# Comparing Fractional Numbers

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?

• Do you mean how to determine if $\frac{a}{b}$ is larger or smaller than $\frac{c}{d}$? – Jason Knapp Aug 11 '14 at 15:52
• @JasonKnapp Yes. – Noob Doob Aug 11 '14 at 15:53
• Scale (e.g. cross multiply) to reduce to integer comparison. – Bill Dubuque Aug 11 '14 at 15:53
• (a/b)-(c/d) is positive, negative or zero and accordingly (a/b) is greater than, lesser than or equal to (c/d) – Vikram Aug 11 '14 at 16:55

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.