Course Properties 1-6 Properties Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Course Properties Warm Up Evaluate  3 – (3 – 1) ÷ (3 + 2) 3. (4 + 1) 2 – 8 ÷ ÷ 3  6 –

Course Properties Problem of the Day Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy? 27

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

Course Properties Vocabulary Commutative Property Associative Property Identity Property Distributive Property

Course Properties

Course Properties

Course Properties

Course Properties 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 factors is 0. Identity Property = The order of the variables is switched. Commutative Property

Course Properties 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

Course Properties 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.

Course Properties Check It Out: Example 2A & B 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.

Course 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 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 = = 324 Use the Distributive Property. Multiply. 6(54) = 6(60 – 6) Rewrite 54 as 60 – 6. = (6  60) – (6  6) = Use the Distributive Property. Multiply. = 324 Subtract. Add. 6(54) = 6(50 + 4)

Course 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 = = 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)

Course Properties 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,