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1-6 Properties Warm Up Evaluate. 1. 2 + 5 3 – 7 10 2. 5(3 – 1) ÷ (3 + 2) 2 3. (4 + 1)2 – 8 ÷ 2 21 4. 12 ÷ 3 6 – 20 4 Course 2 1-6 Properties Learn how to identify properties of rational numbers and use them to simplify numerical expressions. Course 2 1-6 Properties Vocabulary Commutative Property Associative Property Identity Property Distributive Property Course 2 1-6 Properties Commutative Property: allows you to add or multiply in any order. (order is switched) Example: 4 + 8 = 8 + 4 3·9=9·3 Course 2 1-6 Properties Associative Property: When you add or multiply you can regroup the numbers in any combination. (regrouping) Example: ( 4 + 5 ) + 1 = 4 + ( 5 + 1 ) (9 · 2 ) · 6 = 9 · ( 2 · 6 ) Course 2 1-6 Properties Identity Property: the sum of 0 and any number is the number, and the product of 1 and any number is the number.(one of the factors is 0 or 1) Example: 4 + 0 = 4 8·1=8 Course 2 1-6 Properties Example 1 Tell which property is represented. A. (2 6) 1 = 2 (6 1) The numbers are regrouped. Associative Property B. 3 + 0 = 3 One of the factors is 0. Identity Property C. 7 + 9 = 9 + 7 Commutative Property Course 2 The order of the variables is switched. 1-6 Properties Example 2 Tell which property is represented. A. 7 1 = 7 One of the factors is 1. Identity Property B. 3 + 4 = 4 + 3 Commutative Property The order of the numbers is switched. C. (5 1) 2 = 5 (1 2) The numbers are regrouped. Associative Property Course 2 1-6 Properties Example 3 - Lets work these together. Simplify each expression. Justify each step. A. 21 + 16 + 9 21 + 16 + 9 = 16 + 9 + 21 = 16 + (9 + 21) = 16 + 30 B. 20 9 5 = 46 20 9 5 = 20 5 9 = 20 (5 9) = 20 45 = 900 Course 2 Commutative Property. Associative Property. Add. Commutative Property. Associative Property. Multiply. 1-6 Properties Example 4 – You try! Simplify each expression. Justify each step. A. 17 + 14 + 3 17 + 14 + 3 = 14 + 17 + 3 = 14 + (17 + 3) B. 12 3 5 = 14 + 20 = 34 12 3 5 = 3 5 12 = 3 (5 12) = 3 60 = 180 Course 2 Commutative Property. Associative Property. Add. Commutative Property. Associative Property. Multiply. 1-6 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. Course 2 1-6 Properties Example 5 Use the Distributive Property to find 6(54). Method 1: 6(54) = 6(50 + 4) = 300 + 24 Use the Distributive Property. Multiply. = 324 Add. = (6 50) + (6 4) Course 2 Rewrite 54 as 50 + 4. 1-6 Properties Example 6 Use the Distributive Property to find 8(19). Method 1: 8(19) = 8(10 + 9) = (8 10) + (8 9) Course 2 Rewrite 19 as 10 + 9. Use the Distributive Property. = 80 + 72 Multiply. = 152 Add. 1-6 Properties Summary Tell which property is represented. 1. 17 1 = 17 Identity Property Associative Property 3. 2 16 = 16 2 Commutative Property 2. (12 + 14) + 5 = 12 + (14 + 5) Simplify each expression. Justify each step. 4. 4 12 25 1,200 5. 48 + (15 + 2) 65 Use the Distributive Property to find each product. 6. 6 (12 + 5) 7. (20 – 7) 9 Course 2 102 117