Parliamentary Allocation
Suppose we run an election. We want to allocate seats in the parliament proportionally to the number of votes each party received.
Problem:
 $n$  number of voters that participate in the elections
 $N$  number of classes (parties) that are being elected
 $P_1, ..., P_k$  are partitions of the population, \sum_P = N
 size of $P_i$ is $p_i$
 goal: to select $S$ representatives, $S$  the total number of seats that are allocated
A quota $q_i$ of party $i$ is the number of sets the party receives after election:
 $q_i = S \cdot \cfrac{P_i}{n}$
 but it must be an integer! Cannot divide one seat between two parties
This is important not only for seats allocation, but for allocating in general.
For example,
 suppose we have some area that suffers from fire
 we have only 10 medical units
 how to allocate them between the regions in that area?

 can allocate as follows: the number of voters $p_i$  density of a region, $n$  all people of the area
 $S$ is the number of medical units
 $q_i$ the number of medical units sent to region $i$
 $q_i = S \cdot \cfrac{P_i}{n}$  again: it has to be an integer!
Methods
Sources