1. P.1 Real Numbers Be prepared to take notes when the bell rings.

2. Real Numbers • Set of numbers formed by joining the set of rational numbers and the set of irrational numbers • Subsets: (all members of the subset are also included in the set) • {1, 2, 3, 4, …} natural numbers • {0, 1, 2, 3, …} whole numbers • {…-3, -2, -1, 0, 1, 2, 3, …} integers

3. Rational and Irrational Numbers Rational Number Irrational Number • A real number that can be written as the ratio of two integers, where q • Example: • Repeats • = 0.125 • Terminates • Repeats • A real number that cannot be written as the ratio of two integers • *infinite non-repeating decimals • Example:

5. Real Number Line Positive Negative Origin 0 • Coordinate: • Every point on the real number line corresponds to exactly one real number called its coordinate

6. Ordering Real Numbers Inequalities a b Example: a b

7. Describe the subset of real numbers represented by each inequality. • A. • B. • C.

8. Interval: subsets of real numbers used to describe inequalities *Unbounded intervals using infinity can be seen on page 4

9. Properties of Absolute Value

10. Absolute value is used to define the distance (magnitude) between two points on the real number line • Let a and b be real numbers. The distance between a and b is: The distance between -3 and 4 is:

11. Algebraic Expressions • Variables: • letter that represents an unknown quantity • Constant: • Real number term in an algebraic expression • Algebraic Expression: • Combination of variables and real numbers (constants) combined using the operations of addition, subtraction, multiplication and division • Examples of algebraic expressions: • Terms: • Parts of an algebraic expression separated by addition • i.e. • Coefficient: • Numerical factor of a variable term • Evaluate: • Substitute numerical values for each variable to solve an algebraic expression

12. Examples of Evaluation Used Substitution Principle: If a=b, then a can be replaced by b in any expression involving a.

13. Basic Rules of Algebra • 4 Arithmetic operations: • Addition, + • Subtraction, - • Division, / • Multiplication, • Addition and Multiplication are the primary operations. Subtraction is the inverse of Addition and Division is the inverse of Multiplication.

14. Basic Rules of Algebra Subtraction: add the opposite of b Division: multiply by the reciprocal of b; if b0, then • is called the additive inverse (opposite of a real number) • is called the multiplicative inverse (reciprocal of a real number)

15. Let a, b and c be real numbers, variables or algebraic expressions.

16. Let a, b and c be real numbers, variables or algebraic expressions. • Properties of Negation and Equality

17. Let a, b and c be real numbers, variables or algebraic expressions. • Properties of Zero

18. Homework Problems • Page 9 #’s 1-25 odd, 29, 33-39 odd, 43-47, 51-55, 59, 89-93, 99-107, 111-115