Which of the following shows the correct pairing of a property of operations and its example?(1 point)
A) 2(a+3) = 2a+6; Associative Property
B) 2a +3b = 3b + 2a; Distributive Property
C) 2a + 3b = 3b + 2a; Commutative Property
D) 2(a+3) = 2a+6; Commutative Property
C) 2a + 3b = 3b + 2a; Commutative Property
To determine the correct pairing of a property of operations and its example, we need to understand the meaning of each property and then analyze the given examples.
1. Associative Property: This property states that the grouping of numbers being operated upon does not affect the outcome. In other words, when adding or multiplying numbers, you can change the grouping without changing the result.
2. Distributive Property: This property shows the relationship between multiplication and addition or subtraction. It states that multiplying a number by a sum or difference is the same as multiplying the number by each term individually and then adding or subtracting the results.
3. Commutative Property: This property deals with the order in which operations or numbers are arranged. It states that changing the order of operations or the order of the numbers being added or multiplied does not affect the result.
Let's analyze each option:
A) 2(a + 3) = 2a + 6; Associative Property
In this example, we see the expression is not being grouped. Therefore, it does not demonstrate the Associative Property.
B) 2a + 3b = 3b + 2a; Distributive Property
In this example, we can see that the order of the terms is reversed without affecting the result. This demonstrates the Commutative Property, not the Distributive Property.
C) 2a + 3b = 3b + 2a; Commutative Property
In this example, we see that the order of the terms is reversed without affecting the result. This precisely demonstrates the Commutative Property.
D) 2(a + 3) = 2a + 6; Commutative Property
Similar to option A, this example does not demonstrate any property since there is no rearrangement.
Based on the analysis, the correct pairing would be:
C) 2a + 3b = 3b + 2a; Commutative Property
WHAT IS THE ANSWER
The correct pairing of a property of operations and its example is:
A) 2(a+3) = 2a+6; Associative Property
This equation demonstrates the Associative Property because adding parentheses or changing their placement does not affect the outcome of the expression.