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!

[Sullyman2007]

Originally Posted by 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%.}

Interesting. Im not much of a math person...but that makes absolutley no sense.
Perhaps it is that fractions are not a precise way of calculating?

[og4lif]

ok your first problem is a nobrainer 1/3 does equal 33.3% if you are rounding off but the most accurate percent for 1/3 is 33.33333333% now try doing this
33.33333333% + 33.33333333% + 33.33333333%
use a calculator if you have to but you will c that it adds up 2 a 100%

[FlameFalco]

Originally Posted by ruferddude

Divide each side by (A - B): (A + B) = B

1-1=0 You can divide by zero in math

[Litodude]

Originally Posted by ruferddude

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%.}

1/3 is a irrational number. That is why you're getting 99.9% 3(1/3)]. It's called a round off error; math isn't perfect.

[Adamaja456]

Personally, i hate it when people do this.

1/3 does not equal 33.3% its 33.33333 repeating. Once you stop it from repeating, you're rounding the number thus changing the results.
1/3 + 1/3 + 1/3 = 1(100%) fractions have no rounding
.33 + .33 + .33 = .99(.99%) decimals are stopped and rounded

Hope that makes sense

[Litodude]

Originally Posted by FlameFalco

1-1=0 You can't divide by zero in math

Fixed

[FlameFalco]

whoops sorry i meant that lol

[Squeek]

These are all really, really old math problems.

http://www.google.com/search?hl=en&s...+1&btnG=Search
http://www.google.com/search?hl=en&s...em&btnG=Search

And they're not Critical Thinking as they've already been solved. So, moved to Chit Chat.

[Roy Campbell]

Division only makes sense when one of the numbers or factors that you are dividing out is non-zero. You can't divide (A - B) out from each side because (A - B) is zero. Each side can't equal each other because anythng divided by zero is undefined.

[og4lif]

oo and for the 2nd question the reason why 1 = 2 is because of a simple mathematical error it is not possible to divide both sides by a-b since a-b = 0.... in math you cannot divide any number by 0 or it will come out 2 an error

score 2/2

[ruferddude]

Ah. You guys are right. I didn't see that I was dividing by 0. I feel dumb now.

I should have seen it. ><
Thanks for pointing this out and thanks for showing me how dumb I am. ><
And sorry for the misplacement. I didn't realize the answers were so easy to get. I thought it would take some actual thought to figure out but I come back 10 minutes later and like 8 people figured them both out.

Edit: Now I feel doubly dumb. ; ; On the video that I posted to make things more clear, like two people pointed out that it was dividing by zero on their comments. The whole second equation could have been left out if I only had read YouTube comments.

[og4lif]

lol yup u feel dumb but u can make up 4 it if you can solve this
X = variable

(1/sin^2 X) + (1/cos^2 X) = (tan X + 1/tan X)^2
no calculators 4 this 1

[ruferddude]

Originally Posted by og4lif

u can make up 4 it if you can solve this

Nope. I guess I can't make it up. XD I just finished Algebra II last year and we didn't learn about sine, cosine, and tangent. Well sort of but not how to solve equations with them. I'm about to start Pre-Calculus when school starts on Monday. So I think that I'll be learning that stuff this year maybe.

[og4lif]

wow really?? well anyone can try it if they want then if you guys are still clueless i can give you a hint o n btw i hav no clue wat u ment by alegbra II but i lerned that stuff in a course called functions and relations so i guess its a higher lvl of math then alegbra II

[ruferddude]

Well I live in Texas so my Math classes are weird O.o
I'm considered "advanced" so in seventh grade I took Pre-Algebra. Eigth grade was Algebra I. Ninth grade was Geometry. Tenth grade was Algebra II. Now I'm about to be in Pre-Calculus. Then AP Calculus as a senior. If you aren't "advanced" then you take everything a year later than me (you finish off with Pre-Calculus as a senior). I don't know where "functions and relations" rank in my education system.

[og4lif]

lol actually im takin calculus and vectors right now i finished that course a year ago



functions and relations is pre-calculus

[NarutoFoxDemon]

Originally Posted by ruferddude

Ah. You guys are right. I didn't see that I was dividing by 0. I feel dumb now.

I should have seen it. ><
Thanks for pointing this out and thanks for showing me how dumb I am. ><
And sorry for the misplacement. I didn't realize the answers were so easy to get. I thought it would take some actual thought to figure out but I come back 10 minutes later and like 8 people figured them both out.

Edit: Now I feel doubly dumb. ; ; On the video that I posted to make things more clear, like two people pointed out that it was dividing by zero on their comments. The whole second equation could have been left out if I only had read YouTube comments.

Shame shame, dividing by zero.

[solopro]

The second statement, I've looked at it and it's interesting. There's also something on Wikipedia I've seen that says zero is equal to one.

[lord_carbo]

0.99999999999 repeating = 1.

I win. Infinitesimals win. That ****ing dumbass 11th grade math 10th grader at my lunch table who insists I'm wrong about all of this loses.