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