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 5 + 7 = 7 + 5 12= 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) Teacher’s instructions: When you commute to work you are going back and forth but it is the same route. So it is the same backwards and forwards.

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) 5 + 4 = 2 + 7 9 = 9 Teacher’s instructions: You are at a party. You associate with Alan and Barbara and then with Chris. This is the same as associating with Barbara and Chris and then Alan, just in a different order.

The Associative Property is particularly useful when you are combining integers. Example: -15 + 9 + (-4)= -15 + (-4) + 9= Changing it this way allows for the -19 + 9 = 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.

Identify the property of -5 + 3 = 3 + (-5) 1 Identify the property of -5 + 3 = 3 + (-5) A Commutative Property of Addition B Commutative Property of Multiplication C Associative Property of Addition D Associative Property of Multiplication Answer: A

Identify the property of a + (b + c) = (a + c) + b 2 Identify the property of a + (b + c) = (a + c) + b A Commutative Property of Addition B Commutative Property of Multiplication C Associative Property of Addition D Associative Property of Multiplication Answer: C

Discuss why using the associative property would be useful with the following problems: 1. 4 + 3 + (-4) 2. -9 x 3 x 0 3. -5 x 7 x -2 4. -8 + 1 + (-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 6x2 and 2x 5y and 8y 5x and 8y 4x2 and 7x2 4x2y and 7xy2

Identify all of the terms like 2x 4 Identify all of the terms like 2x A 5x B 3x2 C 5y D 12y E 2 Answer: A

Identify all of the terms like 8y 5 Identify all of the terms like 8y A 9y B 4y2 C 7y D 8 E -18x Answer: A, C

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. 9 + 2f + 6 = Sometimes there will be both coeffients and constants to be combined. 3g + 7 + 8g - 2 11g + 5 Notice that the sign before a given term goes with the number.

9 8x + 3x = 11x A True B False Answer: A True

10 7x + 7y = 14xy A True B False Answer: B False

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

15 -6 + y + 8 = 2y A True B False Answer: B False

19 -4x - 6 + 2x - 14 A -22x B -2x - 20 C -6x +20 D 22x Answer: B