Holt CA Course 1 1-4Properties of Numbers Warm Up Warm Up California Standards Lesson Presentation Preview

Holt CA Course 1 1-4Properties of Numbers Warm Up Evaluate  3 – (3 – 1) ÷ (3 + 2) 3. (4 + 1) 2 – 8 ÷ ÷ 3  6 –

Holt CA Course 1 1-4Properties of Numbers

Holt CA Course 1 1-4Properties of Numbers Vocabulary Commutative Property Associative Property Identity Property Distributive Property

Holt CA Course 1 1-4Properties of Numbers

Holt CA Course 1 1-4Properties of Numbers

Holt CA Course 1 1-4Properties of Numbers

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.

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

Holt CA Course 1 1-4Properties of Numbers Additional Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A B. 20  9  = Commutative Property = 16 + (9 + 21) = Associative Property = 46 Add. 20  9  5 = 20  5  9 Commutative Property = 20  (5  9) = 20  45 Associative Property = 900 Multiply.

Holt CA Course 1 1-4Properties of Numbers 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 = = 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)

Holt CA Course 1 1-4Properties of Numbers Check It Out! Example 1 Tell which property is represented. A. 7  1 = 7 B = 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. Commutative Property (5  1)  2 = 5  ( 1  2)The numbers are regrouped. Associative Property

Holt CA Course 1 1-4Properties of Numbers Check It Out! Example 2 Simplify each expression. Justify each step. A B. 12  3  = Commutative Property = 14 + (17 + 3) = Associative Property = 34 Add. 12  3  5 = 3  5  12 Commutative Property = 3  (5  12) = 3  60 Associative Property = 180 Multiply.

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 = = 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)

Holt CA Course 1 1-4Properties of Numbers Lesson Quiz Tell which property is represented  1 = ( ) + 5 = 12 + (14 + 5) 3. 2  16 = 16  2 Simplify each expression. Justify each step  12  (15 + 2) Use the Distributive Property to find each product  (12 + 5) 7. (20 – 7)  9 Identity Property Associative Property Commutative Property 1,