Originally Posted by

**Ragnarok** I am studying the book "Algebra" by Israel Gelfand and am having trouble with this problem:

*Which of the fractions $\displaystyle \frac{12345}{54321}$ and $\displaystyle \frac{12346}{54322}$ is bigger?*

I know I could calculate it by hand by finding a common denominator, but I'm fairly certain the book is not interested in rote calculation of this magnitude, so there must be a simpler way. For example, the previous problem was to determine whether $\displaystyle \frac{10,001}{10,002}$ or $\displaystyle \frac{100,001}{100,002}$ was bigger. By noting that both fractions are very close to one, but that the latter is the closest, you can easily determine which is larger. Is there something similar you can do for this one?

Thanks!