1. Course 2 1-6 Properties Learn how to identify properties of rational numbers and use them to simplify numerical expressions.

2. Course 2 1-6 Properties Vocabulary Commutative Property Associative Property Identity Property Distributive Property

3. Course 2 1-6 Properties

4. Course 2 1-6 Properties

5. Course 2 1-6 Properties

6. Course 2 1-6 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 variables is switched. Commutative Property

7. Course 2 1-6 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

8. Course 2 1-6 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.

9. Course 2 1-6 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.

10. Course 2 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.

11. Course 2 1-6 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)

12. Course 2 1-6 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)

13. Course 2 1-6 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