**Commutative Property**

**:**

Change Order – The order doesn’t matter; you will get the same answer.

Commutative of Addition: 4 + 5 = 5+4

Commutative of Multiplication: (6)(7) = (7)(6)

**Associative Property**:

Grouping Changes – The parenthesis will move but you will get the same answer

Associative of Addition: (4 + 6) + 5 = 4+ (6 + 5)

Associative of Multiplication: (4 x 2) x 3 = 4 x (2 x 3)

**Additive Identity Property**:

Any # plus 0 equals the original number.

Example: -5 + 0 = -5

**Multiplicative Identity Property**:

Any number multiplied by 1 equals the original number

Example: 7 x 1 = 7

**Multiplicative Inverse**:

Any number multiplied by its

**reciprocal**equals 1.

Example: 2 x ½ = 1

**Additive Inverse Property**:

Any number plus its opposite equals 0.

Example: -5 + 5 = 0

**Multiplicative Property of Zero**:

Any number multiplied by 0 equals 0

Example: -23 x 0 = 0

Extra Credit Problems:

Identify the property shown by each example.

**1. 4 + 5 + 6 = 6 + 4 + 5**

**2. a(0) = 0**

**3. 2 (½) = 1**

**4. (a)(d)=(d)(a)**

**5. (8+2)+4 = 8+(2+4)**

**6. 8(1) = 8**

**7. 42 – 6a = 6(7-a)**

**8. a + 0 = a**