1. Part I: Numbers and Operations Lesson 1: Numbers

2. 2 Even Number  A number is even if the reminder is zero when it is divided by 2. (n=2*m)  Examples: 2, 8, 200….  0 is even because 0=2*0

3. 3 Odd Number  A number is odd if the reminder is one when it is divided by 2. (n=2*m+1)  Examples: 1, 9, 11, 1001….  Check the unit digit if the number is big, if the digit is even then the number is even; if the digit is odd then the number is odd.

4. 4 Some Rules  Even + even = even  Odd + odd = even  Odd + even = odd  Even * even = even  Odd * odd = odd  Odd * even = even

5. 5 Prime Number  A natural number that has exactly two distinct natural number divisors: 1 and itself  Except for 2, all even numbers are not prime, why?  1 is not a prime number *Natural numbers are the ordinary counting numbers, 1, 2, 3, …..

6. 6 Composite Number  A number which is not prime is known as a composite number  Every composite number has at least three factors, why?  1 is not a composite number

7. 7 Rational Number  A real number that can be written as a simple ratio a/b, where a and b are integers and b is not zero  Examples: 3/2, 2/3, 9/100, ….  An integer i is rational because i=i/1  Are 0.01, 0.3333….., 1.25 rational numbers? Why?

8. 8 Irrational Number  A real number that cannot be written as a fraction, not rational  Examples: ∏, √2, e, ….  Not all roots are irrational

9. 9 Integer  Natural numbers (1, 2, 3, …), 0, and the negative natural numbers (-1, -2, -3, …)

10. 10 Answers  Prime number: because even numbers can be divided by 2, so at least 2 is one divisor. But 2 can only be divided by 1 and 2 (which is itself), so 2 is prime the other even numbers are not.  Composite number: prime numbers could only be divided by 1 and itself, composite number is not prime, so at least 1, itself and other are divisors.  0.01=1/100, 0.3333….=1/3, 1.25=5/4, so they are rational numbers.

11. 11 References  http://www.proprofs.com/sat/study-guide/index.shtml  http://en.wikipedia.org/wiki/Prime_number http://en.wikipedia.org/wiki/Prime_number  http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Natural_number  http://mathworld.wolfram.com/IrrationalNumber.html http://mathworld.wolfram.com/IrrationalNumber.html  http://www.mathsisfun.com/ http://www.mathsisfun.com/  http://en.wikipedia.org/wiki/Integer http://en.wikipedia.org/wiki/Integer