The question is asking for the equivalent expression using the Associative Property of Addition.

The original expression is:

$(b + c) + a + d$

The Associative Property allows us to group terms in any way without changing the result. Specifically, it states that $(x + y) + z = x + (y + z)$. However, it doesn't change the order of terms, only the grouping.

Let's examine the choices:

1. $d + (b + c) + a$ — This keeps the terms in the same order and regroups them differently. This could be a possible equivalent expression.
2. $d + a + (b + c)$ — This changes the order of terms. It places $d$ and $a$ first, which violates the associative property as it only allows regrouping, not reordering.
3. $(b + c) + d + a$ — This keeps the original grouping and order, which is a possible equivalent expression.
4. $b + (c + a) + d$ — This changes the grouping to include $c$ and $a$, which is valid under the associative property, but this is not exactly equivalent to the original expression.

Correct Answer:

The expression $(b + c) + d + a$ (option 3) is the most appropriate equivalent because it maintains both the order and associative grouping.

Would you like to go over more details on the Associative Property?

Here are 5 related questions to expand your understanding:

1. Can the Associative Property be applied to subtraction or multiplication?
2. How does the Commutative Property differ from the Associative Property?
3. What happens if we change the order of the terms while using the Associative Property?
4. Can the Associative Property be used in equations with more than three terms?
5. How can the Distributive Property interact with the Associative Property?

Tip: The Associative Property focuses on how numbers are grouped, not their order!