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

2. Holt CA Course 1 1-4Properties of Numbers You can multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

3. Holt CA Course 1 1-4Properties of Numbers 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 addends is 0. Identity Property 7 + 9 = 9 + 7The order of the numbers is switched. Commutative Property

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

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

6. Holt CA Course 1 1-4Properties of Numbers Check It Out! 1. Tell which property is represented. (5  1)  2 = 5  (1  2) The numbers are regrouped. Associative Property 2. Simplify each expression. Justify each step. 17 + 14 + 3 17+ 3+ 14Commutative Property Associative Property(17+ 3)+ 14 = 20 + 14 Add. = 34

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