Comparing Fractions is to compare the two fractions and find greatest and smallest fraction among the given two fractions. To compare fractions, we need to see that all the fractions are greater than zero. And, also check that the fraction is a proper fraction or an improper fraction.
Rule 1: If the denominators of the two fractions are same, then the fraction with larger numerator is greater.
Example:
Compare

                           Comparing Like Denominator Fractions
Solution: The fractions $\frac{3}{4}$ and $\frac{1}{4}$ have same denominator. So, $\frac{3}{4}$ is greater than $\frac{1}{4}$

                                                        $\frac{3}{4}$ > $\frac{1}{4}$

Rule 2: If the numerators of the two fractions are same, then the fraction with smaller denominator is greater.
Example:
Compare

                           Comparing Like Numerator Fractions

Solution: The fractions $\frac{2}{4}$ and $\frac{2}{8}$ have same numerator. So, $\frac{2}{4}$ is greater than $\frac{2}{8}$

                                                      $\frac{2}{4}$ > $\frac{2}{8}$
 
Rule 3: If both numerator and denominator of the two fractions are different, then multiply the numerator and denominator of both the fractions with same numbers so as to have same denominator. Then, compare the numerator of the two fractions.
 
Example: Compare  
                           Comparing Unlike Fractions         
                                        
Solution: The fractions $\frac{2}{3}$ and $\frac{3}{4}$ are unlike fractions. We need to multiply $\frac{2}{3}$ by $\frac{4}{4}$ and multiply $\frac{3}{4}$ by $\frac{3}{3}$ to get same denominator.

        $\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}$ and  $\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}$

   Now, on comparing the numerators. The fraction $\frac{3}{4}$ which is equal to $\frac{9}{12}$ is greater than $\frac{2}{3}$ which is equal to $\frac{8}{12}$.

                                    $\frac{2}{3}$ < $\frac{3}{4}$