Does a formula exist for comparing two fractional numbers, without resolving to using anything other than integers and fractions? (Thus not real numbers).
In other words: given $\dfrac{a}{b}$ and $\dfrac{c}{d}$, how to tell which one is greater without using decimal point arithmetics?
Another way of knowing if $\frac{a}{b}$ is greater than $\frac{c}{d}$ is by converting these fractions to fractions with a common denominator. You have to get the LCM of the denominators and use it as the LCD of the two fractions. Convert each fraction to an equivalent fraction whose denominator is the LCD. When comparing two fractions with like denominators, the larger fraction is the one with the greater numerator.