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Topic: Number Sets Questions/Main Ideas: • How are the number sets related? • What are the properties of the real numbers? Name: _______________________________ Date: ______________________ Objective: We will be able to identify subsets of the complex number system and apply properties of real numbers. I can identify what subset of the complex number system a number belongs to and use properties of the real numbers to solve an algebraic proof. Property Addition Multiplication Commutative Associative Identity Inverse Distributive Transitive Substitution • What are some Examples: examples of using 1. − 3 + 3 =0 the properties of real numbers? 3. 1 • (ab) =ab 2. (−6 + 1) + 7 =−6 + (1 + 7) 4. − 3 + 0 =−3 Transformations That Produce Equivalent Equations • How can we solve linear equations using properties or real numbers? Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Ex: 4x + 9 = 21 4x + 9 − 9 = 21 − 9 4x = 12 4x ÷ 4 = 12 ÷ 4 x =3 Examples: ______________ ______________ ______________ ______________ ______________ 2 x − 7 =4 3 1. 7x − 41 =−13 2. 3. x + 5 = 25 − 4 x 4. 5 x + 17 = 4( x + 3) • What is the transitive property? The prefix trans means_______________________ The transitive property takes ________________ statements and unites them by _______________________________. Example: If x y= = and y z , then ___________________. If I am hungry, I eat too many pretzels. If I eat too many pretzels, then I am thirsty. If I am thirsty, then I drink a diet coke. Try these on your own. 1. = If a b= and b c, then 2. If yesterday were Friday, then today is Saturday. If today is Saturday, then tomorrow is Sunday. 3. = If pq rs = , and rs tu , then Summary: 4. If it is snowing, then school is closed. If school is closed, then I hang out with my friends. 5. If you are in Algebra 2, then you take the SOL. If you take the SOL, you will pass the SOL.