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1-6

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

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  1. 1-6 Properties Warm Up Problem of the Day Lesson Presentation Course 2

  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

  3. 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

  4. Learn how to identify properties of rational numbers and use them to simplify numerical expressions.

  5. Vocabulary Commutative Property Associative Property Identity Property Distributive Property

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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.

  11. 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

  12. 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

  13. 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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