Ranking fractions can be done by either converting them to decimals and sorting those values or by converting them to fractions with the least common denominator. If the fractions are improper, then they can be converted into mixed fractions and then they can usually be arranged without any further conversions. After arranging the fractions with the common denominator, they can be switched back to their original form.

Fractions represents part of a whole, where the denominator determines how many parts there are in the whole and the numerator describes how many equal parts are being considered. As such, the denominator of a fraction cannot be zero.

Common fractions can be classified as either proper or improper. Proper fractions are those where the absolute value of the fraction is less than one, that is, the numerator is less than the denominator. An improper fraction occurs in the reverse condition where the numerator is greater than the denominator.

Mixed numbers occur when an improper fraction is broken into a non-zero integer and a proper fraction. Other uses for fractions are to specify a ratio and also to specify the mathematical operation of division. Ratios, unlike fractions, instead represents the relationship between two groups. In layman's terms this represents that for every amount of one group there is a certain amount of another group.