Contemporary Mathematics

# Formula Review

### 11.3Standard Divisors, Standard Quotas, and the Apportionment Problem

Let $AA$ be a particular item and $BB$ another such that there is a constant ratio of $AA$ to $BB$.

• $ratio ofB's toA's=1ratio ofA's toB'sratio ofB's toA's=1ratio ofA's toB's$ and $ratio ofA's toB's=1ratio ofB's toA'sratio ofA's toB's=1ratio ofB's toA's$
• $units ofA=(units ofB)×(ratio ofA's toB's)=units ofBratio ofB's toA'sunits ofA=(units ofB)×(ratio ofA's toB's)=units ofBratio ofB's toA's$
• $units ofB=(units ofA)×(ratio ofB's toA's)=units ofAratio ofA's toB'sunits ofB=(units ofA)×(ratio ofB's toA's)=units ofAratio ofA's toB's$

$Standard Divisor=Total PopulationHouse SizeStandard Divisor=Total PopulationHouse Size$

$State's Standard Quota=State PopulationStandard DivisorseatsState's Standard Quota=State PopulationStandard Divisorseats$

### 11.5Fairness in Apportionment Methods

$population growth rate=current population size-previous population sizeprevious population sizepopulation growth rate=current population size-previous population sizeprevious population size$

$New House Size=New PopulationOriginal Standard Divisorrounded to the nearest whole number.New House Size=New PopulationOriginal Standard Divisorrounded to the nearest whole number.$