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class+February+18 - Math 103, Section 11, Friday, February...

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Math 103, Section 11, Friday, February 18, 2011 Chapter 4 Handout 2 1. Submitted Homework Assignment for Chapter 4 is at Sakai. It is in the Assignments section and is called: Assignment Chapter 4A Please do Exercises Exercises 4, 14, and 20 , pages 144-146 and upload to Sakai. Homework is due by Tuesday, February 22 at midnight. Assignment Chapter 4B Please do Exercises Exercises 26, 36, and 46 , pages 146-147 and upload to Sakai. Homework is due by Thursday, February 24 at midnight. Our first exam will be on Friday, March 4. The exam will cover Chapters 1,2 and 4. Homework to be discussed on Tuesday, February 22. Exercises 27,37,47 Terminology: The standard divisor equals the total population divided by the number of seats . The standard quota of a state equals the state population divided by the standard divisor . Hence the standard quota times the standard divisor = the state population Example 1: There are 20 seats. The total population is 100 people. The standard divisor is 100 people /20 seats =for every 5 people the state gets 1 seat. For every 5 people, there is 1 seat. State Population Standard quota of seats A 25 5 B 50 10 C 10 2 D 10 2 E 5 1 Total 100 20 Look at State B: We divide its population of 50 people by the standard divisor of 5 (meaning for every 5 people, the state gets 1 seat) and we end up with State B’s standard quota of 10 seats.

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The standard quota of a state equals the state population divided by the standard divisor . If we multiply the standard quota by the standard divisor for State B, we get: 10 seats times (for every 5 people there is 1 seat)= a population of 50 people That is, the standard quota times the standard divisor = the state population Adding up all the standard quotas gives the exact number of seats. Remark: This makes sense, since each standard quota represents a state’s proportional share of seats. What we are saying here is that there are 100 people and 20 seats will be given. Equivalently for every 5 people, 1 seat will be given. This is how we obtain the standard quotas of seats. When we add up all the standard quotas (no matter how the breakdown is : 25/5+50/5+10/5+10/5+5/5=20), we must get 20 as the number of seats since 100/5=20. Example2 There are 50 seats. The total population is 100 people. The standard divisor is 100/50=2 people per seat. For every 2 people, there is 1 seat. State Population Standard quota A 50 25 B 25 12.5 C 5 2.5 D 17 8.5 E 3 1.5 Total 100 50 Hamilton’s Method of Apportionment Step1. Calculate each state’s standard quota. Step2. Give to each state its lower quota. Step3. Give the surplus seats (one at a time) to the states with the largest residues (fractional parts) until there are no more surplus seats. Example The total population is 12.500,000
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This note was uploaded on 01/20/2012 for the course MATH 103 taught by Professor Berkowitz during the Spring '07 term at Rutgers.

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class+February+18 - Math 103, Section 11, Friday, February...

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