Algebra 1 Notes: Lesson 1-6: Commutative and Associative Properties

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Presentation transcript:

Algebra 1 Notes: Lesson 1-6: Commutative and Associative Properties

Vocabulary Commutative Property

Vocabulary Commutative Property - The order in which you add or multiply numbers does not change their sum or product.

Vocabulary Commutative Property - The order in which you add or multiply numbers does not change their sum or product. a + b = b + a a  b = b  a

Vocabulary Commutative Property - The order in which you add or multiply numbers does not change their sum or product. a + b = b + a a  b = b  a Associative Property

Vocabulary Commutative Property - The order in which you add or multiply numbers does not change their sum or product. a + b = b + a a  b = b  a Associative Property - The way you group three or more numbers when adding or multiplying does not change their sum or product. (a + b) + c = a + (b + c) (a  b)  c = a  (b  c)

Evaluate 2  8  5  7

Evaluate 2  8  5  7 2  5  8  7

Evaluate 2  8  5  7 2  5  8  7 10  56

Evaluate 2  8  5  7 2  5  8  7 10  56 560

Evaluate 2  25  7  4

Evaluate 2  25  7  4 25  4  2  7

Evaluate 2  25  7  4 25  4  2  7 100  14

Evaluate 2  25  7  4 25  4  2  7 100  14 1,400

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b +

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b + 32

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b + 32 + 7b

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b + 32 + 7b

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b + 32 + 7b = 23b

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b + 32 + 7b = 23b + 32

Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b + 32 + 7b = 23b + 32

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression.

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3( + )

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3( + )

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3(3x + 2y)

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3(3x + 2y)

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3(3x + 2y) +

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3(3x + 2y) +

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3(3x + 2y) + 5( + )

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3(3x + 2y) + 5( + )

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3(3x + 2y) + 5(x + 4y)

Example 2 Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y. Write an algebraic expression for the verbal expression. 3(3x + 2y) + 5(x + 4y)

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y)

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 3(3x)

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 3(3x) + 3(2y)

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 3(3x) + 3(2y) + 5(x)

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 3(3x) + 3(2y) + 5(x) + 5(4y)

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 3(3x) + 3(2y) + 5(x) + 5(4y) Distributive Property

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 3(3x) + 3(2y) + 5(x) + 5(4y) Distributive Property

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive Property = 14x

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive Property = 14x

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive Property = 14x

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive Property = 14x + 26y

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive Property = 14x + 26y Substitution

Example 2 b) Simplify the expression and indicate the properties used. 3(3x + 2y) + 5(x + 4y) = 9x + 6y + 5x + 20y Distributive Property = 14x + 26y Substitution

Assignment Pg. 35 16 – 26 (even) 28 – 31 (all) 32 – 48 (even)