According to the associative property, how can the expression (a + b) + c be rearranged?

According to the associative property, how can the expression (a + b) + c be rearranged?

• A. a + (b + c)
• B. (b + c) + a
• C. a + b + c
• D. (a + c) + b

Answer: (A)

The associative property refers to the principle that the way in which numbers are grouped in addition (or multiplication) does not affect the sum (or product). Applying this property to the expression (a + b) + c allows us to regroup the terms without changing the overall value of the expression. In this case, the expression (a + b) + c can indeed be rearranged as a + (b + c). This new grouping changes which terms are added together first, but because of the associative property, the result remains the same, demonstrating that addition is flexible regarding how terms are associated. The other options either represent different groupings that don't adhere to the essence of the associative property or simply present the expression in varied forms without emphasizing the associative aspect. For instance, (b + c) + a may confuse the context of the original expression, while a + b + c merely lists the terms without emphasizing any association. Meanwhile, (a + c) + b alters the initial relationship within the grouping entirely, failing to demonstrate the intended associative property.

The associative property refers to the principle that the way in which numbers are grouped in addition (or multiplication) does not affect the sum (or product). Applying this property to the expression (a + b) + c allows us to regroup the terms without changing the overall value of the expression.

In this case, the expression (a + b) + c can indeed be rearranged as a + (b + c). This new grouping changes which terms are added together first, but because of the associative property, the result remains the same, demonstrating that addition is flexible regarding how terms are associated.

The other options either represent different groupings that don't adhere to the essence of the associative property or simply present the expression in varied forms without emphasizing the associative aspect. For instance, (b + c) + a may confuse the context of the original expression, while a + b + c merely lists the terms without emphasizing any association. Meanwhile, (a + c) + b alters the initial relationship within the grouping entirely, failing to demonstrate the intended associative property.