1. Objectives
Use the Commutative, Associative, and Distributive Properties to simplify expressions.

3. 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

4. Example 1B: Using the Commutative and Associative Properties
Simplify.
Use the Commutative Property.
( ) + (16 + 4)
Use the Associative Property to make groups of compatible numbers.
(100) + (20)
120

5. Check It Out! Example 1a
Simplify.
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers. 21

6. Check It Out! Example 1b
Simplify.
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
( ) + (58 + 2)
(500) + (60)
560

7. ( ) 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

8. 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.

9. 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
5(60) – 5(1)
Use the Distributive Property.
Multiply.
295
Subtract.

10. 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
8(30) + 8(3)
Use the Distributive Property.
Multiply.
264
Add.

11. 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.

12. Lesson Quiz: Part I
Simplify each expression.
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