1.6 Commutative and Associative Properties

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Presentation transcript:

1.6 Commutative and Associative Properties

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)

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

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

Check Your Progress 2A &2B

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

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

Check Your Progress #3A & B Homework Assignment #5 p. 36 12-42 even, 48-49