1. Commutative and Associative Properties Return to table of contents

2. 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)

3. 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

4. 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

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

6. 1Identify the property of -5 + 3 = 3 + (-5) ACommutative Property of Addition BCommutative Property of Multiplication CAssociative Property of Addition DAssociative Property of Multiplication

7. 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

8. 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

9. 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)

10. Combining Like Terms Return to table of contents

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

12. 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

13. 4 Identify all of the terms like 2x A5x B3x 2 C5y D12y E2

14. 5 Identify all of the terms like 8y A9y B4y 2 C7y D8 E-18x

15. 6 Identify all of the terms like 8xy A8x B3x 2 y C39xy D4y E-8xy

16. 7 Identify all of the terms like 2y A51w B2x C3y D2w E-10y

17. 8 Identify all of the terms like 14x 2 A-5x B8x 2 C13y 2 Dx E-x 2

18. 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

19. Sometimes there are constant terms that can be combined. 9 + 2f + 6 = 2f + 15 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.

20. Try These: 1.) 2b +6g(3) + 4f + 9f 2.) 9j + 3 + 24h + 6 + 7h + 3 3.) 7a + 4 + 2a -19 + 8c -12 + 5c 4.) 8x + 56xy + 5y

21. 98x + 3x = 11x A True B False

22. 107x + 7y = 14xy A True B False

23. 11 2x + 3x = 5x A True B False

24. 12 9x + 5y = 14xy A True B False

25. 13 6x + 2x = 8x 2 A True B False

26. 14 -15y + 7y = -8y A True B False

27. 15 -6 + y + 8 = 2y A True B False

28. 16 -7y + 9y = 2y A True B False

29. 179x + 4 + 2x = A15x B11x + 4 C13x + 2x D9x + 6x

30. 1812x + 3x + 7 - 5 A15x + 7 - 5 B13x C17x D15x + 2

31. 19-4x - 6 + 2x - 14 A-22x B-2x - 20 C-6x +20 D22x