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    1.1 and 1.2 1.1 and 1.2 Presentation Transcript

    • CHAPTER1: EXPRESSIONS,EQUATIONS, AND INEQUALITIES1.1 Patterns and Expressions1.2 Properties of Real Numbers
    • 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
    • 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
    • SETS OF NUMBERS Real Numbers can be graphed on a number line and contain several subsets  Natural Numbers are the counting numbers: 1, 2, 3, 4, …  Whole numbers are the natural numbers and zero 0, 1, 2, 3, 4 ….  Integers are the positive and negative whole numbers and zero
    • SETS OF NUMBERS  Rational numbers are 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
    • SETS OF NUMBERSThis diagram shows how subsets of the real numbers are related.
    • EXAMPLE: CLASSIFY EACH NUMBER.
    • 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. The reciprocal (multiplicative inverse) of any nonzero number is  The Multiplicative Inverse: The product of a number and its reciprocal is 1
    • A set is closed with respect to an operation if the operation can always be completed with elements in the set.Look for clues/key information: • Does the equation contain 0 or 1? • What is different about the left and right side of the equation?
    • EXAMPLE: NAME THE PROPERTY ILLUSTRATEDBY EACH EQUATION.