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[Algebra 2(Y)] 1.1: Properties of Real Numbers and Operations Objectives: To graph and order real numbers To identify properties of real numbers To use properties of real numbers to simplify expressions. Classifying Real numbers A set of real numbers contains the set of rational numbers and the set of irrational numbers. A variable is a symbol, usually a letter, than represents one or more numbers. Example 1: Classifying a Variable Your school is sponsoring a charity race. Which set of numbers best describes the number of people p who participate in the race? If each participant made a donation d of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised? Graphing and Ordering Real Numbers A set of real numbers can be graphed on a number line. Example 2: Graphing Numbers on the Number Line Graph the set of numbers on a number line. Then, list the numbers in order from least to greatest. 11 1.5 0.8 1. 6 7 √5 4 Properties of Real Numbers The following are field properties of real numbers. These properties govern the operations of addition and multiplication. Example 3: Identify Properties of Real Numbers Write the name of the property that is illustrated by each statement. a.) 8 5 c.) 8 5 8 3 4 4 8 3 b.) 3.008 d.) 6∙5 ∙4 3.008 6∙ 5∙4 Example 4: Use Properties of Real Numbers Simplify the following expressions. a.) 12 ∙ 24 ∙ b.) 36 ∙ 0.01 0