2. Commutative and Associative Properties
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3. 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.

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)
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.

5. The Associative Property is particularly useful when you are combining integers.
Example:
(-4)=
-15 + (-4) + 9= Changing it this way allows for the
= negatives to be added together first.
-10

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

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

8. Identify the property of a + (b + c) = (a + c) + b2
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

9. Discuss why using the associative property would be useful with the following problems:
(-4)
x 3 x 0
x 7 x -2
(-6)

10. Combining Like Terms
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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 x2 and 2x
5y and 8y x and 8y
4x2 and 7x x2y and 7xy2

13. Identify all of the terms like 2x4
Identify all of the terms like 2x A 5x B
3x2 C 5y D
12y E 2
Answer: A

14. Identify all of the terms like 8y5
Identify all of the terms like 8y A 9y B
4y2 C 7y D 8 E
-18x
Answer: A, C

15. 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

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

17. 9
8x + 3x = 11x
A True
B False
Answer: A True

18. 10
7x + 7y = 14xy
A True
B False
Answer: B False

19. 12
9x + 5y = 14xy
A True
B False
Answer: B False

20. 15
-6 + y + 8 = 2y
A True
B False
Answer: B False

21. 19
-4x x - 14 A
-22x B
-2x - 20 C
-6x +20 D
22x
Answer: B