Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions.
Example 1A: Using the Commutative and Associative Properties Simplify. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 11(5) 55
Example 1B: Using the Commutative and Associative Properties Simplify. 45 + 16 + 55 + 4 45 + 55 + 16 + 4 Use the Commutative Property. (45 + 55) + (16 + 4) Use the Associative Property to make groups of compatible numbers. (100) + (20) 120
Check It Out! Example 1a Simplify. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 21
Check It Out! Example 1b Simplify. 410 + 58 + 90 + 2 410 + 90 + 58 + 2 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. (410 + 90) + (58 + 2) (500) + (60) 560
( ) Check It Out! Example 1c Simplify. 1 2 7 • 8 1 2 8 • 7 Use the Commutative Property. ( ) 1 2 • 8 7 Use the Associative Property to make groups of compatible numbers. 4 • 7 28
The Distributive Property is used with Addition to Simplify Expressions. The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.
Example 2A: Using the Distributive Property with Mental Math Write the product using the Distributive Property. Then simplify. 5(59) 5(60 - 1) Rewrite 59 as 60 - 1. 5(60) – 5(1) Use the Distributive Property. 300 - 5 Multiply. 295 Subtract.
Example 2B: Using the Distributive Property with Mental Math Write the product using the Distributive Property. Then simplify. 8(33) 8(30 + 3) Rewrite 33 as 30 + 3. 8(30) + 8(3) Use the Distributive Property. 240 + 24 Multiply. 264 Add.
Check It Out! Example 2b Write the product using the Distributive Property. Then simplify. 12(98) 12(100 – 2) Rewrite 98 as 100 – 2. 12(100) – 12(2) Use the Distributive Property. 1200 – 24 Multiply. 1176 Subtract.
Lesson Quiz: Part I Simplify each expression. 1. 165 +27 + 3 + 5 200 2. 8 Write each product using the Distributive Property. Then simplify. 3. 5($1.99) 5($2) – 5($0.01) = $9.95 4. 6(13) 6(10) + 6(3) = 78