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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Warm Up Add or subtract – Multiply or divide (4.8)6. –12 ÷ 1.5 – –8–8

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative) and justify the process used. California Standards

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Vocabulary Commutative Property Associative Property Distributive Property

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Additional Example 1: Identifying Properties of Addition and Multiplication Name the property that is illustrated in each equation. A. (–4) 9 = 9 (–4) B. (–4) 9 = 9 (–4)The order of the numbers changed. Commutative Property of Multiplication Associative Property of Addition The factors are grouped differently.

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Check It Out! Example 1 Name the property that is illustrated in each equation. A. (–13)2 = 2(–13) B. (18 + 4) + 6 = 18 + (4 +6) (–13)2 = 2(–13) The order of the numbers changed. Commutative Property of Multiplication Associative Property of Addition The factors are grouped differently. (18 + 4) + 6 = 18 + (4 + 6)

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Additional Example 2A: Using the Commutative and Associate Properties Simplify each expression. Justify each step = Commutative Property of Addition = (29 + 1) + 37 = Associative Property of Addition = 67 Add.

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Additional Example 2B: Using the Commutative and Associate Properties Simplify each expression. Justify each step. 7 Commutative Property of Multiplication Associative Property of Multiplication Multiply = 7 = (7 ) = 2929 = 1 2929

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Check It Out! Example 2A Simplify each expression. Justify each step = Commutative Property of Addition = (13 + 7) + 14 = Associative Property of Addition = 34 Add.

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Check It Out! Example 2B Simplify each expression. Justify each step. 4 3 Commutative Property of Multiplication Associative Property of Multiplication Multiply 3 = 4 3 1t4 1t = (4 ) = 3 = 1 3

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers The Distributive Property is also helpful when you do math mentally. When you need to find the product of two numbers, write one of the numbers as a sum or difference. Then use the Distributive Property to help you find the product mentally.

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Additional Example 3A: Using the Distributive Property Write each product using the Distributive Property. Then simplify. 9(31) = (9 30) + (9 1) Rewrite 31 as a sum. = = 279 Distributive Property Multiply. Add. 9(31) = 9(30 + 1)

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Additional Example 3B: Using the Distributive Property Write each product using the Distributive Property. Then simplify. 8(59) = (8 60) – (8 1) Rewrite 59 as a difference. = 480 – 8 = 472 Distributive Property Multiply. Subtract. 8(59) = 8(60 – 1)

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Check It Out! Example 3A Write each product using the Distributive Property. Then simplify. 8(19) = (8 10) + (8 9) Rewrite 19 as a sum. = = 152 Distributive Property Multiply. Add. 8(19) = 8(10 + 9)

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Check It Out! Example 3B Write each product using the Distributive Property. Then simplify. 5(48) = (5 50) – (5 2) Rewrite 48 as a difference. = 250 – 10 = 240 Distributive Property Multiply. Subtract. 5(48) = 5(50 – 2)

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Evaluating Algebraic Expressions 3-1Properties of Rational Numbers Lesson Quiz Name the property that is illustrated in each equation. 1. (–3 + 1) + 2 = –3 + (1 + 2) 2. 6 y 7 = 6 ● 7 ● y Simplify the expression. Justify each step. 3. Write each product using the Distributive Property. Then simplify 4. 4(98) 5. 7(32) Associative Property of Add. Commutative Property of Multiplication

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