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48÷2(9+3)=?????


Chiefinonhaze

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OK, i'm beginning to suspect that the people voting and defending 2 as the answer are doing it to deliberately piss everyone else off. And it's working. :)

I'm certain of it. Looking at the list of names that voted for 2, there are some of the smartest posters on this site. No way they actually think it's 2.

---------- Post added April-13th-2011 at 04:16 AM ----------

OK, i'm beginning to suspect that the people voting and defending 2 as the answer are doing it to deliberately piss everyone else off. And it's working. :)

I'm certain of it. Looking at the list of names that voted for 2, there are some of the smartest posters on this site. No way they actually think it's 2.

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and this is the way everyone is viewing it...why am I the only one saying distributive property in this thread...

because you are trying to use calculus on an algebra problem

---------- Post added April-13th-2011 at 07:43 AM ----------

I'm very shocked as are most who have chose 2 as the answer.

Anyone who has done higher level math would most likely agree that the answer is 2, without ever needing a calculator.

I'd bet it would be safe to say anyone who has picked 288 used a calculator and most likely as simple of a question that this is, you are most likely never even intended to use a calculator to solve it which is part of the "trick" if there is one.

The distributive property as mentioned early in the thread is the ONLY way that you solve the problem correctly. I did read about 12 pages, then gave up because the argument looked pretty futile. Figured I'd post my 2 cents and be done, anyone who doesn't understand this needs to do someone else's problem that was posted before:

a / (or divided by sign, however you'd like to view it) X b(c+d)

Should be obvious that the order of operations is (bc + bd) or (c+d)*b is performed first, then a is divided by that result.

again, you are trying to use calculus on an algebra problem, don't make it more difficult than you have to, that's what any good math teacher will tell you

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When I originally saw this problem I thought it was 2.

Then I realized that you have to follow the order of operations, and that it had to be 288.

But I'm coming around to the 2 argument, and here's why.

There is implied multiplication of the 2 over the (9+3).

Most of us went ahead and reduced the 9+3 to 12, multiplied it by 2 to get 24, then divided 48/24 to get 2.

OK, it's wrong to do that the way it's written because of order of operations, but is it actually wrong?

I started to think about a way that you can just ignore the distributive property of the 2 and still get 288, or if you could ignore that at all.

Take this example.

8x² ÷2x =1

Lets reduce it a little

8x²

--- =1

2x

4x = 1

Now lets take the same equation

8x² ÷2x =1

But let’s reduce it a little differently, or more importantly, follow a strict order of operations, and see if it comes out the same…

8x² divided by 2 times x = 1

4x² times x = 1

4x³ = 1

So it really doesn't work. Maybe 2 really is the right answer, lol.

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When I originally saw this problem I thought it was 2.

Then I realized that you have to follow the order of operations, and that it had to be 288.

But I'm coming around to the 2 argument, and here's why.

There is implied multiplication of the 2 over the (9+3).

Most of us went ahead and reduced the 9+3 to 12, multiplied it by 2 to get 24, then divided 48/24 to get 2.

OK, it's wrong to do that the way it's written because of order of operations, but is it actually wrong?

I started to think about a way that you can just ignore the distributive property of the 2 and still get 288, or if you could ignore that at all.

Take this example.

8x² ÷2x =1

Lets reduce it a little

8x²

--- =1

2x

4x = 1

Now lets take the same equation

8x² ÷2x =1

But let’s reduce it a little differently, or more importantly, follow a strict order of operations, and see if it comes out the same…

8x² divided by 2 times x = 1

4x² times x = 1

4x³ = 1

So it really doesn't work. Maybe 2 really is the right answer, lol.

don't over think it, that's where the confusion begins. the stated equation is still only algebra, and has no variables.

---------- Post added April-13th-2011 at 09:49 AM ----------

The answer is 288. Stop making harder than what it really is.

dangit you beat me to it

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I think it is 288 now after looking over stuff.

If you use PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

You would do it like this:

48÷2(9+3)

48÷2(12)

24(12)

288

When I first did it, I did the multiplication first, but after looking up PEMDAS again, you do multiplication and division from left to right, since the division is first, you divide 48 by 2 and get 24, then multiply that by 12 and you're left with 288.

http://www.mathsisfun.com/operation-order-pemdas.html

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Take this example.

8x² ÷2x =1

Lets reduce it a little

8x²

--- =1

2x

4x = 1

Now lets take the same equation

8x² ÷2x =1

But let’s reduce it a little differently, or more importantly, follow a strict order of operations, and see if it comes out the same…

8x² divided by 2 times x = 1

4x² times x = 1

4x³ = 1

So it really doesn't work. Maybe 2 really is the right answer, lol.

The answer is 288. Stop making harder than what it really is.

Wait, what?

Why was I able to solve that equation 2 ways and come up with different answers? It's actually pretty similar. You're a math guy, it seems, so I just want to know why if I use the order of operations strictly in the equation I wrote you get a different answer. Actually, you get the wrong answer. So why is that?

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Wait, what?

Why was I able to solve that equation 2 ways and come up with different answers? It's actually pretty similar. You're a math guy, it seems, so I just want to know why if I use the order of operations strictly in the equation I wrote you get a different answer. Actually, you get the wrong answer. So why is that?

because they aren't the same equation

the first way you have it (8x^2)/(2x)

the second way you have it ((8x^2)/2)x

2 totally different equations, i deduce that by the way you solved that, and only included th parentheses because of the difficulty of typing it out to make sense

in one you have 2x as a number, and the other 2 and x are separate. if it is 2x, that is one number and you can't reduce independently

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I like how these arguments have been whittled down to "this is the way it is, dummy!"

Maybe the answer is that any equation with "÷" treat it like a 2nd grader would. Just go left to right, order of operations and be done with it.

That equation I wrote is a great example. It just does not work with a "÷" . It makes no sense.

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I wonder how many pages this topic would cover in a Chinese forum?

22 pages and counting: http://www.hkttl.com/~hkgolden/?p=v&id=2952513

That thread is actually pretty good, with a bunch of good joke posts and plenty of calculator photos. It looks like 2 is winning the poll by a significant margin, but I'm not sure they are taking it as seriously as we are.

Some photos from the Chinese thread:

875e9430.jpg

5416527.jpg

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I like how these arguments have been whittled down to "this is the way it is, dummy!"

Maybe the answer is that any equation with "÷" treat it like a 2nd grader would. Just go left to right, order of operations and be done with it.

That equation I wrote is a great example. It just does not work with a "÷" . It makes no sense.

please read what i wrote

also, AGAIN, the reason they were having issues prior is because they were using calculus logic to solve algebraic equations

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Wait, what?

Why was I able to solve that equation 2 ways and come up with different answers? It's actually pretty similar. You're a math guy, it seems, so I just want to know why if I use the order of operations strictly in the equation I wrote you get a different answer. Actually, you get the wrong answer. So why is that?

Same issue that most people are getting with the original equation. The first time you implied that 2x was "under" 8x² and the second time, which is correct, you didn't. If it was written as

8x²

--- =1

2x

Then it would be 8x² / (2x) = 1.

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Same issue that most people are getting with the original equation. The first time you implied that 2x was "under" 8x² and the second time, which is correct, you didn't. If it was written as

8x²

--- =1

2x

Then it would be 8x² / (2x) = 1.

HEY stop trying to steal my thunder! ;)

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because they aren't the same equation

the first way you have it (8x^2)/(2x)

the second way you have it ((8x^2)/2)x

2 totally different equations, i deduce that by the way you solved that, and only included th parentheses because of the difficulty of typing it out to make sense

in one you have 2x as a number, and the other 2 and x are separate. if it is 2x, that is one number and you can't reduce independently

Exactly my point. You shouldn't have to determine that two equations by deducing anything! (btw you are making a lot of assumptions with those parentheses that are wrong but that's kind of the point) The "÷" makes it complete bullcrap mathematically. If 2x is a number, I can reduce it any which way. You are wrong, because that number CAN be reduced independently. That's what is great about math. But with a "÷" you are limited, and you cannot. So the answer is that you have to treat this like a 2nd grader. There is no other way.

EDIT

Oh wait. I see what you are saying about them being 2 different equations. But the REASON was that the "÷" is AMBIGUOUS. It IMPLIES a numerator and a denominator, but one really is not there. Answer has to be 288. But that's because the stupid "÷"

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Oh wait. I see what you are saying about them being 2 different equations. But the REASON was that the "÷" is AMBIGUOUS. It IMPLIES a numerator and a denominator, but one really is not there. Answer has to be 288. But that's because the stupid "÷"

I don't believe that it does. I think people are just tricked by it.

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Exactly my point. You shouldn't have to determine that two equations by deducing anything! (btw you are making a lot of assumptions with those parentheses that are wrong but that's kind of the point) The "÷" makes it complete bullcrap mathematically. If 2x is a number, I can reduce it any which way. You are wrong, because that number CAN be reduced independently. That's what is great about math. But with a "÷" you are limited, and you cannot. So the answer is that you have to treat this like a 2nd grader. There is no other way.

no i'm not, if you go the original route in your equation as 8x^2 / 2x = 1, that in turn is ((8x^2) / 2x) = 1, there is no other way, math is not gray it IS black and white

2x is a number and cannot be reduced any way you please, and again, the way you resolved it makes it 2 different equations

you created the below:

8x² divided by 2 times x = 1

4x² times x = 1 ---> this is incorrect unless you have x on the outside of the parentheses, just because you reduced the 2 out of both, doesn't mean you are now multiplying x, you are still dividing the x from 4x^2 because it is still underneath the 4x^2

4x³ = 1 ----> so this would be incorrect as 4x^2/x still reduces to 4x

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