1. 1.6 Commutative and Associative Properties

2. Associative Property Commutative Property
How you group 3 or more items does not matter for addition or multiplication.
(1 + 2) + 3 = 1 + (2 + 3)
[(1)(2)]3 = 1[(2)(3)]
Commutative
Property
Order does not matter for addition or multiplication.
3 + 2 = 2 + 3
3(2) = 2(3)

3. It makes it easier! 83 + 12 + 17 + 8 83 + 17 + 12 + 8 100 + 20 120
Check Your Progress #1A & B

4. Use Multiplication Properties
Example #2: Evaluate 8 • 2 • 3 • 5 using properties of numbers. Name the property used in each step.
8 • 2 • 3 • 5
8 • 3 • 2 • 5 Commutative
(8 • 3) • (2 • 5) Associative
24 • 10 Multiply
240

5. Check Your Progress 2A &2B

6. Put it all together to simplify.
8(2b + 4) + 7b
Distribute 16b b
Comm. 16b + 7b + 32
Substitute 23b + 32
Try 3(4x + 2) + 2x

7. Ex. #3: Four times the sum of a and b increased by twice the sum of a and 2b
Write an algebraic expression.
4(a + b) + 2(a + 2b)
Solve
4a + 4b + 2a + 2(2b) Distribute
4a + 4b + 2a + 4b Multiply
4a + 2a + 4b + 4b Commutative
6a + 8b Combine Like Terms

8. Check Your Progress #3A & B Homework Assignment #5
p even, 48-49