Which of the following represents the associative property?

Which of the following represents the associative property?

• A. A + (B + C) = (A + B) + C
• B. A x (B + C) = A x B + A x C
• C. A + B = B + A
• D. A + B + C = B + C + A

Answer: (A)

The associative property refers to the way in which numbers are grouped in addition or multiplication does not affect the final result. The correct representation of this property is when the grouping of the numbers is changed but their order remains the same. In the case of the first choice, the equation A + (B + C) = (A + B) + C showcases this property perfectly. Here, regardless of how you group the numbers (whether you add B and C first, or A and B first), the sum remains the same. This illustrates the core concept of the associative property for addition. The other options represent different mathematical properties. The second option depicts the distributive property, which shows how multiplication distributes over addition. The third option illustrates the commutative property of addition, indicating that the order of addends does not change the sum. The last option also reflects the commutative property but with three addends.

The associative property refers to the way in which numbers are grouped in addition or multiplication does not affect the final result. The correct representation of this property is when the grouping of the numbers is changed but their order remains the same.

In the case of the first choice, the equation A + (B + C) = (A + B) + C showcases this property perfectly. Here, regardless of how you group the numbers (whether you add B and C first, or A and B first), the sum remains the same. This illustrates the core concept of the associative property for addition.

The other options represent different mathematical properties. The second option depicts the distributive property, which shows how multiplication distributes over addition. The third option illustrates the commutative property of addition, indicating that the order of addends does not change the sum. The last option also reflects the commutative property but with three addends.