I think it only proof that when people are taught cute little things like Please Excuse My Dear Aunt Sally they interpret it to mean Multiplication before division and Addition before subtraction.... PEMDAS could be PEDMSA or BEDMSA or BIDMAS
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Half of you will get this wrong: 48÷2(9+3) = 288 or 2?
- Thread starter AKIRA
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No the brackets should be there in order to solve the problem. Because someone "could" change it to fraction form and get a completely different answer. The entire idea of brackets and parenthesis and the order of operations is to stop that from happening. The division sign has the same function as a fraction bar.
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Yes it doesnt matter in what order as long as they are grouped. (addition and subtraction) (multiplication and division)
Im going to just put some random numbers
7+4-6+7-2+9-4-3-7+5=10
You can rearrange that in any order as long you take the number and the sign that is to the left of the number and you still get the same answer.
*Note that the sign in front of the first 7 is implied to be a +
I didn't change the numbers - I changed the order of these operations. Without tagging the numbers with their signs, you cannot simply switch them around.
For instance,
6 + 3 = 3 + 6 because both 6 and 3 are both positive; the default notation allows us to assume numbers are positive unless otherwise indicated.
Meanwhile,
6 - 3 ≠ 3 - 6, right?
You have to change the notation to indicate your intention, like this:
6 - 3 = -3 + +6
When you - with your advanced degree in Teh Math - screwed up simple arithmetic, you made a simple error; the same one, in fact, that I almost made myself. You assumed notation that would impose a change to the defaults - only that notation wasn't there.
Your credentials don't make your error any less wrong.
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You changed the numbers. Changing notation, is changing the number from a positive to a negative. Which is drastically changing of the number. Subtraction can also be thought of as adding a negative number.....And so forth.
Maybe this is just to difficult to get through on the a website.
And there's the problem. When I switched the positions of the numbers, because of how we use standardized mathematical notation, their signs changed - thus they were no longer the same numbers.
I, personally, did not change the numbers. Their values changed because I transposed them left and right.
And that was my point with what you did, with the division operator, "÷". You made the assumption that everything following a division operator is handled as if it were in square brackets.
By (incorrectly) making this assumption, you changed the original statement:
48 ÷ 2(9+3)
to 48 ÷ 2 ÷ 12
instead of what the notation actually provides us with, which is this:
48 ÷ 2 ?? 12
Now I'm sure the notation you learned when you earned your credential was the same notation I learned when I earned mine. Your mind simply tricked you into thinking otherwise, and it's maddening when it's your area.
I didn't think so. But it's interesting to me that you did.
No it's the same as 48/2*12 which is the only way my iPhone will let me input division...and multiplication the order of operations stay the same no matter the syntax
I believe 288 because when there are two options like with 48/2x12 you work it left to right. That's what I was taught, and when I tutored algebra that's what I told kids to do so I hope that's right
Ditto
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Plus if you put it in Google that's the answer you get. Thread closed.
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Oh, yeah? Oh, yeah???
Well, well, well YOU can't even spell definitely.
So there! HA!
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^ Did you answer? 
(9+3) needs to be raised to the -1 exponent in order to get the answer to be 2.
As the problem currently stands, (9+3) will always be in the numerator.
You cannot arbitrarily put 2(9+3) in the denominator due to the order of operations. The division sign applies to the "2", not to "2(9+3)". The question can be read: 48 ÷ 2 x (9+3).
Perhaps that makes it a bit clearer.
^ Did you answer?
Me? Answer what?
its hard to argue with a calculator...
...built on the other hand 
I never used an acronym to do math... I used understanding of math to understand what was meant
In this case 48÷2(9+3) clearly is different than 48÷2x(9+3)
with 48÷2(9+3), it is implied to be 48÷[2(9+3)]
If you don't understand this, you missed the basics of math
The answer is 2. And yes I had top honors in math
Distributive property anyone?
In this case 48÷2(9+3) clearly is different than 48÷2x(9+3)
with 48÷2(9+3), it is implied to be 48÷[2(9+3)]
If you don't understand this, you missed the basics of math
The answer is 2. And yes I had top honors in math
Distributive property anyone?
More than half of them got it wrong... but can you blame them? It is a body building site.
Oh dear. Is that what you think?
So, to clarify: You think 2(9+3) ≠ 2??(9+3)?
Really?
Okay - what's it equal to, then? Or do you somehow imply that alone, this is true:
2(9+3) = 2??(9+3)
But here, it is not:
48÷2(9+3) ≠ 48÷2??(9+3)
Is that it? Is that the crux of your argument?
except that you are wrong. When you leave the 'x' out between the 2 and the (9+3), the distributive property takes over. If you had 48÷2b you would write it as
48
__
2b
the same thing happens here.
48÷2b =
48 ÷ 2 ÷ b =
48 ÷ (2 x b)
2(9+3) = 2??(9+3) only because there are no other outside operations done to it. It's not really relevant
a ÷ 2(9+3) ≠ a ÷ 2 ?? (9+3) ... this is correct
From Yahoo Answers:
The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it. You do NOT compute this expression from left to right until you use Algebra to simplify the statement 2(9+3).
So this can be rewritten as:
48 / (2*9 + 2*3)
Which leaves us with
48 / 24 = 2
Answer = 2.
Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 * (9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs.
The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it. You do NOT compute this expression from left to right until you use Algebra to simplify the statement 2(9+3).
So this can be rewritten as:
48 / (2*9 + 2*3)
Which leaves us with
48 / 24 = 2
Answer = 2.
Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 * (9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs.
and yes, I wrote my answer about the distributive property BEFORE looking up the yahoo answers... but I was kind weirded out that that post also used the word "clearly" and mentioned the distributive property in the answer
and yes, when you insert the 48 on 48÷2??(9+3), the first thing done is the division because 2??(9+3) isn't as tightly bound as 2(9+3)
adding the 48 on 48÷2(9+3) does not effect the 2(9+3) because the distributive property makes this a single unit that happens before any outside multiplication or division that is otherwise applied
I'm not waiving the white flag yet.
You are suggesting that:
"48÷2b =
48 ÷ 2 ÷ b = "
Actually, that is not correct. In the second expression, you are adding a division sign that was not previously there. 48÷2b can be rewritten as (48/2)b or (48/2) x b or (48b)/2 or 48b/2. It cannot be rewritten as 48 ÷ 2 ÷ b.
Of your original expressions, the third one is simply incorrect -- you are modifying the order of operations by putting in parenthesis that were not expressed originally.
Clearly, the "÷" is an awful convention.
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