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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 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. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 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

  3. California Standards AF1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.

  4. Vocabulary Commutative Property Associative Property Identity Property Distributive Property

  5. 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.

  6. 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 One of the addends is 0. 3 + 0 = 3 Identity Property 7 + 9 = 9 + 7 The order of the numbers is switched. Commutative Property

  7. 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) Associative Property = 16 + 30 Add. = 46 20  9  5 = 20  5  9 Commutative Property = 20  (5  9) Associative Property = 20  45 Multiply. = 900

  8. Additional Example 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: Method 2: Rewrite 54 as 50 + 4. 6(54) = 6(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 = 324 Subtract.

  9. Check It Out! Example 1 Tell which property is represented. A. 7  1 = 7 *Write in KINB* B. 3 + 4 = 4 + 3 *Write in KINB* C. (5  1)  2 = 5  (1  2) *Already in KINB* 7  1 = 7 One of the factors is 1. Identity Property The order of the numbers is switched. 3 + 4 = 4 + 3 Commutative Property (5  1)  2 = 5  ( 1  2) The numbers are regrouped. Associative Property

  10. Check It Out! Example 2 Simplify each expression. Justify each step. A. 17 + 14 + 3 B. 12  3  5…You try it! 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

  11. 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

  12. 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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