1-2 Properties of Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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

1-2 Properties of Numbers 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

1-2 Properties of Numbers Learn how to identify properties of numbers and use them to simplify numerical expressions.

1-2 Properties of Numbers Vocabulary Commutative Property Associative Property Identity Property Distributive Property

1-2 Properties of Numbers

1-2 Properties of Numbers

1-2 Properties of Numbers

1-2 Properties 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 factors is 0. Identity Property = The order of the numbers is switched. Commutative Property

1-2 Properties 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

1-2 Properties 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.

1-2 Properties of Numbers 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.

1-2 Properties 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.

1-2 Properties 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) = Use the Distributive Property. Multiply. = 324 Subtract. Add. 6(54) = 6(50 + 4)

1-2 Properties 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)

1-2 Properties of Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

1-2 Properties 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,

1-2 Properties of Numbers 1. Identify the property that is represented. ( ) + 7 = 21 + (16 + 7) A. Identity Property B. Associative Property C. Commutative Property D. Distributive Property Lesson Quiz for Student Response Systems

1-2 Properties of Numbers 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

1-2 Properties of Numbers 3. Simplify the expression 20 · 11 · 5. Then identify the correct justification for each step. A. 20 · 11 · 5 = 20 · 5 · 11Commutative Property = (20 · 5) · 11Associative Property = 100 · 11 Multiply. = 1,100 B. 20 · 11 · 5 = 11 · 20 · 5Commutative Property = (11 · 20) · 5Associative Property = 110 · 5 Multiply. = 550 Lesson Quiz for Student Response Systems

1-2 Properties of Numbers 4. Simplify the expression 53 + (11 + 7). Then identify the correct justification for each step. A (11 + 7) = 11 + (53 + 7)Associative Property = ( ) + 7Commutative Property = Add. = 67 B (11 + 7) = 53 + (7 + 11)Commutative Property = (53 + 7) + 11Associative Property = Add. = 71 Lesson Quiz for Student Response Systems

1-2 Properties of Numbers 5. Use the Distributive Property to identify the product of 8(20 + 2). A. 196 B. 113 C. 176 D. 85 Lesson Quiz for Student Response Systems