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

Responses

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
; Distributive Property
2 A plus 3 b is equal to 3 b plus 2 A ; Distributive Property

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

2(a+3) = 2a+6
; Associative Property

1 answer

The correct pairing of a property of operations and its example is:

2(a + 3) = 2a + 6; Distributive Property

Here's why:

  • Distributive Property states that a(b + c) = ab + ac. In the example, you are distributing the 2 across the expression (a + 3), hence it exemplifies the Distributive Property.

The other pairs are incorrect as follows:

  1. 2(a + 3) = 2a + 6; Commutative Property - Incorrect (actually demonstrates Distributive Property).
  2. 2a + 3b = 3b + 2a; Distributive Property - Incorrect (this is an example of the Commutative Property).
  3. 2a + 3b = 3b + 2a; Commutative Property - Correct (this is indeed the Commutative Property).
  4. 2(a + 3) = 2a + 6; Associative Property - Incorrect (this is not an example of the Associative Property, as it demonstrates the Distributive Property).

So, the last two examples correctly show the properties, but only the first identifies the corresponding property correctly. If you are looking for the only correct pairing, it would be the last response; however, if your goal was to identify the true distributive property as accurately matched, it's the first.

In conclusion, if you’re looking for the correct identification:

  • Best response: 2(a + 3) = 2a + 6; Distributive Property for the Distributive Property.