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General => General Discussion => Topic started by: bloop on April 17, 2011, 12:41:33 PM
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48÷2(9+3) = ?
Something that has been circulating around the internet recently (sometimes used as troll material due to inevitable shitstorms.) However, I'm interested to know DTF's thoughts on the correct answer. It seems simple enough but there seems to be debate over whether the answer is 2 or 288. Consider order of operations as well as implied multiplication.
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I would say 2, but I suck at math.
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I don't know what implied multiplication means, but order of operations would say that the answer is 2.
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It's 2 by order of operations.
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Also going for 2.
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I don't know what implied multiplication means, but order of operations would say that the answer is 2.
Implied multiplication is what people use to write 2a instead or 2 x a.
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I don't know what implied multiplication means, but order of operations would say that the answer is 2.
Implied multiplication is what people use to write 2a instead or 2 x a.
Oh, then I have no idea how that would change the answer.
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Implied multiplication would mean the 2(12) would take precedence over the 48/2.
48 ÷ 2(9+3)=
48 ÷ 2(12)=
48 ÷ 24=
2
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2? What? The order of operations (https://en.wikipedia.org/wiki/Order_of_operations) says that in this case you do parentheses first and then divide/multiply from left to right.
48÷2(9+3) = ?
48÷2x 12 =?
24x12=?
288
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Implied multiplication would mean the 2(12) would take precedence over the 48/2.
Order of operations also tell you this...
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Order of operations
Parenthesis
Exponents
Multiplication / Division
Addition / Subtraction
So,
9+3 = 12
48 / 2 * 12
Go from left to right because multiplication and division are interchangeable
48 / 2 = 24 * 12 = 288
Alternatively,
Order of operations
Parenthesis
Exponents
Multiplication / Division
Addition / Subtraction
So,
9+3 = 12
48 / 2 * 12
Go from right to left because multiplication and division are interchangeable
48 / 24 = 2
The real answer: I don't care.
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I always thought division/multiplication steps were interchangable, you just go by whatever one is first in the list.
But, like blackngold, I really don't care.
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2? What? The order of operations (https://en.wikipedia.org/wiki/Order_of_operations) says that in this case you do parentheses first and then divide/multiply from left to right.
48÷2(9+3) = ?
48÷2x 12 =?
Isn't it suppose to be 48/2(12)?
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If we consider order of operations in which both multiplication and division are simplified left to right it would pan out this way-
48 ÷ 2(9+3)=
48 ÷ 2(12)=
24(12)=
188
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2? What? The order of operations (https://en.wikipedia.org/wiki/Order_of_operations) says that in this case you do parentheses first and then divide/multiply from left to right.
48÷2(9+3) = ?
48÷2x 12 =?
Isn't it suppose to be 48/2(12)?
Isn't that the exact same thing?
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2? What? The order of operations (https://en.wikipedia.org/wiki/Order_of_operations) says that in this case you do parentheses first and then divide/multiply from left to right.
48÷2(9+3) = ?
48÷2x 12 =?
Isn't it suppose to be 48/2(12)?
Isn't that the exact same thing?
Well, going by order of operations (or rather how I've always use order of operations) that would make the result 2 and not 288.
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2? What? The order of operations (https://en.wikipedia.org/wiki/Order_of_operations) says that in this case you do parentheses first and then divide/multiply from left to right.
48÷2(9+3) = ?
48÷2x 12 =?
Isn't it suppose to be 48/2(12)?
Isn't that the exact same thing?
Well, going by order of operations (or going by how I've always use order of operations) that would make the result 2 and not 288.
I don't know, I thought those were just two different ways of writing 2 multiplied by twelve.
Jamesman, get in here.
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48/2(12) would mean you are diving 48 by 24... 48/2 x 12 would be diving 48 by 2 and then multiplying by 12, I think.
GOD I HATE MATH
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So because dividing by x is the same as multiplying by 1/x.
We can say that 48/2(12) is like (1/24) * 48 which is 2.
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48/2(12) would mean you are diving 48 by 24... 48/2 x 12 would be diving 48 by 2 and then multiplying by 12, I think.
This is how I look at it too.
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All this arguing, and the chef who hasn't done math in fifteen years might havge the right answer?? :metal
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Jamesman, we need you!
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Standard order of operations:
48÷2 X (9+3) = 48÷2 X (12) = 48÷2 X 12 = 24 X 12 = 288
The problem is that with the implied multiplication most people interpret it as 48÷(2 X (9+3))=2, a stronger grouping than than any written division and multiplication symbols. However, implied multiplication isn't clearly defined in the standard order of operations, so is not really treated any different than other multiplication or division symbols, i.e. order is left to right.
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2? What? The order of operations (https://en.wikipedia.org/wiki/Order_of_operations) says that in this case you do parentheses first and then divide/multiply from left to right.
48÷2(9+3) = ?
48÷2x 12 =?
24x12=?
288
This is the correct answer.
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48/2(12) would mean you are diving 48 by 24... 48/2 x 12 would be diving 48 by 2 and then multiplying by 12, I think.
This is how I look at it too.
I do not know of this mathematical operation 'diving' of yours.
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Its written like this
48÷2(9+3)
48÷2(12)
24(12)
288
Since 2(12) is 2 x 12. You divide first then multiply because Division is first in this equation, and is interchangable with multiplying.
Put it into a calculator as its written and you get 288
Pretty simple problem. What does
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2? What? The order of operations (https://en.wikipedia.org/wiki/Order_of_operations) says that in this case you do parentheses first and then divide/multiply from left to right.
48÷2(9+3) = ?
48÷2x 12 =?
24x12=?
288
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Put it into a calculator as its written and you get 288
Not all calculators/languages necessarily interpret things the same. Standard order of operations isn't exactly an enforced standard, which is why using parens when faced with potentially ambiguous operations like this is usually emphasized.
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Put it into a calculator as its written and you get 288
(https://cdn2.knowyourmeme.com/i/000/112/837/original/16h6ja8.jpg?1302454815)
I'm not saying it isn't 288 though.
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Since when is 2x ever any different at all from 2*x? Granted, since High School I've rarely had to use any algebra, but I've never heard such a thing. ???
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There's no consensus in the math community about whether implied multiplication takes precedence over regular multiplication or not. Think about that before you try to argue that there is a "right" answer, because there isn't.
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There's no consensus in the math community about whether implied multiplication takes precedence over regular multiplication or not. Think about that before you try to argue that there is a "right" answer, because there isn't.
Yes there is.
And that answer is 288.
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There's no consensus in the math community about whether implied multiplication takes precedence over regular multiplication or not. Think about that before you try to argue that there is a "right" answer, because there isn't.
Yes there is.
And that answer is 288.
Wrong. It's 2.
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With multiplication and division you just go from left to right, so 288. Not difficult, really.
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There's no consensus in the math community about whether implied multiplication takes precedence over regular multiplication or not. Think about that before you try to argue that there is a "right" answer, because there isn't.
True imo.
You can approach this two separate ways.
w/o implied multiplication
48/x(9+3)=288
(48/x)*12=288 (left to right simplification. Parenthesis around 48/x because you have to do that part first.)
48/x=24 (divide by 12)
x=2
So x=2 when the equation is set equal to 288.
Implied multiplication
48/x(9+3)=2
48/12x=2
4/x=2
x=2
So x=2 when the equation is set equal to 2.
However, 288 is generally the more accepted answer because implied multiplication in terms of order of operations is not entirely clear.
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Also I added a poll.
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There's no consensus in the math community about whether implied multiplication takes precedence over regular multiplication or not. Think about that before you try to argue that there is a "right" answer, because there isn't.
Yes there is.
And that answer is 288.
So to answer your question, I think both answers can be considered
right - which means, of course, that the question itself is wrong.
Some mathematicians hold that multiplication by juxtaposition (omitting the x sign, ex. 2(4+3) ) is a symbol of grouping. No fixed convention exists.
This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.
Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
16 ÷ 2[8 – 3(4 – 2)] + 1
= 16 ÷ 2[8 – 3(2)] + 1
= 16 ÷ 2[8 – 6] + 1
= 16 ÷ 2[2] + 1 (**)
= 16 ÷ 4 + 1
= 4 + 1
= 5
The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:
(https://www.purplemath.com/modules/orderops/order12.gif)
Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!
(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)
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I think he was just joking HF...
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It's just bad syntax. So, "no definite answer" from me.
rumborak
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Implied multiplication being of higher precedence is more an exception rather than the rule, especially in the math classes I've been in as a student and teacher. If you want to deviate from the standard Order of Operations, use parenthesis, that's why they're there.
Quick overview of Order of Operations:
Level 1: Parenthesis {}[]()
Level 2: Exponents x2, sqrt(), logxy
Level 3: Multiplication and Division x, *, /
Level 4: Addition and Subtraction +, -
Each operation on the same level has equal precedence, so you don't always do multiplication first, or addition first. Left to right precedence when dealing with operations residing on the same level.
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It's just bad syntax. So, "no definite answer" from me.
rumborak
If you know how what you're writing for interprets it you're fine. :p ...but yeah, it can't be said enough to not skip out on parens when writing code or expressions. Even if you know how it is interpreted someone else reading your code in the future might get confused. Exponents, negations, and functions are also big ones where it is often good to just be clear with your parens.
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IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.
rumborak
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IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.
rumborak
This. Real men use fractions.
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IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.
rumborak
I dislike those signs as well, but they are a necessity when communicating via text.
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IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.
rumborak
I dislike those signs as well, but they are a necessity when communicating via text.
The forward-slash, yes (e.g. "5/(3+1)"), but the "÷" sign should IMHO never be used outside of the plain "X divided by Y".
rumborak
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IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.
rumborak
This. Real men use fractions.
Speaking of which, one of those "cultural differences" between Europeans and Americans is that Europeans love decimal writing, whereas Americans seem to hate it. There's the "5 and 3/16th of an inch" and the "$3 7/10" as the gas price, where I'm looking at it, thinking "wouldn't it have been easier to just write $3.70?".
rumborak
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IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.
rumborak
This. Real men use fractions.
Speaking of which, one of those "cultural differences" between Europeans and Americans is that Europeans love decimal writing, whereas Americans seem to hate it. There's the "5 and 3/16th of an inch" and the "$3 7/10" as the gas price, where I'm looking at it, thinking "wouldn't it have been easier to just write $3.70?".
rumborak
Really? I absolutely despise decimal writing. It's so imprecise!
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Never seen $3 7/10 at a gas station in the US or Canada. Are you sure you aren't seeing fractions of a cent? I do see a lot of $3.45 9/10, but never fractions of dolars.
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IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.
rumborak
It's not as if the ÷ is ambiguous, as it's the same as /. However I understand what you mean, and if the original equation was in the form of a fraction there wouldn't be anything debatable about it.
(https://i559.photobucket.com/albums/ss37/ibloop/2.png)
For 2.
(https://i559.photobucket.com/albums/ss37/ibloop/1.png)
For 288.
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Never seen $3 7/10 at a gas station in the US or Canada. Are you sure you aren't seeing fractions of a cent? I do see a lot of $3.45 9/10, but never fractions of dolars.
Yeah, sorry, bad example on my part :lol
Yes, it's fractions of a cent. But, what's wrong with "$3.452"? I mean, would people really be that confused by it?
rumborak
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Honestly, yes. Only because Americans are so used to seeing two decimal places so adding another one would completely shatter certain peoples minds.
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What they do in Germany a lot is to have the third digit be slightly different:
(https://www.merkur-online.de/bilder/2009/07/06/388402/379515119-schauplatz-eines-brutalen-verbrechens-wurde-jet-tankstelle-kassierer-wurde-beim-ueberfall-schwerst-v.9.jpg)
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My conclusion: The person that wrote the question did a piss poor job of it. You will never see maths published with ambiguous notation ever, and if someone had asked you to do that you would ask them what they meant. And I'm with everyone else who said that you are better off writing divisions as fractions, the primary school notation is best phased out as quickly as possible!
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It's 288.
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Hmm, that is tricky. So tricky because it looks like shoddy notation/writing rather than some arithmetic black hole. To explain, a THIRD possible answer is to distribute the 2 onto (9 + 3). So this is what happens:
48 ÷ 2(9 + 3) [Given, with spaces added, which is allowed]
=48 ÷ 18 + 6 [Distribute the 2 onto the parentheses to get rid of them]
=8/3 + 6 [48/18 + 6]
=26/3
:biggrin:
But here is my real answer. I believe it is 288, because 48/2 is happening outside of the parentheses, but still to each other. Like, instead of using that elementary division sign, you are allowed to replace it with the forward slash, to get 48/2(9+3). Now if we distribute this number like I did in my joke math up there, we get (48/2)*9 + (48/2)*3 = 216 + 72 = 288. Q.E.D.lol.
All that said, I'm gonna ask some people tomorrow about this. Math professors and math majors alike. They are my people.
EDIT: I think the answer would be 2 if the 2 in the problem were included solely with the (9 + 3)...but then that would be obvious.
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The answer is 2. What kind of moron would say that there is no definitive "correct answer"? :facepalm:
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The answer is 288. :P
At least the way I'm being taught in school.
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The answer is 2. What kind of moron would say that there is no definitive "correct answer"? :facepalm:
And what kind of person comes onto a message board, calls some people a moron, gives an answer to a tricky question and does not back it up?
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The answer is 288. :P
At least the way I'm being taught in school.
Your school is obviously wrong.
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The syntax doesn't make it clear, so there's no definitive answer to this imo.
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The answer is 2. What kind of moron would say that there is no definitive "correct answer"? :facepalm:
And what kind of person comes onto a message board, calls some people a moron, gives an answer to a tricky question and does not back it up?
The kind of person that doesn't feel the need to repeat what several people have already said :\
It's a mathematical equation. There is one answer to it.
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The answer is 2. What kind of moron would say that there is no definitive "correct answer"? :facepalm:
People who actually think about the question rather than being knee-jerk about the issue?
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The answer is 2. What kind of moron would say that there is no definitive "correct answer"? :facepalm:
And what kind of person comes onto a message board, calls some people a moron, gives an answer to a tricky question and does not back it up?
The kind of person that doesn't feel the need to repeat what several people have already said :\
It's a mathematical equation. There is one answer to it.
There's one answer to a correctly written, unambiguous equation.
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It's a mathematical equation. There is one answer to it.
You really missed the problem, didn't you? Equations have to be parsed.
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/troll
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Alright alright...here is another way to look at this. Division and multiplication are in the same rank, and an expression must be read left to right when operations are of the same rank.
48 ÷ 2(9 + 3) [Given]
= 48 ÷ 2 x (9+3) [Multiplication sign added to further show it is multiplication]
= 48 ÷ 2 x (12) [Parentheses, dogg]
= 24 x 12 [Read it left to right] [Smart]
= 288
Edit: Equations need an equal sign.
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In order for a problem to have a an answer, it first must be a problem. And this problem sucks at being a problem.
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Alright alright...here is another way to look at this. Division and multiplication are in the same rank, and an expression must be read left to right when operations are of the same rank.
48 ÷ 2(9 + 3) [Given]
= 48 ÷ 2 x (9+3) [Multiplication sign added to further show it is multiplication]
= 48 ÷ 2 x (12) [Parentheses, dogg]
= 24 x 12 [Read it left to right] [Smart]
= 288
Exactly.
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In order for a problem to have a an answer, it first must be a problem. And this problem sucks at being a problem.
I guess the problem is that it sucks at being a problem...which is itself a problem, recursively becoming more and more problematic. Fibonacci headache.
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It's just bad syntax. So, "no definite answer" from me.
rumborak
IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.
rumborak
I agree everything rumborak has said.
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Except that...
2(9+3) =
(9x2 + 3x2) =
(18+6) =
24
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That expression is true. But putting a "48 ÷" before it forces you to read it left to right starting with the 48.
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The answer is 2. What kind of moron would say that there is no definitive "correct answer"? :facepalm:
And what kind of person comes onto a message board, calls some people a moron, gives an answer to a tricky question and does not back it up?
The kind of person that doesn't feel the need to repeat what several people have already said :\
It's a mathematical equation. There is one answer to it.
Tell me, oracle boy, what happened in the sentence "the old lady hit the man with an umbrella"?
rumborak
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That expression is true. But putting a "48 ÷" before it forces you to read it left to right starting with the 48.
Nope. Since the addition operation was in the parentheses, it must be done before the division.
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That expression is true. But putting a "48 ÷" before it forces you to read it left to right starting with the 48.
Nope. Since the addition operation was in the parentheses, it must be done before the division.
Yes, the parenthetical addition must be done first, but the mulitplication with 2 is not a correct step according to the OoO.
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If you simplify the inside first (like you are supposed to), you get 12. So then it is read 48 ÷ 2(12). Division and multiplication are of the same rank, so when that happens, you read it left to right. So 48 ÷ 2 first, which is 24, and THEN multiply by 12, to get 288.
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In order for a problem to have a an answer, it first must be a problem. And this problem sucks at being a problem.
I guess the problem is that it sucks at being a problem...which is itself a problem, recursively becoming more and more problematic. Fibonacci headache.
(https://www.wordans.us/wordansfiles/images/2011/1/18/63050/63050_popup.jpg?1295376369)
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According to Wolfram Alpha its 288. The main point this example makes however is not to use the divide sign when you can help it.
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In order for a problem to have a an answer, it first must be a problem. And this problem sucks at being a problem.
I guess the problem is that it sucks at being a problem...which is itself a problem, recursively becoming more and more problematic. Fibonacci headache.
(https://www.wordans.us/wordansfiles/images/2011/1/18/63050/63050_popup.jpg?1295376369)
:lol
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I only did maths up to A-Level standard - no university stuff, so I'm no expert - but I was always taught BODMAS. Brackets onto Division, Multiplication, Addition and Subtraction - in that order. The implicit hierarchy.
Which probably means my knowledge of maths is incomplete, seeing as everyone else is saying it's on level pegging with multiplication, but hey.
I do naturally convert it into 48 / 2(9+3) in my head, plus I tend to expand brackets first just to make things nice and easy, so I got 2, too. In spite of the hierarchy.
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Obviously 288 wtf?
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By order of operations, this means divide 48 by 2, and then multiply it by (9+3) which comes to 288. However in most math books and courses it is written wrongly for the sake of clarity. 1/2pi to me looks like 1 divided by 2pi but actually it's one half of pi. The correct notation here would be 1/(2pi). It's just that sometimes the parentheses left out for reasons of speed or ease or whatever.
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All I got now is a fucking headache, thanks guys.
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I get it nao lol.
I automatically jumped to this conclusion:
48
______
2(9+3)
In which case it's 2. This is the same as 48 ÷ (2(9+3)). But that was not the given though.
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MAKE IT STOP!!! :zeltar:
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I get it nao lol.
I automatically jumped to this conclusion:
48
______
2(9+3)
In which case it's 2. This is the same as 48 ÷ (2(9+3)). But that was not the given though.
Yes, that is the initial conclusion, based on what kari rightfully said. This is why I always use extra parentheses to indicate what I mean when I am writing mathematics, because I want to leave no room for ambiguity.
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What they do in Germany a lot is to have the third digit be slightly different:
(https://www.merkur-online.de/bilder/2009/07/06/388402/379515119-schauplatz-eines-brutalen-verbrechens-wurde-jet-tankstelle-kassierer-wurde-beim-ueberfall-schwerst-v.9.jpg)
holy shit. and i thought gas was expensive here.
and in europe, they go by the liter right? which is less than a gallon.
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The way it's written in the OP, the problem is as follows:
48/2(9+3)
The first thing that happens is:
9+3 = 12
THEN.
48/2 = 24
And 24 * 12 = 288.
If it was written as such:
__48__
2(9+3)
The answer would be 2.
It is not written this way. The answer is 288.
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What they do in Germany a lot is to have the third digit be slightly different:
(https://www.merkur-online.de/bilder/2009/07/06/388402/379515119-schauplatz-eines-brutalen-verbrechens-wurde-jet-tankstelle-kassierer-wurde-beim-ueberfall-schwerst-v.9.jpg)
holy shit. and i thought gas was expensive here.
and in europe, they go by the liter right? which is less than a gallon.
But then you have to factor in exchange rate. But if those are in Euros then its easily more expensive than even expensive American fuel. And IIRC, gas is about $2-4 (US) more expensive than it is in the US for some reason, maybe because we can produce some of our own gasoline as well.
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What they do in Germany a lot is to have the third digit be slightly different:
(https://www.merkur-online.de/bilder/2009/07/06/388402/379515119-schauplatz-eines-brutalen-verbrechens-wurde-jet-tankstelle-kassierer-wurde-beim-ueberfall-schwerst-v.9.jpg)
holy shit. and i thought gas was expensive here.
and in europe, they go by the liter right? which is less than a gallon.
But then you have to factor in exchange rate. But if those are in Euros then its easily more expensive than even expensive American fuel. And IIRC, gas is about $2-4 (US) more expensive than it is in the US for some reason, maybe because we can produce some of our own gasoline as well.
I know right, its crazy
but one thing i never understood is that in England (or Great britain, the UK, or whatever the proper term is, im still confused about that) is a part ot the EU. but they don't use the Euro. Why?
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Because we are a bunch of euroskeptics who will have to be dragged in kicking and screaming.
In seriousness, there are 10 EU states that do not use the euro, so we aren't alone.
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Because we are a bunch of euroskeptics who will have to be dragged in kicking and screaming.
In seriousness, there are 10 EU states that do not use the euro, so we aren't alone.
really? i didn't know that.
im kinda confused though, is there a significant reason why?
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Xenophobia mostly. Britain is stuck in an anti-europe sentiment for the most part.
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I do naturally convert it into 48 / 2(9+3) in my head, plus I tend to expand brackets first just to make things nice and easy, so I got 2, too. In spite of the hierarchy.
This is the way it looks to me, and to me it is obviously 2. But I was an English major, which means that I don't care.
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Xenophobia mostly. Britain is stuck in an anti-europe sentiment for the most part.
wait so it is Britain.
but wait again don't you mean england? im confused.
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Great Britain( informally Britain)= England, Scotland, and Wales.
Great Britain is an island.
England is a country that is a part of the island that is Great Britain.
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Great Britain( informally Britain)= England, Scotland, and Wales.
Great Britain is an island.
England is a country that is a part of the island that is Great Britain.
What about North Ireland. I'm pretty sure that fits in somewhere.
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Great Britain( informally Britain)= England, Scotland, and Wales.
Great Britain is an island.
England is a country that is a part of the island that is Great Britain.
What about North Ireland. I'm pretty sure that fits in somewhere.
It's part of Great Britain.
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um, ok. one last question then.
whats the UK?
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I don't think Northern Ireland is a part of Great Britain, however it is a part of the UK.
To answer your question, the UK is Great Britain and Northern Ireland. (Hence "The United Kingdom of Great Britain and Northern Ireland")
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I don't think Northern Ireland is a part of Great Britain, however it is a part of the UK.
To answer your question, the UK is Great Britain and Northern Ireland. (Hence "The United Kingdom of Great Britain and Northern Ireland")
Correct, Great Brittan is the major land mass of Brittan, including England Wales and Scotland, a few islands and such. Ireland is separate.
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they should just call everything by one name to keep it simple.
and they should use the euro like most other union countries do, since they are part of the EU.
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The way it's written in the OP, the problem is as follows:
48/2(9+3)
The first thing that happens is:
9+3 = 12
THEN.
48/2 = 24
The whole point of this discussion is that many math texts and mathematicians state that implied multiplication occurs before any other operations and many others disagree. So it's not a given that you divide in the 2nd step.
Another example of this is that one could say x^2y = (x^2)*y or x^(2*y).
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Another example of this is that one could say x^2y = (x^2)*y or x^(2*y).
I'm really intrigued to know how that is anything else but x^(2*y).
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what's confusing to me isn't the answer to this problem.
its people doing math in their spare time.
jk. kinda.
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I would immediately read that as x^(2y) but my logic tells me that it is (x^2)(y)
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Another example of this is that one could say x^2y = (x^2)*y or x^(2*y).
I'm really intrigued to know how that is anything else but x^(2*y).
The only way it is x^(2*y) is by saying "the parentheses are implied" or by saying "implied multiplication comes before all other operations" but the fact of the matter is that there are no parentheses in the x^2y and it is not a given that implied multiplication comes before the other operations.
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Another example of this is that one could say x^2y = (x^2)*y or x^(2*y).
I'm really intrigued to know how that is anything else but x^(2*y).
The only way it is x^(2*y) is by saying "the parentheses are implied" or by saying "implied multiplication comes before all other operations" but the fact of the matter is that there are no parentheses in the x^2y and it is not a given that implied multiplication comes before the other operations.
Huh, I see. I would immediately read that as x^(2*y) and not be able to see it any other way.
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I typed x^2x into my graphing calculator and it graphed x^3, so it seems to be the same deal...read it left to right and with PEMDAS, not what is implied.
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Ok, my only serious post in this thread. This is like a 6th grade problem.
So, here we go, ill make this simple.
48÷2(9+3). PEMDAS = Parenthesis, then exponents, then Multi, then division, addition, subtraction. In that order. and remember, ITS FROM LEFT TO RIGHT.
k. so.
1. Parenthesis = 48÷2(12)
2. No exponents
3. MULTIPLICATION = 48÷24
4. Then division = 2.
YOU GUYS FORGET THE MOST IMPORTANT RULE, ITS FROM LEFT TO RIGHT.
yep.
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PEMDAS = Parenthesis, then exponents, then Multi, then division, addition, subtraction. In that order.
Wrong.
PEMDAS = Parenthesis, exponents, multiplication & division, addition & subtraction. Multiplication and division have the same precedence.
15/3*4 is not 15/12 but is 20.
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Division is multiplication.
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i spent part of my free time talking about math.
i fail.
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You wouldn't be the first person to think that multiplication comes first before division. I was taught that way in third grade but our fourth grade teacher corrected it...
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Only DTF could argue four pages in six hours about a fucking math problem. :rollin
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You wouldn't be the first person to think that multiplication comes first before division. I was taught that way in third grade but our fourth grade teacher corrected it...
and im correcting your fourth grade teacher.
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Only DTF could argue four pages in six hours about a fucking math problem. :rollin
well, we spent part of that debating why england (or britain, at this point i dont care) doesn't use the euro.
which doesn't make sense, if youre part of the EU you should use the Euro.
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WTF since when does multiplication come before division? They are on the exact same level of importance. Whichever one is first is what you do. In this case it's division.
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Where in PEMDAS does it mention importance?
parenthesis, exponents, muli, division, add, sub, IN THAT ORDER. FROM LEFT TO RIGHT.
theres nothing in pemdas that says "both mulit and division are of equal importance". thats merely interpretation.
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Where in PEMDAS does it mention importance?
parenthesis, exponents, muli, division, add, sub, IN THAT ORDER. FROM LEFT TO RIGHT.
theres nothing in pemdas that says "both mulit and division are of equal importance". thats merely interpretation.
You do whatever comes first, it's multiplication OR division, add OR substraction. One doesn't come first than the other, one isn't more important than the other.
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and im correcting your fourth grade teacher.
Then I guess my math teachers in junior high, high school, and college (where I got a math degree) corrected both my former teacher and you.
As noted above, division *is* multiplication. Dividing by a number is the same as multiplying by the number's inverse.
But in case you don't believe me:
https://en.wikipedia.org/wiki/Order_of_operations
https://www.mathsisfun.com/operation-order-pemdas.html
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Where in PEMDAS does it mention importance?
parenthesis, exponents, muli, division, add, sub, IN THAT ORDER. FROM LEFT TO RIGHT.
theres nothing in pemdas that says "both mulit and division are of equal importance". thats merely interpretation.
You do whatever comes first, it's multiplication OR division, add OR substraction. One doesn't come first than the other, one isn't more important than the other.
THERE IS NO OR. if there was or, it would be PoEoMoDoAoS.
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and im correcting your fourth grade teacher.
Then I guess my math teachers in junior high, high school, and college (where I got a math degree) corrected both my former teacher and you.
As noted above, division *is* multiplication. Dividing by a number is the same as multiplying by the number's inverse.
But in case you don't believe me:
https://en.wikipedia.org/wiki/Order_of_operations
https://www.mathsisfun.com/operation-order-pemdas.html
division isn't multiplication.
here's why.
2/2 = 1
2 *2 = 4.
how is that the same?
EDIt = AND WIKIPEDIA ISNT A VALID SOURCE *college professor rant*. I shit on eggs is a perfect example.
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oh boy.
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and im correcting your fourth grade teacher.
Then I guess my math teachers in junior high, high school, and college (where I got a math degree) corrected both my former teacher and you.
As noted above, division *is* multiplication. Dividing by a number is the same as multiplying by the number's inverse.
But in case you don't believe me:
https://en.wikipedia.org/wiki/Order_of_operations
https://www.mathsisfun.com/operation-order-pemdas.html
division isn't multiplication.
here's why.
2/2 = 1
2 *2 = 4.
how is that the same?
You apparently don't know what a number's inverse is...
2/2 = 1
2 * (1/2) = 1
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He's trolling.
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and im correcting your fourth grade teacher.
Then I guess my math teachers in junior high, high school, and college (where I got a math degree) corrected both my former teacher and you.
As noted above, division *is* multiplication. Dividing by a number is the same as multiplying by the number's inverse.
But in case you don't believe me:
https://en.wikipedia.org/wiki/Order_of_operations
https://www.mathsisfun.com/operation-order-pemdas.html
division isn't multiplication.
here's why.
2/2 = 1
2 *2 = 4.
how is that the same?
You apparently don't know what a number's inverse is...
2/2 = 1
2 * (1/2) = 1
I realize that.
but were not talking about inverses.
were talking about multiplication and division.
its one thing to talk about the RELATION of the two, but the reality is THEY ARE SO DIFFERENT THINGS.
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Nobody addressed my point of diving by x is also the same as multiplying by 1/x
Therefore 48 * (1/24) = 2
Also, nowhere in the order of operations can I find "read it left to right." It's what I was taught, but you learn a lot of bullshit in school.
EDIT: ninja'd kind of
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Where in PEMDAS does it mention importance?
parenthesis, exponents, muli, division, add, sub, IN THAT ORDER. FROM LEFT TO RIGHT.
theres nothing in pemdas that says "both mulit and division are of equal importance". thats merely interpretation.
You are dead wrong. You first do parentheses. Then exponents. Then multiplication/division, which, if there is more than one of those going on, you do it from left to right. Then addition/subtraction (same rule as multi/div.). PEMDAS is merely a mnemonic device to help you remember the order of the tiers, and it is NOT a literal order for ALL of the operations.
If you think I am even slightly wrong I will slap you across our monitors.
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its one thing to talk about the RELATION of the two, but the reality is THEY ARE SO DIFFERENT THINGS.
Maybe you are not trolling, but division is technically multiplication.
When we divide something by 4, we are actually multiplying that something by (1/4). This may not make sense to you, but it is true.
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Where in PEMDAS does it mention importance?
parenthesis, exponents, muli, division, add, sub, IN THAT ORDER. FROM LEFT TO RIGHT.
theres nothing in pemdas that says "both mulit and division are of equal importance". thats merely interpretation.
You are dead wrong. You first do parentheses. Then exponents. Then multiplication/division, which, if there is more than one of those going on, you do it from left to right. Then addition/subtraction (same rule as multi/div.). PEMDAS is merely a mnemonic device to help you remember the order of the tiers, and it is NOT a literal order for ALL of the operations.
If you think I am even slightly wrong I will slap you across our monitors.
yah but the poll says the answer is two.
and everyone in a dream theater forum is smart.
so yah.
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I asked my cousin about this on Facebook. This was his response. Not sure sure this helps or not.
The order of operations dictates that everything in parentheses is done first, then multiplication/division, then addition/subtraction.
The misleading bit about this equation is that the easy assumption is that, since the 2 is adjacent to the "(9+3)," '2 x 12' should be done next. The reason for this is because we are taught to incorporate the distributive property -- a(b + c) = ab + ac -- without the important caveat that 'a(b + c)' should be viewed as 'a x (b + c)' when it exists in a longer equation such as the one listed above.
The most common answer to the equation in question is 2: 48 ÷ 2(9 + 3) = 48 ÷ (2 x 12) = 48 ÷ 24 = 2
This violates the procedural guidelines of order of operations.
The correct way to solve this equation is this:
48 ÷ 2(9 + 3) = (48 ÷ 2) x (9 + 3) = 24 x (9 + 3) = 24 x 12 = 288
I'm not sure what the debate is here. Putting a number adjacent to a parenthesis is simply shorthand for saying that the first number is to be multiplied by the second. There is not special consideration given to it just because it is written that way.
Hope this helps.
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^That has been said a bunch of times already. ;)
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Where in PEMDAS does it mention importance?
parenthesis, exponents, muli, division, add, sub, IN THAT ORDER. FROM LEFT TO RIGHT.
theres nothing in pemdas that says "both mulit and division are of equal importance". thats merely interpretation.
You are dead wrong. You first do parentheses. Then exponents. Then multiplication/division, which, if there is more than one of those going on, you do it from left to right. Then addition/subtraction (same rule as multi/div.). PEMDAS is merely a mnemonic device to help you remember the order of the tiers, and it is NOT a literal order for ALL of the operations.
If you think I am even slightly wrong I will slap you across our monitors.
yah but the poll says the answer is two.
and everyone in a dream theater forum is smart.
so yah.
Currently known, there are 24 people who can't do basic math. :biggrin:
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Where in PEMDAS does it mention importance?
parenthesis, exponents, muli, division, add, sub, IN THAT ORDER. FROM LEFT TO RIGHT.
theres nothing in pemdas that says "both mulit and division are of equal importance". thats merely interpretation.
You are dead wrong. You first do parentheses. Then exponents. Then multiplication/division, which, if there is more than one of those going on, you do it from left to right. Then addition/subtraction (same rule as multi/div.). PEMDAS is merely a mnemonic device to help you remember the order of the tiers, and it is NOT a literal order for ALL of the operations.
If you think I am even slightly wrong I will slap you across our monitors.
yah but the poll says the answer is two.
and everyone in a dream theater forum is smart.
so yah.
Currently known, there are 24 people who can't do basic math. :biggrin:
yah but 24 > 14.
basic math says im right.
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Trollllllllllllllllllllllllllll
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Trollllllllllllllllllllllllllll
His whole existence is that.
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Trollllllllllllllllllllllllllll
https://youtu.be/iwGFalTRHDA
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^That has been said a bunch of times already. ;)
Eh. I figured it would have.
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no no, i wasn't trolling. but technically, isn't calling someone a troll "trolling"? you can call me a troll, but i haven't resorted to namecalling, all ive done is make legitimate arguments.
the only thing i dont get is when people say multiplication and division are the same thing.
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You are saying that, because 2 has the most votes, it must be right.
How is that a legitimate argument?
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The answer is 288 because of BEDMAS. I hear most call it PEMDAS though. Maybe BEDMAS is the Canadian thing.
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The answer is 288 because of BEDMAS. I hear most call it PEMDAS though. Maybe BEDMAS is the Canadian thing.
what does the b stand for?
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Yeah, we use the word parentheses and y'all use brackets.
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Yeah, we use the word parentheses and y'all use brackets.
ohhhhhh. my bad.
idk to me brackets makes more sense.
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Did the math before entering the thread, also didn't read the thread.
The answer is 288.
/late
-J
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the only thing i dont get is when people say multiplication and division are the same thing.
When we divide something by 4, we are actually multiplying that something by (1/4). This may not make sense to you, but it is true.
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the only thing i dont get is when people say multiplication and division are the same thing.
When we divide something by 4, we are actually multiplying that something by (1/4). This may not make sense to you, but it is true.
i just learned about this in my useless *math and physics theory* course.
saying "dividing something by 4" and saying "multiplying something by 1/4" are two completely different arguments. I really don't feel like copying and pasting the lecture.
Edit - I MEANT MATH APPLICATIONS COURSE.
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(https://t0.gstatic.com/images?q=tbn:ANd9GcSNapm6j7Ncfj3PyQphQVtnx7aHedD2-XaPoAJi3t9W7KYfNbdPTA)
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the only thing i dont get is when people say multiplication and division are the same thing.
When we divide something by 4, we are actually multiplying that something by (1/4). This may not make sense to you, but it is true.
i just learned about this in my useless *math and physics theory* course.
saying "dividing something by 4" and saying "multiplying something by 1/4" are two completely different arguments. I really don't feel like copying and pasting the lecture.
Edit - I MEANT MATH APPLICATIONS COURSE.
You're right. Taking 14 math courses makes me wrong and you right. :)
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the only thing i dont get is when people say multiplication and division are the same thing.
When we divide something by 4, we are actually multiplying that something by (1/4). This may not make sense to you, but it is true.
i just learned about this in my useless *math and physics theory* course.
saying "dividing something by 4" and saying "multiplying something by 1/4" are two completely different arguments. I really don't feel like copying and pasting the lecture.
Edit - I MEANT MATH APPLICATIONS COURSE.
You're right. Taking 14 math courses makes me wrong and you right. :)
i never said you were wrong. never in one of my posts did i say that.
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(https://t0.gstatic.com/images?q=tbn:ANd9GcSNapm6j7Ncfj3PyQphQVtnx7aHedD2-XaPoAJi3t9W7KYfNbdPTA)
+1
me too. it makes me fight with jamesman who in reality i <3.
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I hate it when people overly rely on operator precedence, especially in programming languages.
Stuff like
int x = ++i * 5 + i;
makes me want to track down the originator of the code and "++" him myself a bit.
rumborak
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(https://cdn3.knowyourmeme.com/i/000/113/276/original/206483_1776491504605_1608886476_1688467_6580770_n.jpg?1302609835)
:biggrin:
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..and were back to the OP of this thread.
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I'm surprised people are still arguing in this thread. :|
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I'm surprised people are still arguing in this thread. :|
Welcome to DTF.
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well, two is still winning, so i guess that must be the answer.
and i officially give up.
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EDIt = AND WIKIPEDIA ISNT A VALID SOURCE *college professor rant*. I shit on eggs is a perfect example.
This however is.
https://mathworld.wolfram.com/Precedence.html
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I'm surprised people are still arguing in this thread. :|
Welcome to DTF.
Maybe I should make a 1 = 0.999... thread. :neverusethis:
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(https://t0.gstatic.com/images?q=tbn:ANd9GcSNapm6j7Ncfj3PyQphQVtnx7aHedD2-XaPoAJi3t9W7KYfNbdPTA)
+1
me too. it makes me fight with jamesman who in reality i <3.
Well, your assertions fly in the face of mathematical logic, so.....ya know. You're roughing me up, son
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I'm surprised people are still arguing in this thread. :|
Welcome to DTF.
Maybe I should make a 1 = 0.999... thread. :neverusethis:
Hehe
It's true though!
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(https://t0.gstatic.com/images?q=tbn:ANd9GcSNapm6j7Ncfj3PyQphQVtnx7aHedD2-XaPoAJi3t9W7KYfNbdPTA)
+1
me too. it makes me fight with jamesman who in reality i <3.
Well, your assertions fly in the face of mathematical logic, so.....ya know. You're roughing me up, son
sorry, ill apologize in the chat thread tomorrow. you might have to remind me tho, k?
THAT REMINDS ME, ITS BEEN 36 HOURS. my avatar can go back to normal now.
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Hehe
It's true though!
DON'T START. Though I agree.
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1 = 1
1/9 = 1/9
1/9 = 0.11111...
9*(1/9) = 9*(0.11111...)
1 = .99999...
QED
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RPN shits on this thread. My first calculator in college had RPN, that was pretty badass.
rumborak
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1 = 1
1/9 = 1/9
1/9 = 0.11111...
9*(1/9) = 9*(0.11111...)
1 = .99999...
QED
I prefer this: https://upload.wikimedia.org/math/6/f/a/6fa510b44742046a167b4b8515162825.png
And I wish I could change my vote to 288. Ah well.
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^Nice, using infinite series to show it. I've never seen that version before, thank you
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1 = 1
1/9 = 1/9
1/9 = 0.11111...
9*(1/9) = 9*(0.11111...)
1 = .99999...
QED
The bolded part is kinda the weak part in the argument. You're essentially trying to prove this by relying on a convenient shorthand.
rumborak
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What do you mean exactly?
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I would kind of agree with rumby. The fact that 1/9 = 0.111... comes from the same logic that 1 = 0.999....
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Then what does 1/9 equal in decimal form?
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What do you mean exactly?
I'm saying that the "..." notation isn't really a proper notation for numbers, and it kinda means "reader, I assume you know what I mean, and I'm too lazy to write infinite numbers here". Using this notation for proving something doesn't really work too well.
Then what does 1/9 equal in decimal form?
There is none. There are many numbers that don't have a decimal expansion, including Pi.
1 = 1
1/9 = 1/9
1/9 = 0.11111...
9*(1/9) = 9*(0.11111...)
1 = .99999...
QED
I prefer this: https://upload.wikimedia.org/math/6/f/a/6fa510b44742046a167b4b8515162825.png
This one isn't really that great either. It just relies on a different assumption, which is that the limit of x going towards a number is that number. So, in the end you have a tautology, since the limit notation relies on exactly the same thing as the thing you're trying to prove.
To me, it's mostly just a matter of definition that 0.99999... = 1. The argument goes that the difference is infinitely small and thus you could never define a meaningful difference between the two.
rumborak
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Then what does 1/9 equal in decimal form?
0.111... but if that's the case you might as well cut out the first two steps in your proof. I dunno. I feel like it's cheating. I'm actually not an expert.
To me, it's mostly just a matter of definition that 0.99999... = 1. The argument goes that the difference is infinitely small and thus you could never define a meaningful difference between the two.
rumborak
I'm sure there are huge math texts that explain it, but I don't know how to respond. You're kind of right, I guess.
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I'm saying that the "..." notation isn't really a proper notation for numbers, and it kinda means "reader, I assume you know what I mean, and I'm too lazy to write infinite numbers here". Using this notation for proving something doesn't really work too well.
It's just a way to represent the bar symbol to indicate a repeating decimal.
There are many numbers that don't have a decimal expansion, including Pi.
The difference is that Pi is an irrational number which cannot be represented as a ratio of two whole numbers. A repeating decimal is still a decimal.
To me, it's mostly just a matter of definition that 0.99999... = 1. The argument goes that the difference is infinitely small and thus you could never define a meaningful difference between the two.
Some may argue that, but the proof is meant to show that they are in fact equal to each other.
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The difference is that Pi is an irrational number which cannot be represented as a ratio of two whole numbers. A repeating decimal is still a decimal.
My point is that neither 0.9999... nor 3.1415... describe through their notation the number correctly. Using a flawed notation to prove something leads to a weak argument. From Wikipedia:
William Byers argues that a student who agrees that 0.999... = 1 because of the above proofs, but hasn't resolved the ambiguity, doesn't really understand the equation.[2] Fred Richman argues that the first argument "gets its force from the fact that most people have been indoctrinated to accept the first equation without thinking".[3]
Some may argue that, but the proof is meant to show that they are in fact equal to each other.
I am not disputing the truth of the statement. I'm saying the proofs need to be better than just the superficial proofs mentioned above.
rumborak
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Rumby, the thing is, we KNOW that 1/9 = .11111... or .1 with the bar over it. It is a repeating decimal. Then, since we know that, by multiplying .11111....by 9, we can logically conclude that all those 1's turn into 9's, because (1)(9) = 9.
I agree that it is more of a definition, but these "proofs" are a good way to see why it's true.
Then what does 1/9 equal in decimal form?
0.111... but if that's the case you might as well cut out the first two steps in your proof. I dunno. I feel like it's cheating. I'm actually not an expert.
Eh, I just like to start with 1 = 1 in those proofs, it makes it more elegant to me. That's just me, though.
Edit: This thread has been burned. Also I put "nonrepeating" facepaaaaalm
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And it's all my fault! :'(
((https://files.sharenator.com/success_baby_asshole_Justin_Bieber_Hit_With_Water_Bottle-s462x338-84972-535.jpg))
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You guys have gone over my head so many times in this thread, I have no hair left up there.
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You guys have gone over my head so many times in this thread, I have no hair left up there.
One divided by zero equals infinity.
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How is it possible :huh:
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You guys have gone over my head so many times in this thread, I have no hair left up there.
Maybe if they explained in tbsp and tsp.............
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(https://i11.photobucket.com/albums/a194/QWERTYkid911/Status.png)
:corn
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You guys have gone over my head so many times in this thread, I have no hair left up there.
"Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo." is a grammatically valid sentence.
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You guys have gone over my head so many times in this thread, I have no hair left up there.
One divided by zero equals infinity.
(https://t1.gstatic.com/images?q=tbn:ANd9GcTKDMSdGPiM98oNCAT9zr599-9wmuW4G8EOS6I03Afma9_NF38k8A)
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Rumby, the thing is, we KNOW that 1/9 = .11111... or .1 with the bar over it. It is a repeating decimal. Then, since we know that, by multiplying .11111....by 9, we can logically conclude that all those 1's turn into 9's, because (1)(9) = 9.
Err, no, James, we DON'T know that 1/9 = .11111..., because it is just a rewording of what you are trying to prove!! (that 0.9999... = 1)
A tautology is not a proof.
rumborak
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(https://www.yesfans.com/images/smilies/horse.gif)
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:deadhorse:
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:deadhorse:
Huh. Didn't know we had that one.
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I also posted this on facebook. Got two people that said 2, posted it step by step showing how to get 288. And then someone else answered 144. :justjen
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OK, last one of the night...
(https://t3.gstatic.com/images?q=tbn:ANd9GcT84zF6NG28uUxKZSQ6d2T3rjj1tF11iYl6qteV0eb9ugow1HYC)
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Rumby, the thing is, we KNOW that 1/9 = .11111... or .1 with the bar over it. It is a repeating decimal. Then, since we know that, by multiplying .11111....by 9, we can logically conclude that all those 1's turn into 9's, because (1)(9) = 9.
Err, no, James, we DON'T know that 1/9 = .11111..., because it is just a rewording of what you are trying to prove!! (that 0.9999... = 1)
A tautology is not a proof.
rumborak
What does your calculator tell you then? I'm not getting your logic here.
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What they do in Germany a lot is to have the third digit be slightly different:
(https://www.merkur-online.de/bilder/2009/07/06/388402/379515119-schauplatz-eines-brutalen-verbrechens-wurde-jet-tankstelle-kassierer-wurde-beim-ueberfall-schwerst-v.9.jpg)
holy shit. and i thought gas was expensive here.
and in europe, they go by the liter right? which is less than a gallon.
Those prices are outdated.. Diesel is € 1,45 or so at the moment, and gasoline is about 1,65... That's $7,858 and $8,672 per gallon.
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The reason gas is pricier in most european countries is because of taxes.
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Well of course... But that doesn't make it any better or does it?
Only DTF could argue four pages in six hours about a fucking math problem. :rollin
This thread reached 27 pages in 2 days on some other forum and was locked because there was too much flaming etc...
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Rumby, the thing is, we KNOW that 1/9 = .11111... or .1 with the bar over it. It is a repeating decimal. Then, since we know that, by multiplying .11111....by 9, we can logically conclude that all those 1's turn into 9's, because (1)(9) = 9.
Err, no, James, we DON'T know that 1/9 = .11111..., because it is just a rewording of what you are trying to prove!! (that 0.9999... = 1)
A tautology is not a proof.
rumborak
How about
x = 0.99...
10x = 9.99...
9x = 9.99... - x
9x = 9
x = 1
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Rumby, the thing is, we KNOW that 1/9 = .11111... or .1 with the bar over it. It is a repeating decimal. Then, since we know that, by multiplying .11111....by 9, we can logically conclude that all those 1's turn into 9's, because (1)(9) = 9.
Err, no, James, we DON'T know that 1/9 = .11111..., because it is just a rewording of what you are trying to prove!! (that 0.9999... = 1)
A tautology is not a proof.
rumborak
Forgive me, but can't you arrive at 1/9 = 0.1... through simple long division?
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I think rumborak's point is that 0.11... isn't a correct notation for what you get when you divide 1 by 9. Or something like that.
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Well it definitely is the correct notation for that fraction. I think Rumborak's point was that the proof was relying on two unproved axioms, each a different wording of the same problem, whereas in the case of 1/9, the answer of 0.111... can be found using simple mathematics (long division). Admittedly its not the best proof in the world but its not a tautology as Rumborak suggested.
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Well this thread has moved on quite a bit from when I saw it yesterday...
All I would say is (and all this has probably already been said) this is just poor notation, it should be written using fractions rather than the ÷ sign as it leads to the ambiguity.
Multiplication and division have the same priority, even though the common acronym to remember the order might put them one in front of the other (BODMAS or PEMDAS). But this is just a way of remembering it, there is no rule saying a direct multiplication should go before division because they are essentially the same thing. Going left to right technically leads to 288 as it is 48 * 1/2 * (9+3).
However, intuitively I would be inclined to say that the 2(9+3) is supposed to be grouped together because of the way it is written. The 2(9+3) represents (9+3) with a common factor of 2 taken outside, which is 24. Then it becomes 48 * 1/24 which is 2. But I see in this thread people saying that the 2(9+3) notation isn't accepted as a form of grouping any more than 2 x (9+3), so using a left to right convention would lead to 288.
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Well it definitely is the correct notation for that fraction. I think Rumborak's point was that the proof was relying on two unproved axioms, each a different wording of the same problem, whereas in the case of 1/9, the answer of 0.111... can be found using simple mathematics (long division). Admittedly its not the best proof in the world but its not a tautology as Rumborak suggested.
This is my belief as well. I understand that the proof may have some shakiness to it, but it still works to support the definition that 0.999... = 1.
-
B - brackets
E - exponents
D - division
M - multiplication
A - addition
A - subtraction
BEDMAS.
Learn it.
-
48/2(9+3) = 24 * 12 = 288
48/(2(9+3)) = 48 / 24 = 2
That's what I've been taught and what I've seen in any math book I've ever used/read.
-
B - brackets
E - exponents
D - division
M - multiplication
A - addition
A - subtraction
BEDMAS.
Learn it.
Yeah, except the whole point of this is that division and multiplication aren't done in any certain order the same way addition and subtraction aren't...
Also, that's BEDMAA.
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Well it definitely is the correct notation for that fraction. I think Rumborak's point was that the proof was relying on two unproved axioms, each a different wording of the same problem, whereas in the case of 1/9, the answer of 0.111... can be found using simple mathematics (long division). Admittedly its not the best proof in the world but its not a tautology as Rumborak suggested.
To elaborate on my point: In the end, 0.999... = 1 makes a statement about the infinitely small remainder between the two numbers, i.e. that the remainder *is* indeed zero and they are thus the same numbers.
Now, 1/9 = 0.1111.... makes exactly the same point! Just as in 0.9999... the argument goes there is always another "9" that makes it closer to 1, in 0.1111... there is always another 1 that makes it closer to 1/9.
So, my point is that you are starting out with the thing you are actually trying to prove, and then, duh, you magically prove it!
Again, I do not question the overall truth of the statement, I'm just commenting on that a lot of those "easy proofs" for this are inherently flawed.
rumborak
-
Well it definitely is the correct notation for that fraction. I think Rumborak's point was that the proof was relying on two unproved axioms, each a different wording of the same problem, whereas in the case of 1/9, the answer of 0.111... can be found using simple mathematics (long division). Admittedly its not the best proof in the world but its not a tautology as Rumborak suggested.
To elaborate on my point: In the end, 0.999... = 1 makes a statement about the infinitely small remainder between the two numbers, i.e. that the remainder *is* indeed zero and they are thus the same numbers.
Now, 1/9 = 0.1111.... makes exactly the same point! Just as in 0.9999... the argument goes there is always another "9" that makes it closer to 1, in 0.1111... there is always another 1 that makes it closer to 1/9.
So, my point is that you are starting out with the thing you are actually trying to prove, and then, duh, you magically prove it!
Again, I do not question the overall truth of the statement, I'm just commenting on that a lot of those "easy proofs" for this are inherently flawed.
rumborak
Then what is the "real proof"? I think we proved it last semester in one of my courses called "Proving and reasoning" using Dedekindsneden, whatever that means in English.. Dedekind cuts?
-
B - brackets
E - exponents
D - division
M - multiplication
A - addition
A - subtraction
BEDMAS.
Learn it.
Yeah, except the whole point of this is that division and multiplication aren't done in any certain order the same way addition and subtraction aren't...
Also, that's BEDMAA.
Correct. In school I was taught "Please Excuse My Dear Aunt Sally" which reverses division and multiplication.
-
Well it definitely is the correct notation for that fraction. I think Rumborak's point was that the proof was relying on two unproved axioms, each a different wording of the same problem, whereas in the case of 1/9, the answer of 0.111... can be found using simple mathematics (long division). Admittedly its not the best proof in the world but its not a tautology as Rumborak suggested.
To elaborate on my point: In the end, 0.999... = 1 makes a statement about the infinitely small remainder between the two numbers, i.e. that the remainder *is* indeed zero and they are thus the same numbers.
Now, 1/9 = 0.1111.... makes exactly the same point! Just as in 0.9999... the argument goes there is always another "9" that makes it closer to 1, in 0.1111... there is always another 1 that makes it closer to 1/9.
So, my point is that you are starting out with the thing you are actually trying to prove, and then, duh, you magically prove it!
Again, I do not question the overall truth of the statement, I'm just commenting on that a lot of those "easy proofs" for this are inherently flawed.
rumborak
Then what is the "real proof"? I think we proved it last semester in one of my courses called "Proving and reasoning" using Dedekindsneden, whatever that means in English.. Dedekind cuts?
There's many of them, https://en.wikipedia.org/wiki/0.999... has a lot of them, including Dedekind's cut.
rumborak
-
Rumby, the thing is, we KNOW that 1/9 = .11111... or .1 with the bar over it. It is a repeating decimal. Then, since we know that, by multiplying .11111....by 9, we can logically conclude that all those 1's turn into 9's, because (1)(9) = 9.
Err, no, James, we DON'T know that 1/9 = .11111..., because it is just a rewording of what you are trying to prove!! (that 0.9999... = 1)
A tautology is not a proof.
rumborak
How about
x = 0.99...
10x = 9.99...
9x = 9.99... - x
9x = 9
x = 1
Correct me if I am wrong but, you can't just subtract x from one side of your equation without also subtracting it from the other. you should end up with 8x=9 with x being = to 8/9 not 1.
-
Well it definitely is the correct notation for that fraction. I think Rumborak's point was that the proof was relying on two unproved axioms, each a different wording of the same problem, whereas in the case of 1/9, the answer of 0.111... can be found using simple mathematics (long division). Admittedly its not the best proof in the world but its not a tautology as Rumborak suggested.
To elaborate on my point: In the end, 0.999... = 1 makes a statement about the infinitely small remainder between the two numbers, i.e. that the remainder *is* indeed zero and they are thus the same numbers.
Now, 1/9 = 0.1111.... makes exactly the same point! Just as in 0.9999... the argument goes there is always another "9" that makes it closer to 1, in 0.1111... there is always another 1 that makes it closer to 1/9.
So, my point is that you are starting out with the thing you are actually trying to prove, and then, duh, you magically prove it!
Again, I do not question the overall truth of the statement, I'm just commenting on that a lot of those "easy proofs" for this are inherently flawed.
rumborak
Then what is the "real proof"? I think we proved it last semester in one of my courses called "Proving and reasoning" using Dedekindsneden, whatever that means in English.. Dedekind cuts?
There's many of them, https://en.wikipedia.org/wiki/0.999... has a lot of them, including Dedekind's cut.
rumborak
I see, thanks. It also includes the proof I gave a few posts above... Does it also make use of the same tautology you are referring to?
Rumby, the thing is, we KNOW that 1/9 = .11111... or .1 with the bar over it. It is a repeating decimal. Then, since we know that, by multiplying .11111....by 9, we can logically conclude that all those 1's turn into 9's, because (1)(9) = 9.
Err, no, James, we DON'T know that 1/9 = .11111..., because it is just a rewording of what you are trying to prove!! (that 0.9999... = 1)
A tautology is not a proof.
rumborak
How about
x = 0.99...
10x = 9.99...
9x = 9.99... - x
9x = 9
x = 1
Correct me if I am wrong but, you can't just subtract x from one side of your equation without also subtracting it from the other. you should end up with 8x=9 with x being = to 8/9 not 1.
You are correct, but I did subtract x.. 10x - x = 9x.
-
Sorry actually we are both wrong.
you subtract x from both sides.
so you have (10x) -x = 9.99 -x
so 10(x) - x = 9
You can't subtract an x out of that multiplication.
EDIT: Never mind. I seemed to have forgotten that 10x is actually x + x + x + x etc. lol I've been out of math classes for far too long.
-
:lol What you said above your last line made no sense at all.
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I see, thanks. It also includes the proof I gave a few posts above... Does it also make use of the same tautology you are referring to?
It does seem to rely on the same thing, yeah. The key step is when you subtract 0.9999... from 9.99999...., where you are in the same kind of business of working with this incomplete notation. Even though, in that case it's not as blatant as the other one I find.
rumborak
-
Really? I would've thought that it's no problem to write 9.99... as 9 + 0.99...
I thought the "key step" was 10*(0.99...) = 9.99...
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i can't believe the wrong answer is leading this poll WTF.
-
i can't believe the wrong answer is leading this poll WTF.
This xD
-
To be honest I got it wrong before I looked up why. I would never write the equation like that so preference of operations rarely comes up for me.
-
That's why I voted for "no definite answer". It's still bad syntax.
rumborak
-
In order of operations, division trumps multiplication. Always do the division first.
-
It's always great to see someone come in and post something that has been shown to be wrong in the previous posts. Multiplication and division are of equal precedence, and you must disambiguate with brackets.
rumborak
-
I would think 288 would be correct, but I haven't taken a math class in like eight years, so I am going from memory as far as order of operations.
-
:rollin
Still at it, eh guys?
-
:rollin
Still at it, eh guys?
We're a prog forum, aren't we? :lol
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Well, rumby, I will just disagree with you on that 0.999 business. But I really don't feel like arguing it
I asked some people today in the math field, they all initially said 2, and when I asked "Are you sure?", most changed their mind and came to 288.
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I see the 2(9+3) as one term, so the implied multiplication does in effect take precedence.
For example, if it was 48÷2x, you would definitely simplify 2x first, then divide 48 by the result. It's not 48÷2*x. The implied multiplication isn't the same in hierarchy, it comes in with higher priority. It never even occurred to me to go left to right, because there's no multiplication sign there. You divide by 2(9+3).
So the answer is 2. Asking someone "Are you sure?" isn't just asking if they're sure; it makes them think that you know they're wrong and you're giving them another chance to get it right, so they switch to the only other possibility.
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According to the rules of math, the answer is 288. It's as simple as that. Whether it looks messed up or not, it's 288.
-
According to the rules of math, the answer is 288. It's as simple as that. Whether it looks messed up or not, it's 288.
-
Re: the 0.999... snafu:
Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.
1 - 0.999... = 0.000...1
=10-∞
=1/10∞
=1/∞
IFF 1/∞ = 0, then 0.999... = 1.
The problem is, 1/∞ is debatable. One can say the answer is zero, an infinitesimally small number, or undefinable.
My answer is: yes, 0.99... is equal to 1, but only because we need it to be.
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Re: the 0.999... snafu:
Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.
1 - 0.999... = -0.000...1
Pretty sure you can't do that.
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So the answer is 2. Asking someone "Are you sure?" isn't just asking if they're sure; it makes them think that you know they're wrong and you're giving them another chance to get it right, so they switch to the only other possibility.
But to me, math is concrete. Me asking them makes them look at it deeper and discover that there may be more to it. So I interjected a little doubt to their answer; I didn't say theirs was wrong. They all switched because they reasoned it out like I did in the end.
The problem is, 1/∞ is debatable. One can say the answer is zero, an infinitesimally small number, or undefinable.
My answer is: yes, 0.99... is equal to 1, but only because we need it to be.
In calculus, when we take limits for a variable approaching infinity, we do say that 1/∞ = 0. Just like 0.999 = 1, that is just what it is.
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I say 2. Yay for PEMDAS! PLEASE excuse my dear aunt sally!!! :biggrin:
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I see the 2(9+3) as one term, so the implied multiplication does in effect take precedence.
So they'd be separate terms if I made it "2*(9+3)"?
And this seems like a circular argument. Why is it one term? Because implied multiplication takes precedence. Why does implied multiplication take precedence? Because I see it as one term.
-
48 / 2(9+3)
48 / ((2x9)+(2x3))
48 / (18 + 6)
48 / (24)
2
Where is the difficulty?
-
I hearby declare both 2 and 288 to be correct, if only to save my sanity.
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Sorry, that's not how the internet works.
-
48 / 2(9+3)
48 / ((2x9)+(2x3))
48 / (18 + 6)
48 / (24)
2
Where is the difficulty?
48 / 2(9+3)
48 / 2 * (9+3)
48 / 2 * (12)
24 * 12
288
Where is the difficulty?
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I say 2. Yay for PEMDAS! PLEASE excuse my dear aunt sally!!! :biggrin:
Why is it no one seems to know how to do PEMDAS/BEDMAS?
-
Where is the difficulty?
For the nth time, division and multiplication are in the same rank.
-
Where is the difficulty?
For the nth time, division and multiplication are in the same rank.
Yes, but in the syntax that Quad wrote it, it is 2.
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Where is the difficulty?
For the nth time, division and multiplication are in the same rank.
Yes, but in the syntax that Quad wrote it, it is 2.
Oh, so he did a separate problem. Gotcha.
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It's 288. Regardless of PEMDAS/BEDMAS, multiplication and division are equal in the order of operations. So after doing the parenthesis, you go left to right.
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Re: the 0.999... snafu:
Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.
1 - 0.999... = 0.000...1
Pretty sure you can't do that.
Of course you can, it just reduces the argument. The 0.000...1 either represents an infinitely small number or zero, which is exactly what we are trying to determine. People who argue that 0.999... is not equal to 1 imply that 0.000...1 is in fact a number of measurable substance greater than zero, while those who argue that 0.999... is equal to 1 imply that 0.000...1 is zero. I do not agree that a number approaching a number, even to the point of being infinitely similar, can ever be equal to the number.
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It's 37.
-
It's 37.
:|
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It's 37.
:|
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I see the 2(9+3) as one term, so the implied multiplication does in effect take precedence.
So they'd be separate terms if I made it "2*(9+3)"?
And this seems like a circular argument. Why is it one term? Because implied multiplication takes precedence. Why does implied multiplication take precedence? Because I see it as one term.
If it said 48÷2x = ? would you divide by 2, then multiply by x? No, you would find 2x and divide by the result. Why is 48÷2(9+3) any different?
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288 all up in this bitch.
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If it said 48÷2x = ? would you divide by 2, then multiply by x? No, you would find 2x and divide by the result. Why is 48÷2(9+3) any different?
I would ask you to clarify, because the equation is too amboguous.
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I see the 2(9+3) as one term, so the implied multiplication does in effect take precedence.
So they'd be separate terms if I made it "2*(9+3)"?
And this seems like a circular argument. Why is it one term? Because implied multiplication takes precedence. Why does implied multiplication take precedence? Because I see it as one term.
If it said 48÷2x = ? would you divide by 2, then multiply by x? No, you would find 2x and divide by the result. Why is 48÷2(9+3) any different?
What about 48÷2(9+3)(5+3)(2+8) ?
Do you just assume everything after the ÷ sign to be in the denominator? That's a pretty arbitrary decision given multiplication and division are of equal rank.
rumborak
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Yeah, I would. I always presumed that implied multiplication gave it some kind of precedence. But it's not in the formal rules, so I guess not.
But I noticed that no one has answered my 48÷2x question, and it's techinically the same thing. All you're saying is 48÷2abc. I would still find 2abc and divide it into 48. I guess it's because there's no actual multiplication sign in the expression. It seems like you'd simplify it first.
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Re: the 0.999... snafu:
Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.
1 - 0.999... = 0.000...1
Pretty sure you can't do that.
Of course you can, it just reduces the argument. The 0.000...1 either represents an infinitely small number or zero, which is exactly what we are trying to determine. People who argue that 0.999... is not equal to 1 imply that 0.000...1 is in fact a number of measurable substance greater than zero, while those who argue that 0.999... is equal to 1 imply that 0.000...1 is zero. I do not agree that a number approaching a number, even to the point of being infinitely similar, can ever be equal to the number.
0.000...1 is not a correct number in any notation. You can't put a "1" at the end of an INFINITE string of zeros. That's the whole reason 0.999... is equal to 1, because there is no number inbetween and no difference between them.
1 - 0.999... = 0.000... = 0
-
Why is the wrong answer winning.
-
Why do people still say there is a right answer?
rumborak
-
multiplication and division are of equal rank
/thread
-
P
E
M
D
A
S
2 is the right answer.
-
P
E
M
D
A
S
2 is the right answer.
You are misinterpreting PEMDAS.
P
E
MD (in order of left to right)
AS (in order of left to right)
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I love how people are choosing 2, and then giving PEMDAS as the reason. It's PEMDAS that shows that 288 is the correct answer. It's only when you take into account implied multiplication that the answer comes out as 2.
-
I love how people are choosing 2, and then giving PEMDAS as the reason. It's PEMDAS that shows that 288 is the correct answer. It's only when you take into account implied multiplication that the answer comes out as 2.
-
P
E
M
D
A
S
2 is the right answer.
You are misinterpreting PEMDAS.
P
E
MD (in order of left to right)
AS (in order of left to right)
THIS. The only people saying 2 are those that mistakingly believe that multiplication takes priority over division in all equations, which is incorrect.
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Re: the 0.999... snafu:
Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.
1 - 0.999... = 0.000...1
No. Please go learn some more math so you know what you are talking about.
Also, 1/∞ = 0. Not infinitesimal, not undefined, it's 0.
Why do people still say there is a right answer?
rumborak
Because there is... Regardless of whether you think it is bad syntax or not, the right answer is 288.
-
How long does this have to go on? Lol.
Move to P/R? :neverusethis:
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Re: the 0.999... snafu:
Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.
1 - 0.999... = 0.000...1
No. Please go learn some more math so you know what you are talking about.
Also, 1/∞ = 0. Not infinitesimal, not undefined, it's 0
"Learn math or gtfo." :clap: brilliant constructive answer. Kari, I think you misunderstand that what I posted is entirely hypothetical. What people are implying when they say 1 is not equal to 0.999... is that there is an infinitessimal difference between it and 1. I just took the problem and rephrased it to better state the problem at hand. Why am I getting so much "derp, you can't do that," crap?
Also, I am a bit confused, are you saying the infinitesimal doesn't exist? If an infinitely large number exists, why doesn't an infinitely small number exist, and why can't they be multiplied to be 1?
-
The notation you used implied an infinite number of zeros with a one on the end, which is nonsensical, as an infinite sequence can not have an end number.
-
Re: the 0.999... snafu:
Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.
1 - 0.999... = 0.000...1
No. Please go learn some more math so you know what you are talking about.
Also, 1/∞ = 0. Not infinitesimal, not undefined, it's 0
"Learn math or gtfo." :clap: brilliant constructive answer. Kari, I think you misunderstand that what I posted is entirely hypothetical. What people are implying when they say 1 is not equal to 0.999... is that there is an infinitessimal difference between it and 1. I just took the problem and rephrased it to better state the problem at hand. Why am I getting so much "derp, you can't do that," crap?
Also, I am a bit confused, are you saying the infinitesimal doesn't exist? If an infinitely large number exists, why doesn't an infinitely small number exist, and why can't they be multiplied to be 1?
That wasn't what I was saying, I was trying to say that what you wrote is entirely incorrect. You're confusing the set of real numbers with some extension of it that includes infinitesimal numbers. But that was never the point. The point is that in the set of real numbers, 0.99.. = 1.
Also in the set of real numbers, 1/∞ = 0. Infinitesimal numbers "exist", but not in the set real numbers. ∞ is also not an element of the set of real numbers, that's why, when working with it, certain operations have been exactly defined. 1/∞ = 0 because lim(x->∞)(1/x) = 0.
Also, writing the infinitesimal difference between 1/∞ and 0 in that extended set of the reals as 0.00...1 makes no sense as well. There is no 1 at the end, since there is no end. There's no way to write an infinitesimal number like you would write another real number. Just like you can't write infinity, which is why the symbol ∞ was introduced. What you mean when you say that 1/∞ is infinitesimal is that 1/∞ is as close as you can get to 0, without writing 0. It has no meaning however.
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The notation you used implied an infinite number of zeros with a one on the end, which is nonsensical, as an infinite sequence can not have an end number.
That's the exact point of the debate, though, surely? Whether there's a difference between something that's infinitesimally small, and something that doesn't exist.
I'd say the difference between the two is nil, and I'd therefore say that nought point nine-with-a-dot-above-it is equal to 1. I agree with you. But it's not a foregone conclusion, I don't think. I wouldn't tell anyone who disagrees with me to learn more maths. Poss to reconsider, but I get where ScioPath was coming from. The point of the ... isn't saying that the series ends, rather to demonstrate that the eventual "...01" is always, always a step further away.
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The only people saying 2 are those that mistakingly believe that multiplication takes priority over division in all equations, which is incorrect.
No. There are some who were taught that implied multiplication pre-empts normal left-to-right precedence and have yet to hear any counterargument. It is not the same issue as order of operations.
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The notation you used implied an infinite number of zeros with a one on the end, which is nonsensical, as an infinite sequence can not have an end number.
That's the exact point of the debate, though, surely? Whether there's a difference between something that's infinitesimally small, and something that doesn't exist.
I'd say the difference between the two is nil, and I'd therefore say that nought point nine-with-a-dot-above-it is equal to 1. I agree with you. But it's not a foregone conclusion, I don't think. I wouldn't tell anyone who disagrees with me to learn more maths. Poss to reconsider, but I get where ScioPath was coming from. The point of the ... isn't saying that the series ends, rather to demonstrate that the eventual "...01" is always, always a step further away.
I wasn't trying to be rude or so, I was just trying to say that in order to really know what you are talking about you have to know some stuff about certain branches of math. If you don't, you don't really have much ground to stand on. This is not like the original topic of this thread where anyone can participate as the problem is mundane.
It would be like you or me joining some quantum physicists in a discussion about quantum entanglement and go "Hey, why are you debating this? It can't be possible for something to have an effect on something else without anything in between knowing about it". Or astrophysicists discussion black hole radiation and saying "Black holes can't emit stuff, nothing can escape them, not even light."
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No. There are some who were taught that implied multiplication pre-empts normal left-to-right precedence and have yet to hear any counterargument. It is not the same issue as order of operations.
^Turns out this may be true: https://mathforum.org/library/drmath/view/54341.html
Although the most common way is to do it the way to get 288, not 2. I still stick with 288, but I am more with rumby that it's just bad syntax, and I agree with the above article that parentheses are definitely a plus to make sure there is no ambiguity. Parentheses are an expression's best friend, and they can be yours, too.
I was taught left to right and not the implied multiplication (never heard of IM until this thread).
-
Same here James. Either way, it's not a standard form, nor should it be. Parentheses should be used.
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(never heard of IM until this thread)
Me neither, at least not as a formalized term.
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Day 3, and the battle still rages. :rollin
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Awesome, isn't it?
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It's especially entertaining to me because I am worthless at math. It would be like you guys watching me and ten other chefs arguing whether sous vide or slow roasting garners a better duck breast.
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It's especially entertaining to me because I am worthless at math. It would be like you guys watching me and ten other chefs arguing whether sous vide or slow roasting garners a better duck breast.
I don't even know what you're talking about...
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It's especially entertaining to me because I am worthless at math. It would be like you guys watching me and ten other chefs arguing whether sous vide or slow roasting garners a better duck breast.
I don't even know what you're talking about...
My point exactly.
-
Did someone say "breast"?
-
Saying "breast" in a thread about math is like giving a 12-year-old boy a copy of Maxim after a dog has torn it up. Such a tease and that's all we are getting.
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The notation you used implied an infinite number of zeros with a one on the end, which is nonsensical, as an infinite sequence can not have an end number.
That's the exact point of the debate, though, surely? Whether there's a difference between something that's infinitesimally small, and something that doesn't exist.
I'd say the difference between the two is nil, and I'd therefore say that nought point nine-with-a-dot-above-it is equal to 1. I agree with you. But it's not a foregone conclusion, I don't think. I wouldn't tell anyone who disagrees with me to learn more maths. Poss to reconsider, but I get where ScioPath was coming from. The point of the ... isn't saying that the series ends, rather to demonstrate that the eventual "...01" is always, always a step further away.
As a conceptual argument that makes sense but he used the notion in a mathematical proof, which simply doesn't work.
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Implied multiplication is a lie.
Honestly, division signs and /'s are just amateur. Real mathematicians use horizontal lines to indicate division.
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Actually I think real mathematicians use whatever symbol their computer code uses, therefore allowing them to bugger off whilst it runs to drink some more coffee.
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Honestly, division signs and /'s are just amateur. Real mathematicians use horizontal lines to indicate division.
Lol?
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I think given what real mathematicians works on, 48÷2(9+3) comes out to be 3+0.8i, or something.
rumborak
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Or 2222222
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https://en.wikipedia.org/wiki/Graham%27s_number
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As many have pointed out, it's really completely pointless. The rules for simplifying or evaluating an expression are only so that students learning algebra will know how to read and write the shorthand. In an actual application, it would be pretty obvious whether you're supposed to divide or multiply first to get the correct answer.
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I think it's 288 because we have to go one after the other :-\
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And since I was asked, I would in fact evaluate 48÷2x as 24x. I err on the side of assuming that implied multiplication is of equal rank to normal multiplication since I've seen less mathematicians claiming otherwise.
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sly, maybe you can help me with this
I was tutoring and a kid asked me this problem:
"Suppose a cylinder full of sugar has a mass of 5.81. When it is 3/8 full, its mass is 3.8. What is the mass of the cylinder when it is empty?"
The thing that is confusing me is that it is mass. I know volume and mass aren't the same thing, so I am unsure of how to approach this problem. Supposed to be an Algebra 1 problem and I am drawing a blank.
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No radius or height was given, by the way, which further perplexed me. I hope I'm not missing something obvious.
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That is why application problems should always include units. When units are provided, as they should be, there's no ambiguity.
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Let's say the units are in kilograms
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Volume and mass are proportional. Whatever unit system you would use doesn't matter, it would cancel out anyway.
rumborak
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That is what I figured, but that isn't my issue...how do I solve this? Argh, I feel dumb for not knowing this
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That is what I figured, but that isn't my issue...how do I solve this? Argh, I feel dumb for not knowing this
Mass of Sugar = S
Mass of Cylinder = C
S + C = 5.81
(3/8)S + C = 3.8
System of two equations. :tup Took me a second too.
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*bangs head on keyboard*
I don't understand why I can do all sorts of calculus problems and these system of 2 equations algebra 1 problems always get me. There's like a gap in my knowledge there. I sorta had an idea it was gonna be a system of equations, but it eluded me.
Thank you FW, you rock
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"Suppose a cylinder full of sugar has a mass of 5.81.
5.81 = 1.0*C+M0
1.0*C : "1.0 of the volume, times whatever conversion factor into mass"
M0 : Mass of the cylinder
When it is 3/8 full, its mass is 3.8.
3.8 = (3/8)*C + M0
From equation 1:
C = 5.81 - M0
into equation 2:
3.8 = (2/8)*(5.81-M0) + M0
<=> 3.8-(2/8)*5.81 = (6/8)*M0
<=> M0 = 3.13
Gnaah, ninja edit!!
rumborak
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Hey guys. 288 is winning. Let's celebrate by me asking another argument inducing question.
So there's a plane on a conveyor belt... :neverusethis:
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It would take off.
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Massive text haha get it MASSive haha oh man haha...ha
Man, I was tired last night, looking back I really should have known all that, it being mass doesn't have that much to do with setting up the system of equations...gah!
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2? What? The order of operations (https://en.wikipedia.org/wiki/Order_of_operations) says that in this case you do parentheses first and then divide/multiply from left to right.
48÷2(9+3) = ?
48÷2x 12 =?
24x12=?
288
In the UK it's BIDMAS
Brackets first.
Indicies next
Division
Multiplication
Addition
Subtraction...
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But wouldn't that expression be the exact same thing as:
48
___
2(9+3)
So
48
_____ = 2
24
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But wouldn't that expression be the exact same thing as:
48
___
2(9+3)
So
48
_____ = 2
24
No, it's not the same thing. Check my post a few pages back.
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But wouldn't that expression be the exact same thing as:
48
___
2(9+3)
So
48
_____ = 2
24
Yeah, I forgot to add that bit :P
I was gonna add "So it's definitely 2" :P
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To get 288 shouldnt it be (48/2)*(9+3) Other wise, you write it the way I wrote it above ^^.
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I get it nao lol.
I automatically jumped to this conclusion:
48
______
2(9+3)
In which case it's 2. This is the same as 48 ÷ (2(9+3)). But that was not the given though.
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To get 288 shouldnt it be (48/2)*(9+3) Other wise, you write it the way I wrote it above ^^.
Yeah, because with the order of operations it goes something like this:
48/2(9+3) = 48/24 = 2
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To get 288 shouldnt it be (48/2)*(9+3) Other wise, you write it the way I wrote it above ^^.
No.
1) The equation given is 48/2(9+3). You rewrote this as 48/(2(9+3)) . You can't both say "You can only get 288 if you add some parentheses" while yourself saying that the answer is 2 while implicitly adding them in there yourself.
2) And no. You don't have to put parentheses around the 48/2 term... because multiplication and division are of equal rank and when they both occur together in an equation you do the first one that appears in it while going from left-to-right.
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But in school you are told to ALWAYS expand the brackets first?
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But in school you are told to ALWAYS expand the brackets first?
And I never said otherwise. A 2 that isn't in a bracket isn't part of the bracket.
1) 48/2(9+3)
2) 48/2*(9+3)
3) 48/2*(12)
*and here, since multiplication and division are equal rank, I do the first one that appears in left-to-right, which is the division*
4) 24*(12)
5) 288
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That's the dichotomy. I've always thought the the 2 being adjacent to the (9+3) gave it some kind of precedence, but apparently there is no such rule. So a strict application of the rules yields the above result.