avril 2011 - 05:50
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That's exactly what I say. We use that particular convention because it's more practical, nothing more. It's correct, of course, but other conventions are correct, too, though less useful.AwesomeName wrote...
Maybe I'm being stupid, but it seems that you're saying that left-associative is used only because it's easy to. Not because it's actually correct. Which, in my opinion it is, as product commutativity seems to verify it.
You can do 2/2/2 = (1/2)*(1/2)*(1/2) because the operator / allows you to do so. Other operators will allow other kinds of transformations. There's really nothing more to it.
#167
Posté 09 avril 2011 - 06:27
Mistress9Nine
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Godak wrote...
I...I don't know how it happened...
Says the one who kept standing by the wrong answer. Appology accepted by the way.
Modifié par Mistress9Nine, 09 avril 2011 - 06:43 .
#168
Posté 09 avril 2011 - 06:54
OBakaSama
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Nyoka wrote..
You can do 2/2/2 = (1/2)*(1/2)*(1/2) because the operator / allows you to do so. Other operators will allow other kinds of transformations. There's really nothing more to it.
Being serious for a moment (for a change); Nyoka, you sure that equation you have there is correct?
#169
Guest_AwesomeName_*
Posté 09 avril 2011 - 06:59
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Nyoka wrote...
That's exactly what I say. We use that particular convention because it's more practical, nothing more. It's correct, of course, but other conventions are correct, too, though less useful.AwesomeName wrote...
Maybe I'm being stupid, but it seems that you're saying that left-associative is used only because it's easy to. Not because it's actually correct. Which, in my opinion it is, as product commutativity seems to verify it.
You can do 2/2/2 = (1/2)*(1/2)*(1/2) because the operator / allows you to do so. Other operators will allow other kinds of transformations. There's really nothing more to it.
How can they all be correct if they're giving different answers??
#170
Posté 09 avril 2011 - 07:07
Rose of Mars
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Mistress9Nine wrote...
Godak wrote...
I...I don't know how it happened...
Says the one who kept standing by the wrong answer. Appology accepted by the way.
#171
Posté 09 avril 2011 - 08:11
Wittand25
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No it is wrong. the first 1/2 should still be a two.OBakaSama wrote...
Nyoka wrote..
You can do 2/2/2 = (1/2)*(1/2)*(1/2) because the operator / allows you to do so. Other operators will allow other kinds of transformations. There's really nothing more to it.
Being serious for a moment (for a change); Nyoka, you sure that equation you have there is correct?
The method is however right because that is just how division is defined in a field (like the rational numbers).
a/b:=a*(1/b) where (1/b) is the reverse element regarding multiplication for the element b of the field.
#172
Posté 09 avril 2011 - 09:19
Macrake
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If you want to remove the parantheses(sp?) you have to multiply into it first. 2(12)=24
Rewriting it to 2x12 is wrong.
Rewriting it to 2x12 is wrong.
#173
Posté 09 avril 2011 - 09:23
Macrake
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Maria Caliban wrote...
48÷2(9+3) = 48/2*12 = 24*12 = 288
going from 2(12) to 2x12 messes up the equation priority. Always remove parantheses first. 2(9+3)=24. Not 2x12
#174
Posté 09 avril 2011 - 09:31
Macrake
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Creature 1 wrote...
I can tell you which calculator I wouldn't use when the right answer really matters.Strangely Brown wrote...
Okay here is something really strange.
I have tried 2 different calculators. The one I have in my hand is a Sharp EL-520W scientific calculator.
When I enter the equation exactly as it is written in the OP : 48÷2(9+3) = With this ÷ division symbol the answer I get is 2.
However when I use a different calculator and I use the / as the division symbol so that the equation reads 48/2(9+3) =
I get the answer 288.
Does it make more sense when you change to 48*0.5*(9+3)? The answer is 288, I would bet my beloved mother's life on it.
You're making the same mistake. You cant remove the parantheses without multiplying into it. 48/2(12). You remove the parantheses by doing 2x12=24. So 48/24.
48/2x12 is NOT the same as 48/2(12).
#175
Posté 09 avril 2011 - 09:33
Kronner
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Macrake wrote...
48/2x12 is NOT the same as 48/2(12).
LOL
Of course it is. This is elementary school stuff. Geez.
48 / 2 * 12 IS THE SAME as 48 / 2 * (12)
Modifié par Kronner, 09 avril 2011 - 09:34 .
