Question

Which equation shows an example of the associative property of addition?

A. (–4 + i ) + 4i = -4+ (i + 4i)
B. (4+i ) + 4i = 4i + (-41 + i)
C.4i * (-41 + i) = (4i - 4i) + (4i * i)
D. (-41 + i) + 0 = (-4i + i)

Answer 1

Choice A (–4 + i) + 4i = -4 + (i + 4i) is the correct equation that demonstrates the associative property of addition, which states that grouping does not affect the sum of terms.

Step-by-step explanation:

The question is asking which equation demonstrates the associative property of addition. The associative property states that no matter how you group the numbers when adding (or multiplying), you will get the same result—changing the grouping does not change the sum. Therefore, the equation representing the associative property should show that changing the grouping of the terms still results in an equivalent expression.

Choice A is the correct example of the associative property: (–4 + i) + 4i = -4 + (i + 4i). This equation shows that whether you add –4 and i first and then add 4i, or you add i and 4i first and then combine that sum with –4, you will end up with the same result. This is an application of the associative property of addition.