1. Holt CA Course 1 1-4Properties of Numbers AF1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process. California Standards

2. Holt CA Course 1 1-4Properties of Numbers VOCABULARY CARDS Commutative Property Associative Property Identity Property Distributive Property

3. Holt CA Course 1 1-4Properties of Numbers

4. Holt CA Course 1 1-4Properties of Numbers

5. Holt CA Course 1 1-4Properties of Numbers

6. Holt CA Course 1 1-4Properties of Numbers

7. Holt CA Course 1 1-4Properties of Numbers Teacher Example 1: Identifying Properties of Addition and Multiplication Tell which property is represented. 1A. (2  6)  1 = 2  (6  1) 1B. 3 + 0 = 3 1C. 7 + 9 = 9 + 7 (2  6)  1 = 2  (6  1) The numbers are regrouped. Associative Property 3 + 0 = 3 One of the addends is 0. Identity Property 7 + 9 = 9 + 7The order of the numbers is switched. Commutative Property

8. Holt CA Course 1 1-4Properties of Numbers Student Practice 1: Tell which property is represented. 1A. 7  1 = 7 1B. 3 + 4 = 4 + 3 1C. (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

9. Holt CA Course 1 1-4Properties of Numbers Teacher Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. 2A. 21 + 16 + 9 2B. 20  9  5 21 + 16 + 9 = 16 + 9 + 21Commutative 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.

10. Holt CA Course 1 1-4Properties of Numbers Student Practice 2: 2A. (5  1)  2 = 5  (1  2) 2B. 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.

11. Holt CA Course 1 1-4Properties of Numbers 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.

12. Holt CA Course 1 1-4Properties of Numbers Teacher 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. = 324Subtract. Add. 6(54) = 6(50 + 4)

13. Holt CA Course 1 1-4Properties of Numbers Student Practice 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)

14. Holt CA Course 1 1-4Properties of Numbers 1.4 Warm- Up Identify the Property 1. 2. 3.