Commutative and Associative Properties Return to table of contents

Commutative Property of Addition: The order in which the terms of a sum are added does not change the sum. a + b = b + a = = 12 Commutative Property of Multiplication: The order in which the terms of a product are multiplied does not change the product. ab = ba 4(5) = 5(4)

Associative Property of Addition: The order in which the terms of a sum are grouped does not change the sum. (a + b) + c = a + (b + c) (2 + 3) + 4 = 2 + (3 + 4) = = 9

The Associative Property is particularly useful when you are combining integers. Example: (-4)= (-4) + 9=Changing it this way allows for the = negatives to be added together first. -10

Associative Property of Multiplication: The order in which the terms of a product are grouped does not change the product.

1Identify the property of = 3 + (-5) ACommutative Property of Addition BCommutative Property of Multiplication CAssociative Property of Addition DAssociative Property of Multiplication

2Identify the property of a + (b + c) = (a + c) + b ACommutative Property of Addition BCommutative Property of Multiplication CAssociative Property of Addition DAssociative Property of Multiplication

3Identify the property of (3 x -4) x 8 = 3 x (-4 x 8) ACommutative Property of Addition BCommutative Property of Multiplication CAssociative Property of Addition DAsociative Property of Multiplication

Discuss why using the associative property would be useful with the following problems: (-4) x 3 x x 7 x (-6)

Combining Like Terms Return to table of contents

An Expression - contains numbers, variables and at least one operation.

Like terms: terms in an expression that have the same variable raised to the same power Examples: LIKE TERMS NOT LIKE TERMS 6x and 2x 6x 2 and 2x 5y and 8y 5x and 8y 4x 2 and 7x 2 4x 2 y and 7xy 2

4 Identify all of the terms like 2x A5x B3x 2 C5y D12y E2

5 Identify all of the terms like 8y A9y B4y 2 C7y D8 E-18x

6 Identify all of the terms like 8xy A8x B3x 2 y C39xy D4y E-8xy

7 Identify all of the terms like 2y A51w B2x C3y D2w E-10y

8 Identify all of the terms like 14x 2 A-5x B8x 2 C13y 2 Dx E-x 2

If two or more like terms are being added or subtracted, they can be combined. To combine like terms add/subtract the coefficient but leave the variable alone. 7x +8x =15x 9v-2v = 7v

Sometimes there are constant terms that can be combined f + 6 = 2f + 15 Sometimes there will be both coeffients and constants to be combined. 3g g g + 5 Notice that the sign before a given term goes with the number.

Try These: 1.) 2b +6g(3) + 4f + 9f 2.) 9j h h ) 7a a c c 4.) 8x + 56xy + 5y

98x + 3x = 11x A True B False

107x + 7y = 14xy A True B False

11 2x + 3x = 5x A True B False

12 9x + 5y = 14xy A True B False

13 6x + 2x = 8x 2 A True B False

14 -15y + 7y = -8y A True B False

y + 8 = 2y A True B False

16 -7y + 9y = 2y A True B False

179x x = A15x B11x + 4 C13x + 2x D9x + 6x

1812x + 3x A15x B13x C17x D15x + 2

19-4x x - 14 A-22x B-2x - 20 C-6x +20 D22x