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Warm Up

Warm Up. Tell whether each expression is equal by completing each statement with = or ≠. 1.) 34 + 12 _?_ 12 + 34 2.) 100 – 1 _?_ 1 – 100 3.) 0 + 180 _?_ 180 4.) 18 ÷ _?_ 1. 1.4 Properties of Real Numbers. Objectives. Identify and use properties of real numbers. Vocabulary.

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Warm Up

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  1. Warm Up • Tell whether each expression is equal by completing each statement with = or ≠. • 1.) 34 + 12 _?_ 12 + 34 • 2.) 100 – 1 _?_ 1 – 100 • 3.) 0 + 180 _?_ 180 • 4.) 18 ÷ _?_ 1

  2. 1.4 Properties of Real Numbers

  3. Objectives • Identify and use properties of real numbers.

  4. Vocabulary • Equivalent expressions – two algebraic expressions that have the same value for all values of the variable(s). • Deductive reasoning – the process of reasoning logically from given facts to a conclusion. • Counterexample – an example showing that a statement is false.

  5. Properties of Real Numbers Commutative Properties of Addition and Multiplication • Changing the order of the addends does not change the sum. • Changing the order of the factors does not change the product.

  6. Properties Cont. Associative Properties of Addition and Multiplication • Changing the grouping of the addends does not change the sum. • Changing the grouping of the factors does not change the product.

  7. Properties Cont. Identity Properties of Addition and Multiplication • The sum of any real number and 0 is the original number. • The product of any real number and 1 is the original number.

  8. Properties Cont. Zero Product Property of Multiplication • The product of a and 0 is 0. Multiplication Property of -1 • The product of -1 and a is –a.

  9. Example 1 – Identifying Properties • Which property is illustrated by each statement? • A.) 31 * 0 = 0 • B.) (x + 3) + 6 = x + (3 + 6) • C.) 5x + 0 = 0

  10. Example 2 – Using Properties for Mental Calculations • A movie ticket costs $6.75. A drink costs $1.90. Popcorn costs $2.25. What is the total cost for a ticket, a drink, and popcorn? Use mental math.

  11. Example 3 – Writing Equivalent Expressions • What is the simplified form of each expression? • A.) 4(8n) • B.) (3 + 5b) + 7 • C.)

  12. Example 4 – Using Deductive Reasoning and Counterexamples • Is the statement true or false? If false, give a counterexample. • A.) For all real numbers a and b, a – b = b – a. • B.) For all real numbers a, b, and c, a x b x c = a x c x b.

  13. Assignment • Pg. 26 – 27 • (7 – 18 all, 20 – 30 even, 32, 33)

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