The two fractions are:
2 3
— and —–
5 7
The goal is to find which one is smaller.
If we replace
2 2 2
—- with —- that is ——–
5 3 5 – 2
and replace
3 3 3
—- with —- that is ——–
7 4 7 – 3
And then replace each of the two new fractions
2 2 2
—- with —- that is ——-
3 1 3 – 2
and
3 3 3
—- with —- that is ——
4 1 4 – 3
Since 2 is less than 3, then the first fraction is smaller.
Is this method always valid? Or was it just a coincidence?
This would be much easier with LaTeX. I tried it in one of my blog posts and it works great.
Since you’re doing math & programming, you may enjoy this: Mozart’s Dice Game
http://www.pianonoise.com/Article.dice.htm
http://www.amaranthpublishing.com/MozartDiceGame.htm
She was just asking about implementing LaTex into your website. That would be great if you can do that.
I guess I will have to do that. Sorry, I’ve been lazy.
It is always true as long as both fractions do not change signs or both of them change signs.
True