A fraction is a part of a whole. To find the greater fraction you need to find the fraction that contains a greater part of the whole.
If fractions have the same denominator, you can compare numerators:
It is possible to draw it to see the result:
If there is a common numerator, the fraction with the greater denominator is actually smaller:
You can draw it as well:
If two fractions do not have common numerator or denominator, you can find equivalent fractions with the same denominator.
E.g. compare $3/8$ and $1/3$:
If you compare a fraction with a whole number, you can turn the whole number into a fraction with the same denominator:
Compare 3 and $9/4$: