1. 1-1 Properties of Real Numbers Big Idea: -Graph, order, identify, and use properties of real numbers.

2. Subsets of Real Numbers: Natural numbers: Positive, whole numbers 1, 2, 3, …. Whole Numbers: whole numbers including 0 0, 1, 2, 3 …. Integers: Natural numbers, their opposites, and 0. …-3, -2, -1, 0, 1, 2, 3 …

3. Rational Numbers: numbers that can be written as fractions, can be terminating decimals, or repeating decimals Irrational Numbers: numbers that cannot be written as a fraction and decimals that have no pattern

4. Ex 1: A) Graph the numbers on a number line.

5. Ex 2: Compare each. A) -10 -8B) 0.5 0.01 C) D) 0.4

6. More Properties Opposite or additive inverse. The sum of opposites is 0. Reciprocal or multiplicative inverse. The product of reciprocals is 1.

7. Ex 3: Find the opposite and reciprocal of each number. A) 4B) C) D) 5.6

8. Properties of Addition and Multiplication Closure5 +x is a real number. xy is a real number. Commutative 6 + 3 = 3 + 6 2y = y2 Associative (5 + 6) + 7 = 5 + (6 +7) (8·9)10 = 8(9·10)

9. Identity 4 + 0 = 4 8·1 = 8 Inverse x + (-x) = 0 2·½ = 1 Distributive 5(x + y)= 5x + 5y

10. Ex 4: Which property is illustrated? a. (-7)(2 · 5) = (-7)(5 · 2) b. 3 · (8 + 0) = 3 · 8

11. Absolute Value The absolute value of a number is the distance from zero on the number line.

12. Ex 5: Find the absolute value. A)B) C) D)

13. Essential Question: What are the similarities and differences of the subsets of Real Numbers? Write down this question at the end of your notes and answer it in complete sentences. Your answer must be in your own words and must be at least 3 sentences long. This is a part of your Notes grade.