Warm Up Evaluate. 1. 2 + 5  3 – 7 2. 5(3 – 1) ÷ (3 + 2) 10 3. (4 + 1)2 – 8 ÷ 2 4. 12 ÷ 3  6 – 20 10 2 21 4

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

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

Vocabulary Commutative Property Associative Property Identity Property Distributive Property

Tell which property is represented. A. (2  6)  1 = 2  (6  1) 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 numbers is switched. Commutative Property

Tell which property is represented. A. 7  1 = 7 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

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) Associative Property. = 16 + 30 Add. = 46 20  9  5 = 20  5  9 Commutative Property. = 20  (5  9) Associative Property. = 20  45 Multiply. = 900

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) Associative Property. = 14 + 20 Add. = 34 12  3  5 = 3  5  12 Commutative Property. = 3  (5  12) Associative Property. = 3  60 Multiply. = 180

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.

Use the Distributive Property to find 6(54). Method 1: Additional Example 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: Method 2: 6(54) = 6(50 + 4) Rewrite 54 as 50 + 4. Use the Distributive Property. = (6  50) + (6  4) = 300 + 24 Multiply. = 324 Add. 6(54) = 6(60 – 6) Rewrite 54 as 60 – 6. = (6  60) – (6  6) Use the Distributive Property. Multiply. = 360 - 36 = 324 Subtract.

Use the Distributive Property to find 8(19). Method 1: Check It Out: Example 3 Use the Distributive Property to find 8(19). Method 1: Method 2: 8(19) = 8(10 + 9) Rewrite 19 as 10 + 9. Use the Distributive Property. = (8  10) + (8  9) = 80 + 72 Multiply. = 152 Add. 8(19) = 8(20 – 1) Rewrite 19 as 20 – 1. = (8  20) – (8  1) Use the Distributive Property. Multiply. = 160 – 8 = 152 Subtract.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Identity Property Associative Property 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

Lesson Quiz for Student Response Systems 1. Identify the property that is represented. (21 + 16) + 7 = 21 + (16 + 7) A. Identity Property B. Associative Property C. Commutative Property D. Distributive Property

Lesson Quiz for Student Response Systems 2. Identify the property that is represented. 17 · 9 = 9 · 17 A. Associative Property B. Commutative Property C. Distributive Property D. Identity Property

Lesson Quiz for Student Response Systems 3. Simplify the expression 20 · 11 · 5. Then identify the correct justification for each step. A. 20 · 11 · 5 = 20 · 5 · 11 Commutative Property = (20 · 5) · 11 Associative Property = 100 · 11 Multiply. = 1,100 B. 20 · 11 · 5 = 11 · 20 · 5 Commutative Property = (11 · 20) · 5 Associative Property = 110 · 5 Multiply. = 550

Lesson Quiz for Student Response Systems 4. Simplify the expression 53 + (11 + 7). Then identify the correct justification for each step. A. 53 + (11 + 7) = 11 + (53 + 7) Associative Property = (11 + 53) + 7 Commutative Property = 60 + 7 Add. = 67 B. 53 + (11 + 7) = 53 + (7 + 11) Commutative Property = (53 + 7) + 11 Associative Property = 60 + 11 Add. = 71

Lesson Quiz for Student Response Systems 5. Use the Distributive Property to identify the product of 8(20 + 2). A. 196 B. 113 C. 176 D. 85