Diablo® III

48÷2(9+3) = ? cont.

(a + b)(c + d)

= (c(a+b) + d(a + b))
= ac + bc + ad + db

a = 1, b = 2, c = 3, d = 4

= (1)(3) + 2(5) + 1(4) + 4(2)
= 3 + 10 + 4 + 8
= 25


Where did the 5 come from?
Edited by Yipe#1219 on 6/16/2012 2:39 PM PDT
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ITT: People who claim the answer is 2 are wrong and should be ignored
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90 Blood Elf Paladin
14935
Posts: 2,678
2
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I was successfully trolled by all of the trolls saying thins other than The original = 288 and 48/2x simplifies to 24x. The got a rise out of me. I am ashamed.
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07/04/2012 10:27 PMPosted by Namelesdeath
I was successfully trolled by all of the trolls saying thins other than The original = 288 and 48/2x simplifies to 24x. The got a rise out of me. I am ashamed.


Yeah. The fact that in most of their arguments they throw an insult like "Go back to grade school." is a dead giveaway of a bad troll. It's pretty funny how obvious they are.
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As simple as usual.

= 48÷2(12)
= 24(12)
= 288
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if you are getting 288, this is what you are doing, and it is wrong.

(48÷2)(9+3) which is not equal to

48÷2(9+3)

since there are no brackets separating the 2 and the (9+3) this means that the 2 is a coefficient of the term inside the brackets. you cant divide 48 by 2, and then multiply 24 by (9+3).

lets substitute x=(9+3) for !@#$s and giggles

the original term is 48÷2(9+3) and it becomes:

=48÷2x

if you now divide 48 by 2, you still have not divided it by x, and the term now becomes:

=24÷x
( a lot of people were multiplying 24 by (9+3) which you cannot do, because (9+3) is in the denominator of the fraction and you still have to divide 24 by it)

if we substitute (9+3) back in, we now get:

=24÷(9+3)

=24÷(12)

=2


you sir, explained it clear and simple...perfect!!!
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Look at the given problem: 48÷2(9+3) = ?

It is clearly a Division problem with 48 as the Numerator and 2(9+3) as the Denominator.
48 is already simplified to 48 so just leave it alone in the Numerator position.

The Denominator is 2(9+3) and needs to be simplified before you can continue.
Parinthesis first (9+3) = 12
Now do the resulting multiplication 2(12) = 24
The Denominator is now simplified to 24.

With the Numerator and Denominator fully simplified your problem is now 48÷24=?
48÷24=2

Those of you that got 288 please stop letting your calculators do your thinking for you!
Edited by BattleTag#1134 on 7/17/2012 10:15 AM PDT
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=D

Lets say 48÷2(9+3) = X And 288 = Y (or 2=Y if your in the special crowd, and cannot tell what is in the denominator vs numerator)

Then X=Y
Now lets do so extra math
Multiply both sides by X
X^2=XY
Now subtract Y^2 from both sides
X^2-Y^2=XY-Y^2
Factor!
(X+Y)(X-Y)=Y(X-Y)
cancel out the common factors
(X+Y)=Y
Substitute the X=Y from the top
Y+Y=Y
Add the Ys
2Y=Y
Divide both side by Y
2=1

Therefore the original equation of 48÷2(9+3) is false an can never equal 288 (or 2)

;)
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PEMDAS = Please excuse my dear Aunt Sally. Grade school memory thing.

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

ie Parenthesis first

48/2(12)

No exponents

Multiplication next

48/24

Division 3rd

2

edit:

Nope, it's 288

PEMDAS has a corollary stating multiplication and division are equal in rank

Thus 48÷2(12) = 24(12) = 288

edit2:

Absolutely 100% certain it's 288 now
Edited by Eustacia#1174 on 7/18/2012 9:21 PM PDT
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Posts: 351
The confusion lies in the usage of the division symbol. Nobody past the third grade uses the division symbol, and this is why.
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48/2x = 288

24x = 288

x/24 = x

288/24 = 12

48 / 2 (9+3)

48 / 2 (12)

48 / 24 = 2

Lol'd at whoever said they did Calculus 4 and different !@#$ like that, and ended up with 288.
Edited by ShawnD#1936 on 7/19/2012 5:00 PM PDT
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07/17/2012 10:08 AMPosted by BattleTag
Those of you that got 288 please stop letting your calculators do your thinking for you!


You see, the thing is, calculators (and code, for that matter) are completely logic based. Arithmetic at this level is completely logic based. Given there is no chance for an overflow on the floating point (working with tops 3 digit numbers here, so absolutely no problem) the calculator is completely reliable in this situation.

And, as it has been stated many times in this argument, and as I am once again repeating, this equation is poorly written. From a completely technical standpoint, 288 is correct. That is why Ti-89s and other equal level calculators get 288. The argument at hand boils down to one of two interpretations. There is no theorem out there that states that implied multiplication is beyond the series logic that exists with the regular use of order of operations. Implied multiplication is just that: multiplication, and adheres to the same laws as such. Those getting the answer as 2 are making an assumption that the author meant for the (9 + 3) to be in the denominator. It's a reasonable assumption, yes, but breaks the pure logic standpoint of arithmetic that assumes there can only be one right answer.

Logically, the answer is 288.

Given the poor writing of the problem though, the answer is subjective. If you see a statement like this one in any sort of engineering field, that engineer should be fired immediately. Ambiguity has cost lives before.

=D

Lets say 48÷2(9+3) = X And 288 = Y (or 2=Y if your in the special crowd, and cannot tell what is in the denominator vs numerator)

Then X=Y
Now lets do so extra math
Multiply both sides by X
X^2=XY
Now subtract Y^2 from both sides
X^2-Y^2=XY-Y^2
Factor!
(X+Y)(X-Y)=Y(X-Y)
cancel out the common factors
(X+Y)=Y
Substitute the X=Y from the top
Y+Y=Y
Add the Ys
2Y=Y
Divide both side by Y
2=1

Therefore the original equation of 48÷2(9+3) is false an can never equal 288 (or 2)

;)


Funny things happen when you divide by 0.

Sorry, I couldn't resist.
Edited by SweetWilly#1217 on 7/26/2012 12:16 PM PDT
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Posts: 2,723
These operations are binary, which means that they take two numbers and associate a third to the initial pair.

So x + y takes the pair (x, y) and associates the third number (x + y) to it. The fact that they only take two numbers is important. In order to add three numbers, for example x, y and z, we take (x, y), associate the number (x + y) to it, then take the pair ((x + y), z) and associate the number ((x + y) + z) to it. Now obviously when dealing with a lot of numbers, it becomes a pain in the rear to keep using those brackets (brackets mean we treat the expression as a single object), especially when there is no risk of ambiguity. (x + y) + z = x + (y + z), so we just define x + y + z as being equivalent to either. By induction we can define an arbitrarily large number of additions.

Enter orders of operations. If we're being rigorous, we must have a bracket around every binary operation, e.g. (3 + ((7 * 2) / 3)), but that's tedious. So instead, we have a set of rules to minimize the amount of writing we need to do without risking ambiguity.

So there are two kinds of answers to the problem of something like 48 / 2(9+3). One is that it's ambiguous because it's unclear whether the pair being associated to a third number by division is (48, 2) or (48, 2(9+3)), due to the lack of bracketing.

The other is that it has a definite answer depending on which convention you're following. Do note, however, that this answer is strictly conventional. You're not stating anything about mathematics when you state that division takes precedence or is equivalent in order to multiplication, or even that you should operate left to right.

According to the conventions I'm familiar with from high school (I've never seen these conventions mentioned or used in university math), we first explicitly write the expression as 48 / 2*(9 + 3) to make explicit the operations. Then we do brackets 48 / 2*12, then exponents (none), then multiplication and division, in equal priority, from left to right. So we treat it as (48 / 2)*12 = 24*12 = 288. Different conventions may yield different results.
Edited by Saigyouji#1546 on 8/1/2012 5:58 AM PDT
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Well, I hope I do this right because I have literally failed math courses my whole life.

48÷2(9+3)
= 48÷2(12)
= 48/2*12
= 24*12
= 288

If it's 2 I wouldn't be surprised but only because like I've said I'm not very smart. I was placed into remedial math so often :(.

The most embarrassing moment I can recall was getting an A in pre-calculus and doing so well on those trigonometric problems, then I got to calculus one month later and I couldn't recall any of the trigonometric functions we were taught. I got to enjoy some more remedial math after that.
Edited by Marion#1711 on 8/1/2012 3:49 AM PDT
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I think everyone agree that
48÷2(9+3) = 48÷2(12)

This 21 pages long discussion prove that not everyone agree on what means the line 48÷2(12)

This line is a succession of mathematical symbols and for it to be a valable operation we need to define what those symbols means and agree and how to do the calculation.

If we agree on the convention saying that : "Multiplication and division have same level of priority and should be done in the order from left to right"
In that case 48÷2(12) = (24)(12) = 288

But we can also agree on : "Multiplication has a higher priority than division"
then 48÷2(12) = 48÷24 = 2
This convention is not usually used in mathematics, but if you say that before writting 48÷2(9+3) in the first place then you are right in saying that it equals 2.

In this post I've seen some comparaisons between 48÷2(12) and 48÷2x to say that 48÷2x = 48÷(2x)
It is basically saying that 48÷2(12) and 48÷2*12 are different, something you have the right to say, but you need a convention to be clear on what is the meaning of these lines.

These two lines uses different mathematical symbols and it's possible to say that those different symbols have different meanings.
In that case the convention would be that : "If a multiplication is the consequence of to adjacent numbers without the use of the symbol * it's priority is higher than a multiplication or a division written with their respective symbols"

I'd like to say that this last convention is not used. No one activelly state that there is two type of multiplication with different priority levels, but that is how a lot of people feel when seeing an operation like 48÷2(9+3).
Some people who have answered 2 in this thread may have said 288 if we had asked them how much is 48÷2*12.

This 21 pages long discussion is further proof that '÷' is not a good symbol. It's almost not used anymore passed elementary school with good reasons, it leads to lots of confusion for too little gain if at all.
Edited by Cognus#2405 on 8/1/2012 6:15 PM PDT
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08/01/2012 06:13 PMPosted by Cognus
This 21 pages long discussion is further proof that '÷' is not a good symbol. It's almost not used anymore passed elementary school with good reasons, it leads to lots of confusion for too little gain if at all.


Yeah well, I still think using the vinculum instead of excessive brackets is cool... even if I kept getting points marked off for it.
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this topic is a waste of time. why would people argue over what notations they should use?

Each answer, whether its 288 or 2 or something else, depends on how you read the notations. the answer could be one under one person's, and a different one under another.

mathematical expressions are nothing but a language, expressed in simplified terms. if the notations are read differently by many people then there's something wrong with the way you have expressed it. discussing over a problem that is not well-defined is simply a waste of time.

side note: wolfram alpha gives 288.
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Posts: 2,723
If we agree on the convention saying that : "Multiplication and division have same level of priority and should be done in the order from left to right"
In that case 48÷2(12) = (24)(12) = 288

But we can also agree on : "Multiplication has a higher priority than division"
then 48÷2(12) = 48÷24 = 2
This convention is not usually used in mathematics, but if you say that before writting 48÷2(9+3) in the first place then you are right in saying that it equals 2.

In this post I've seen some comparaisons between 48÷2(12) and 48÷2x to say that 48÷2x = 48÷(2x)
It is basically saying that 48÷2(12) and 48÷2*12 are different, something you have the right to say, but you need a convention to be clear on what is the meaning of these lines.

These two lines uses different mathematical symbols and it's possible to say that those different symbols have different meanings.
In that case the convention would be that : "If a multiplication is the consequence of to adjacent numbers without the use of the symbol * it's priority is higher than a multiplication or a division written with their respective symbols"

I'd like to say that this last convention is not used. No one activelly state that there is two type of multiplication with different priority levels, but that is how a lot of people feel when seeing an operation like 48÷2(9+3).
Some people who have answered 2 in this thread may have said 288 if we had asked them how much is 48÷2*12.

This 21 pages long discussion is further proof that '÷' is not a good symbol. It's almost not used anymore passed elementary school with good reasons, it leads to lots of confusion for too little gain if at all.


Alternatively, it's proof that you should use bracketing instead of relying on conventions about ordering. Ambiguity is the bane of mathematical reasoning. Binary operations, as well-defined functions, have a unique, unambiguous image point corresponding to any pair of numbers. As long as you use brackets, it's always explicit which two numbers are in that pair.

What division symbol is being used is irrelevant.
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