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1-6. Properties. Warm Up. Problem of the Day. Lesson Presentation. Course 2. Warm Up Evaluate. 1. 2 + 5 3 – 7 2. 5 x [(3 – 1 )] ÷ (3 + 2) 3. (4 + 1) 2 – 8 ÷ 2 4. 12 ÷ 3 6 – 20. 10. 2. 21. 4. Problem of the Day

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**1-6**Properties Warm Up Problem of the Day Lesson Presentation Course 2**Warm Up**Evaluate. 1. 2 + 5 3 – 7 2.5 x [(3 – 1)] ÷ (3 + 2) 3.(4 + 1)2– 8 ÷ 2 4. 12 ÷ 3 6 – 20 10 2 21 4**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**Learn how to identify properties of rational numbers and use**them to simplify numerical expressions.**Vocabulary**Commutative Property Associative Property Identity Property Distributive Property**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 The numbers are regrouped. (2 6) 1 = 2 (6 1) Associative Property One of the factors is 0. 3 + 0 = 3 Identity Property The order of the variables is switched. 7 + 9 = 9 + 7 Commutative Property**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 The order of the numbers is switched. 3 + 4 = 4 + 3 Commutative Property The numbers are regrouped. (5 1) 2 = 5 ( 1 2) Associative Property**Additional Example 2: Using Properties to Simplify**Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 B. 20 9 5 Commutative Property. 21 + 16 + 9 = 16 + 9 + 21 Associative Property. = 16 + (9 + 21) Add. = 16 + 30 = 46 Commutative Property. 20 9 5 = 20 5 9 Associative Property. = 20 (5 9) Multiply. = 20 45 = 900**Check It Out: Example 2A & B**Simplify each expression. Justify each step. A. 17 + 14 + 3 B. 12 3 5 Commutative Property. 17 + 14 + 3 = 14 + 17 + 3 Associative Property. = 14 + (17 + 3) Add. = 14 + 20 = 34 Commutative Property. 12 3 5 = 3 5 12 Associative Property. = 3 (5 12) Multiply. = 3 60 = 180**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.**Additional Example 3: Using the Distributive Property to**Multiply Mentally Use the Distributive Property to find 6(54). Method 1: Method 2: 6(54) = 6(50 + 4) Rewrite 54 as 50 + 4. Use the Distributive Property. = (6 50) + (6 4) = 300 + 24 Multiply. = 324 Add. Rewrite 54 as 60 – 6. 6(54) = 6(60 – 6) = (6 60) – (6 6) Use the Distributive Property. Multiply. = 360 - 36 Subtract. = 324**Check It Out: Example 3**Use the Distributive Property to find 8(19). Method 1: Method 2: 8(19) = 8(10 + 9) Rewrite 19 as 10 + 9. Use the Distributive Property. = (8 10) + (8 9) = 80 + 72 Multiply. = 152 Add. Rewrite 19 as 20 – 1. 8(19) = 8(20 – 1) = (8 20) – (8 1) Use the Distributive Property. Multiply. = 160 – 8 Subtract. = 152**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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