1.1/1.2 Properties of Real Numbers
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  • 1. Chapter1: Expressions, Equations, and Inequalities
    1.1 Patterns and Expressions
    1.2 Properties of Real Numbers
  • 2. Definitions
    A mathematical quantity is anything that can be measured or counted.
    Quantities whose value stay the same are constants
    Quantities whose values change or vary are called variable quantities
  • 3. Definitions
    A variable is a symbol, usually a letter, that represents one or more numbers.
    Examples: and
    A numerical expression is a mathematical phrase that contains numbers and operation symbols.
    Examples: and
    An algebraic expression is a mathematical phrase that contains one or more variables.
    Examples: and
  • 4. Sets of Numbers
    Real Numbers can be graphed on a number line and contain several subsets
    Natural Numbersare the counting numbers:
    1, 2, 3, 4, …
    Whole numbersare the natural numbers and zero
    0, 1, 2, 3, 4 ….
    Integers are the positive and negative whole numbers and zero
  • 5. Sets of Numbers
    Rational numbersare number that can be written as a ratio of two integers (this includes fractions, terminating decimals, and repeating decimals)
    Irrational Numbers cannot be written as a ratio of two integers and have decimal representations that do not terminate or repeat
  • 6. Sets of Numbers
    This diagram shows how subsets of the real numbers are related.
  • 7. Example: Graph each number on the number line and classify each number.
  • 8. Properties of Real Numbers
    The properties of real numbers are relationships that are true for all real numbers (except in one case, zero)
    The opposite (additive inverse) of any number a is –a.
    The Additive Inverse: The sum of a number and its opposite is 0.
    Thereciprocal (multiplicative inverse) of any
    nonzero number is
    The Multiplicative Inverse: The product of a number and its reciprocal is 1
  • 9. Look for clues/key information:
    • Does the equation contain 0 or 1?
    • 10. What is different about the left and right side of
    the equation?
  • 11. Example: Name the property illustrated by each equation.