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P.1 Real Numbers

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

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P.1 Real Numbers

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  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:

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

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

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

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

  8. Properties of Absolute Value

  9. 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:

  10. 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

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

  12. 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.

  13. 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)

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

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

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

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

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