Which of the following shows the correct pairing of a property of operations and its example?(1 point)

Question

Responses

2(a+3) = 2a+6
; Associative Property
2 times open paren A plus 3 close paren is equal to 2 A plus 6 ; Associative Property

2a +3b = 3b + 2a
; Distributive Property
2 A plus 3 b is equal to 3 b plus 2 A ; Distributive Property

2(a+3) = 2a+6
; Commutative Property
2 times open paren A plus 3 close paren is equal to 2 A plus 6 ; Commutative Property

2a + 3b = 3b + 2a
; Commutative Property

Answer 1

Let's analyze the properties of operations and their examples:

1. Associative Property: This property relates to how numbers are grouped in an operation, but not the order. An example would be \( (a + b) + c = a + (b + c) \) or \( (ab)c = a(bc) \).

2. Commutative Property: This property deals with the order of numbers in an operation. For addition, it states that \( a + b = b + a \), and for multiplication, \( ab = ba \).

3. Distributive Property: This property relates to how multiplication distributes over addition. An example as you mentioned is \( a(b + c) = ab + ac \).

Now, looking at the provided responses:

1. (2(a+3) = 2a + 6; Associative Property: Incorrect. This is an application of the Distributive Property.

2. (2a + 3b = 3b + 2a; Distributive Property: Incorrect. This is actually an example of the Commutative Property.

3. (2(a+3) = 2a + 6; Commutative Property: Incorrect. This is again an application of the Distributive Property.

4. (2a + 3b = 3b + 2a; Commutative Property: Correct. This shows that the addition operation is commutative.

So the only correct pairing is:

(2a + 3b = 3b + 2a; Commutative Property.