Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1-4 Properties of Numbers Preview Warm Up California Standards Lesson Presentation Holt CA Course 1 1-4 Properties of Numbers Warm Up Evaluate. 1. 2 + 5 3 – 7 10 2. 5(3 – 1) ÷ (3 + 2) 2 3. (4 + 1)2 – 8 ÷ 2 21 4. 12 ÷ 3 6 – 20 4 Holt CA Course 1 1-4 Properties of Numbers California Standards AF1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process. Holt CA Course 1 1-4 Properties of Numbers Vocabulary Commutative Property- add numbers in any order and multiply numbers in any order “switch order” Associative Property- add or multiply, you can group the numbers together in any combination “re-group” Identity Property- the sum of 0 and any number is the number, and the product of 1 and any number is the number Distributive Property- multiply numbers mentally by “breaking apart” one of the numbers and writing it as a sum or difference. Holt CA Course 1 1-4 Holt CA Course 1 Properties of Numbers 1-4 Holt CA Course 1 Properties of Numbers 1-4 Holt CA Course 1 Properties of Numbers 1-4 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. Holt CA Course 1 1-4 Properties of Numbers Additional Example 1: Identifying Properties of Addition and Multiplication Tell which property is represented. A. (2 6) 1 = 2 (6 1) (2 6) 1 = 2 (6 1) Associative Property The numbers are regrouped. B. 3 + 0 = 3 3+0=3 Identity Property One of the addends is 0. C. 7 + 9 = 9 + 7 7+9=9+7 Commutative Property Holt CA Course 1 The order of the numbers is switched. 1-4 Properties of Numbers Additional Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 21 + 16 + 9 = 16 + 9 + 21 = 16 + (9 + 21) = 16 + 30 Commutative Property Associative Property Add. = 46 B. 20 9 5 20 9 5 = 20 5 9 = 20 (5 9) Associative Property = 20 45 Multiply. = 900 Holt CA Course 1 Commutative Property 1-4 Properties of Numbers Additional Example 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: 6(54) = 6(50 + 4) = 300 + 24 Rewrite 54 as 50 + 4. Use the Distributive Property. Multiply. = 324 Add. = (6 50) + (6 4) Method 2: 6(54) = 6(60 – 6) = (6 60) – (6 6) = 360 – 36 = 324 Holt CA Course 1 Rewrite 54 as 60 – 6. Use the Distributive Property. Multiply. Subtract. 1-4 Properties of Numbers Check It Out! Example 1 Tell which property is represented. A. 7 1 = 7 71=7 Identity Property One of the factors is 1. B. 3 + 4 = 4 + 3 3+4=4+3 Commutative Property The order of the numbers is switched. C. (5 1) 2 = 5 (1 2) (5 1) 2 = 5 ( 1 2) Associative Property Holt CA Course 1 The numbers are regrouped. 1-4 Properties of Numbers Check It Out! Example 2 Simplify each expression. Justify each step. A. 17 + 14 + 3 17 + 14 + 3 = 14 + 17 + 3 = 14 + (17 + 3) B. 12 3 5 = 14 + 20 = 34 12 3 5 = 3 5 12 = 3 (5 12) = 3 60 = 180 Holt CA Course 1 Commutative Property Associative Property Add. Commutative Property Associative Property Multiply. 1-4 Properties of Numbers Check It Out! Example 3 Use the Distributive Property to find 8(19). Method 1: 8(19) = 8(10 + 9) = (8 10) + (8 9) Method 2: = 80 + 72 Multiply. = 152 Add. 8(19) = 8(20 – 1) = (8 20) – (8 1) = 160 – 8 = 152 Holt CA Course 1 Rewrite 19 as 10 + 9. Use the Distributive Property. Rewrite 19 as 20 – 1. Use the Distributive Property. Multiply. Subtract. 1-4 Properties of Numbers Lesson Quiz Tell which property is represented. 1. 17 1 = 17 Identity Property Associative Property 3. 2 16 = 16 2 Commutative Property 2. (12 + 14) + 5 = 12 + (14 + 5) Simplify each expression. Justify each step. 4. 4 12 25 1,200 5. 48 + (15 + 2) 65 Use the Distributive Property to find each product. 6. 6 (12 + 5) 7. (20 – 7) 9 Holt CA Course 1 102 117