According to the Associative Property of Addition, which of the following is equivalent to the expression (b+c)+a+d(b+c)+a+d ?(1 point) Responses b+(c+a)+db+(c+a)+d b plus left parenthesis c plus a right parenthesis plus d (b+c)+d+a(b+c)+d+a left parenthesis b plus c right parenthesis plus d plus a d+(b+c)+ad+(b+c)+a d plus left parenthesis b plus c right parenthesis plus a d+a+(b+c)

Answer 1

According to the Associative Property of Addition, the grouping of the numbers does not affect the sum. Therefore, we can rearrange the expression \((b+c)+a+d\) in any way.

All the provided responses, when simplified, should give the same result.

Let's analyze the options:

1. \( b+(c+a)+d \) – This is equivalent to \((b+c)+a+d\).
2. \( b + (c + a) + d \) – This is the same as \( b+(c+a)+d \).
3. \( (b+c)+d+a \) – This is equivalent to \((b+c)+a+d\).
4. \( (b+c)+a+d \) – This is the original expression itself.
5. \( d+(b+c)+a \) – This is also equivalent to \((b+c)+a+d\).
6. \( d+(b+c)+a \) (repeated).
7. \( a+(b+c)+d \) – This is still equivalent to \((b+c)+a+d\).

From these analyses, all of the above expressions are indeed equivalent to \((b+c)+a+d\) because they respect the Associative Property of Addition.

Thus, all provided options are valid representations of the original expression. If you need to choose one, consider the first one: \( b+(c+a)+d \), as it clearly illustrates the associative property.