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1-5 Properties Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes Objective: Students identify properties of rational umbers and use them to simplify numerical expressions.

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1-5 Properties Warm Up Evaluate. 1. 2 + 5 3 – 7 2. 5(3 – 1) ÷ (3 + 2) 3. (4 + 1) 2 – 8 ÷ 2 4. 12 ÷ 3 6 – 20 10 2 21 4

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1-5 Properties Problem of the Day Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy? 27

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1-5 Properties Learn how to identify properties of numbers and use them to simplify numerical expressions.

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1-5 Properties Vocabulary Commutative Property Associative Property Identity Property Distributive Property

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1-5 Properties

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1-5 Properties

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1-5 Properties

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1-5 Properties Additional Example 1: Identifying Properties of Addition and Multiplication Tell which property is represented. A. (2 6) 1 = 2 (6 1) B. 3 + 0 = 3 C. 7 + 9 = 9 + 7 (2 6) 1 = 2 (6 1) The numbers are regrouped. Associative Property 3 + 0 = 3 One of the factors is 0. Identity Property 7 + 9 = 9 + 7 The order of the numbers is switched. Commutative Property

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1-5 Properties Check It Out: Example 1 Tell which property is represented. A. 7 1 = 7 B. 3 + 4 = 4 + 3 C. (5 1) 2 = 5 (1 2) 7 1 = 7 One of the factors is 1. Identity Property 3 + 4 = 4 + 3 The order of the numbers is switched. Commutative Property (5 1) 2 = 5 ( 1 2) The numbers are regrouped. Associative Property

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1-5 Properties Additional Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 B. 20 9 5 21 + 16 + 9 = 16 + 9 + 21 Commutative Property. = 16 + (9 + 21) = 16 + 30 Associative Property. = 46 Add. 20 9 5 = 20 5 9 Commutative Property. = 20 (5 9) = 20 45 Associative Property. = 900 Multiply.

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1-5 Properties Check It Out: Example 2A & B Simplify each expression. Justify each step. A. 17 + 14 + 3 B. 12 3 5 17 + 14 + 3 = 14 + 17 + 3 Commutative Property. = 14 + (17 + 3) = 14 + 20 Associative Property. = 34 Add. 12 3 5 = 3 5 12 Commutative Property. = 3 (5 12) = 3 60 Associative Property. = 180 Multiply.

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1-5 Properties You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

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1-5 Properties Additional Example 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: Method 2: = (6 50) + (6 4) Rewrite 54 as 50 + 4. = 300 + 24 = 324 Use the Distributive Property. Multiply. 6(54) = 6(60 – 6) Rewrite 54 as 60 – 6. = (6 60) – (6 6) = 360 - 36 Use the Distributive Property. Multiply. = 324 Subtract. Add. 6(54) = 6(50 + 4)

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1-5 Properties Check It Out: Example 3 Use the Distributive Property to find 8(19). Method 1: Method 2: = (8 10) + (8 9) Rewrite 19 as 10 + 9. = 80 + 72 = 152 Use the Distributive Property. Multiply. 8(19) = 8(20 – 1) Rewrite 19 as 20 – 1. = (8 20) – (8 1) = 160 – 8 Use the Distributive Property. Multiply. = 152 Subtract. Add. 8(19) = 8(10 + 9)

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1-5 Properties Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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1-5 Properties Lesson Quiz Tell which property is represented. 1. 17 1 = 17 2. (12 + 14) + 5 = 12 + (14 + 5) 3. 2 16 = 16 2 Simplify each expression. Justify each step. 4. 4 12 25 5. 48 + (15 + 2) Use the Distributive Property to find each product. 6. 6 (12 + 5) 7. (20 – 7) 9 Identity Property Associative Property Commutative Property 1,200 65 102 117

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