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Post by Eugene 2.0 on Aug 18, 2019 19:28:06 GMT
A not really normal math example that wanders around the Internet is not clear enough to solve it. I has, I'd say, a problem of priority of operations to start with. Here is the example:
8 ÷ 2(2+2) = ?
Usually, they say that the answer should be '16', because - according to the straight sequence - we need to complete a division firstly, and only after it we could multiply it with '(2+2)'. So, in this case we have something like this: A ÷ B x C.
An operation of multiplying is absent here, and it's not clear to see what '2(2+2)' means considering the priority status.
I wondered about two possible answers at the same time, but I was warned by the professionals that that had no sense. (x^2=9; x1 = 3, x2 = -3 has a sense though.)
What do you think about the example itself?
What do you think about the sign '÷'?
Is it correct to divide firstly and then to multiply?
And maybe we should change '÷' on '/'?
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Post by Elizabeth on Aug 20, 2019 16:03:02 GMT
8-:-2(2+2) or 8/2(2+2)
In either case: the formula = (A) 8/[8] =1 by clearing the brackets first (B) (8/2)(2+2) = 4(2) + 4(2) = 16 by applying the distributive law The obvious contradiction results from the original improper formulation (as to what the writer means to say). Two possible intents: (brackets needed, as Eugene at al. have pointed out) 8/[2(2+2)]…=1 (8/2)[2(2+2)]…= 16 Conventual abbreviations, which we all are accepting, are usually not written down. E.g.: (2)(3) = 2 x 3. They have to be written down [incorporated] in a demonstrative treatise. Similarly, in a demonstrative treatise of the Pythagorean theorem, you would have to incorporate the fact that you are dealing with a right-angle triangle. All existing demonstrations fail in this respect, even if -- from Euclid on -- they are otherwise logically sound. (We assume the 90-degree angle, or, geometrically speaking, [CLUE:] the angle formed by two intersecting perpendicular lines.) Three lines on a plane whose lengths are 4, 5, and 6 need not be the sides of a triangle. Add this to your other problems, if you have time to spare. The problem happens when people don't use order of operations correctly. That's why we have PEMDAS rules. They tell us what operation must be done first or else people will get wrong answers.  |
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Post by Elizabeth on Aug 20, 2019 18:09:15 GMT
Let me explain more...also go left to right (or top to bottom) when doing PEMDAS correctly.    I'm very grateful to you, Elizabeth! Never heard of it... It's so shamy for me. PEMDAS works cool as a memorize tip. I should put it into my mind for good. Your conspectus look nice; also, your handwriting is really interesting too. Let me ask you - do you always write using this type of handwriting? The letters of your handwriting leaned to left a little. I knew some people with a similar handwriting and they all were persons with strong will, and also they were very friendly. I usually don't pay too close attention to how I write  . But it's probably like that or close to it. I just wrote that fast because was going to sleep so it probably came out slightly more sloppy/different than usual |
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thinqtv
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Post by thinqtv on Aug 20, 2019 21:18:19 GMT
You're using the P part of PEMDAS incorrectly.  |
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Post by runswithsharks on Aug 20, 2019 21:24:40 GMT
You brought PEMDAS up but forgot to mention that its actual more like P>E>M>D>A>S... So in order of operations multiplication goes before Division.
So for example we can prove that multiplication goes before division in the case above.
8/2(2+2) = Y
Lets assume that Y does indeed equal 16 and we substitute x = 2(2+2) into the equation.
We get 8/x = 16
Solve for x and it equals .5 or 1/2
Plug it back into the equation and we get 1/2 = 2(2+2). Which is false because 1/2 does not equal 8.
Now lets try it again with Y equaling 1 and substituting x = 2(2+2)
We get 8/x = 1
Solve for x and it equals 8.
Plug it back into the equation and we get 8 = 2(2+2). Which is true. 8 does equal 8.
Thus the answer is 1.
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Post by Elizabeth on Aug 21, 2019 0:40:14 GMT
You brought PEMDAS up but forgot to mention that its actual more like P>E>M>D>A>S... So in order of operations multiplication goes before Division. So for example we can prove that multiplication goes before division in the case above. 8/2(2+2) = Y Lets assume that Y does indeed equal 16 and we substitute x = 2(2+2) into the equation. We get 8/x = 16 Solve for x and it equals .5 or 1/2 Plug it back into the equation and we get 1/2 = 2(2+2). Which is false because 1/2 does not equal 8. Now lets try it again with Y equaling 1 and substituting x = 2(2+2) We get 8/x = 1 Solve for x and it equals 8. Plug it back into the equation and we get 8 = 2(2+2). Which is true. 8 does equal 8. Thus the answer is 1. What do you mean? With PEMDAS the division will go first. Because you go left to right. And PEMDAS can be written as PEDMSA too because left to right matters more. Answer can only be 16 with order of operations. |
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Post by Elizabeth on Aug 21, 2019 0:48:59 GMT
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Post by thesageofmainstreet on Aug 21, 2019 18:40:54 GMT
8 ÷ 2(2+2)=1 (8 ÷ 2)(2+2)=16 The second equation plays a silly game with numbers. If the same is done with words, it would be like objecting to " Parentheses is plural" by saying, "Why isn't it ' parentheses are plural' then?" |
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. But it's probably like that or close to it. I just wrote that fast because was going to sleep so it probably came out slightly more sloppy/different than usual 
