Commutative and Associative Properties

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Commutative Property of Addition: The order in which the terms of a sum are added does not change the sum.a + b = b + a5 + 7 = 7 + 5 12= 12Commutative Property of Multiplication: The order in which the terms of a product are multiplied does not change the product.ab = ba4(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) 5 + 4 = 2 + 7

9 = 9

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.

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

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

3 Identify the property of (3 x -4) x 8 = 3 x (-4 x 8)

A Commutative Property of AdditionB Commutative Property of MultiplicationC Associative Property of AdditionD Asociative Property of Multiplication

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

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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 7x

2 4x

2y

and 7xy

2

4 Identify all of the terms like 2x

A 5xB 3x

2

C 5yD 12yE 2

5 Identify all of the terms like 8y

A 9yB 4y

2

C 7yD 8E -18x

6 Identify all of the terms like 8xy

A 8xB 3x

2y

C 39xyD 4yE -8xy

7 Identify all of the terms like 2y

A 51wB 2xC 3yD 2wE -10y

8 Identify all of the terms like 14x2

A -5xB 8x

2

C 13y2

D xE -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 =15x9v-2v = 7v

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

2f + 15Sometimes there will be both coeffients and constants to

be combined.3g + 7 + 8g - 2

11g + 5Notice that the sign before a given term goes with the

number.

Try These:

1.) 2b +6g(3) + 4f + 9f

2.) 9j + 3 + 24h + 6 + 7h + 3

3.) 7a + 4 + 2a -1 9 + 8c -12 + 5c

4.) 8x + 56xy + 5y

9 8x + 3x = 11x

A TrueB False

10 7x + 7y = 14xy

A TrueB False

11 2x + 3x = 5x

A TrueB False

12 9x + 5y = 14xy

A TrueB False

13 6x + 2x = 8x2

A TrueB False

14 -15y + 7y = -8y

A TrueB False

15 -6 + y + 8 = 2y

A TrueB False

16 -7y + 9y = 2y

A TrueB False

17 9x + 4 + 2x =

A 15x B 11x + 4 C 13x + 2x D 9x + 6x

18 12x + 3x + 7 - 5

A 15x + 7 - 5 B 13x C 17x D 15x + 2

19 -4x - 6 + 2x - 14

A -22x B -2x - 20 C -6x +20 D 22x