When denominators match
Compare the numerators. The fraction with the larger numerator is greater.
3/8 > 1/8
Both fractions are split into eighths, and 3 eighths is more than 1 eighth.
When denominators are different
One reliable method is to find a common denominator.
1/2 = 3/6 and 2/3 = 4/6
Since 4/6 is greater than 3/6, 2/3 > 1/2.
Another useful clue
For unit fractions (fractions with 1 on top), the larger the denominator, the smaller the fraction.
1/3 > 1/5
A whole split into 3 equal parts gives larger pieces than a whole split into 5 equal parts.
Watch out: a larger denominator does not automatically mean a larger fraction. Consider the size of the pieces and how many you have.