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how much is this 1/2+3=??? if you say .2 then you are lost.. and nothing will change your mind...
if you say 3.5 then put the same principle to the original equation.
The way I do it, though a bit unorthodox and perhaps confusing to some, instead of a question mark, I put an X which signifies an unknown value and try to balance both sides of the equal sign:
48 ÷ 2 (9+3) = X
which means ==> (9+3) = (X÷ 48) x 2
which means ==> 12 = (X÷ 48) x 2
and you get ==> 12 = X ÷ 24 or 12 ÷ 2 = X ÷ 48 (whichever you prefer)more simplified ==> 12 = X÷ 24 [or] 6 = X÷ 48
let's leave X alone ==> 12 x 24 = X [or] 6 x 48 = X
Math is a language. Math is reasoning. Math is philosophy. It can be proofed that 48÷2(9+3) is both 2 and 288, even if you follow the left to right rule of Order of Operations. However, even if you follow the left to right rule, the universal Order of Operations states that you use PEMDAS (parentheses, exponents, multiplication, division, addition, then subtraction). So, if you use PEMDAS, the answer is 2. Or 0.5 depending on your calculator.
Then again, it can be proofed that 1+1 does not equal 2.
Who cares. That proof is not widely accepted and only pompous nerdlings really care for that "truth".
So, for those who believe that 48÷2(9+3) = 288, let's see your proofs.
The way I do it, though a bit unorthodox and perhaps confusing to some, instead of a question mark, I put an X which signifies an unknown value and try to balance both sides of the equal sign:
48 ÷ 2 (9+3) = X
which means ==> (9+3) = (X÷ 48) x 2
which means ==> 12 = (X÷ 48) x 2
and you get ==> 12 = X ÷ 24 or 12 ÷ 2 = X ÷ 48 (whichever you prefer)more simplified ==> 12 = X÷ 24 [or] 6 = X÷ 48
let's leave X alone ==> 12 x 24 = X [or] 6 x 48 = X
288 = X
Come to think, I used to suck at math!
If you set the 2 to equal X, and set the equation equal to 288, x then = 1/72. Thus proving 2 is the correct answer.
Most people think it is 288 because they do not see the multiplication sign.
And some people will argue, even with PEMDAS, that multiplication does not take precedence over division....to which they are wrong.
Math is a language. Math is reasoning. Math is philosophy. It can be proofed that 48÷2(9+3) is both 2 and 288, even if you follow the left to right rule of Order of Operations. However, even if you follow the left to right rule, the universal Order of Operations states that you use PEMDAS (parentheses, exponents, multiplication, division, addition, then subtraction). So, if you use PEMDAS, the answer is 2. Or 0.5 depending on your calculator.
Then again, it can be proofed that 1+1 does not equal 2.
Who cares. That proof is not widely accepted and only pompous nerdlings really care for that "truth".
So, for those who believe that 48÷2(9+3) = 288, let's see your proofs.
There's two things here which lead to your conclusion being flawed:
1. You are forgetting that in PEMDAS, it's Parenthesis, Exponents, Multiplication & Division (same weight), Addition and Subtraction.
2. Division is multiplication. They are the same thing, thus they can only have the same weight. Division is just multiplication of the inverse. For example, dividing by 2 is really multiplying by 0.5 or 1/2.
----
In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If PEMDAS is followed without remembering that multiplication and division have the same weight, and addition and subtraction have the same weight, the wrong answer may be calculated. Some grade school books teach this incorrectly. For example: 6÷2×3 = 9, not 1. 6-2+3 = 7, not 1.
Let's leave out the calculators because it appears that some are programmed to ignore order of operations and/ left to right. This is noted in the wiki article as well.
Of course, if you had 1 apple, and picked up another apple, you would have two apples. But, you need to think abstractly here. 1 cat plus 1 dog may equal 2 animals, but if you change the unit, it only equals 1 pair (of animals). It also depends on the base. In binary, 1 + 1 = 10 (which, of course is the decimal base 2)
It also depends on the unit value of 1:
1 small jug of water plus 1 small jug of water = 1 big jug of water.
Or,
1 pair of shoes plus 1 pair of shoes = 4 shoes.
Quote:
Originally Posted by NJBest
There's two things here which lead to your conclusion being flawed:
1. You are forgetting that in PEMDAS, it's Parenthesis, Exponents, Multiplication & Division (same weight), Addition and Subtraction.
2. Division is multiplication. They are the same thing, thus they can only have the same weight. Division is just multiplication of the inverse. For example, dividing by 2 is really multiplying by 0.5 or 1/2.
Let's leave out the calculators because it appears that some are programmed to ignore order of operations and/ left to right. This is noted in the wiki article as well.
There are two things here; yes, in basic arithmetic, you simply go from left to right. So, some people are reading the problem as 48 divided by 2, then times the sum of 9 plus 3. Which is not wrong.
Or, you can read it as 48 divided by product of 2 times the sum of 9 + 3, which I, and many other people do. In higher levels of math, the tendency is to treat everything to the left of the ÷ / : sign as one term. Then again, it really depends on the problem itself.
Anyways, here is another way to show how I "calculated" the problem:
If you had 48 ÷ 2x, the tendency would be to multiply 2 by x, then divide (which is how I read the equation).
But, it could also be written as 48 ÷ 2 * x, which, is a completely different equation, but right none-the-less depending on the particular issue the equation is attempting to solve.
x = (9+3)
This is one of those Are you smarter than a 5th grader social memes used to "prove" how smart some people are.
The answer is both, as I have shown, depending on how the equation is laid out to solve the issue.
As for PEMDAS, I've always did the multiplication first. Perhaps it was just the way the equations were written (perhaps in such a manner as to place multiplication operations first before division?), but I generally got the right answer, including on a GRE practice test I took a few months ago.
Last edited by K-Luv; 05-24-2011 at 09:44 AM..
Reason: changed "OP" to "some people"
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