Math problems

[ruferddude]

Ok. So this is my first post in the "critical thinking" department so if this is misplaced then sorry. >< I have found two interesting math problems. These are probably old and the answer can probably be found on the internet but I was interested to see what the FFR community would have to offer on these problems:

1. (1/3) + (1/3) + (1/3) = (3/3) That's fine. But now let's use their percent value instead:
(33.3%) + (33.3%) + (33.3%) = (99.9%) {The numbers after the decimals are repeating of course.}
So does this go to show that (3/3) = only 99.9% instead of 100%?
{The same thing can be done to (1/9) or 11.1%. It would work out to be (9/9) = 99.9%.}


2. Let's say A=1 and B=1.
So now we can say that: A=B.
Multiply both sides by A. Now we have: A sqaured = A*B
Subtract (B squared) from both sides: ((A squared) - (B squared)) = AB - (B squared)
Factor: (A + B)(A - B) = B(A - B)
Divide each side by (A - B): (A + B) = B
Substitute: (1 + 1) = 1
Simplify: 2 = 1
If you can't follow this (because I don't know how to put the squared sybol so it may seem confusing) here is a link to a more clear video: here. I read this in my algebra II book last year but didn't think of posting it until now. My teacher never used the book so he never could explain this to the class. But if I remember correctly, the page had this eqaution going down the center and on one of the side notes, it said something like "It seems that 1 = 2. But that is impossible right? So what is wrong with this equation?" Seeming to imply that there is an error in the logic somewhere that I am not able to find.


So I'm interested in seeing how these problems work out. Please post if you have some insight that will clear this up for me. Thanks!