Question

According to the Associative Property of Addition, which of the following is equivalent to the expression (b+c)+a+d?

d+(b+c)+a
d plus left parenthesis b plus c right parenthesis plus a

(b+c)+d+a
left parenthesis b plus c right parenthesis plus d plus a

d+a+(b+c)
d plus a plus left parenthesis b plus c right parenthesis

b+(c+a)+d

Answer 1

The Associative Property of Addition states that the grouping of numbers does not affect their sum. This means that for any numbers \( a \), \( b \), \( c \), and \( d \):

\[
(a + b) + c = a + (b + c)
\]

Now, let's analyze the expression \((b+c)+a+d\):

According to the Associative Property, we can rearrange and group the terms in any order without changing the sum. Therefore, the equivalent expressions can be rewritten as follows:

1. \( d + (b + c) + a \)
2. \( (b + c) + d + a \)
3. \( d + a + (b + c) \)
4. \( b + (c + a) + d \)

All of these expressions are equivalent to \((b+c)+a+d\).

So, the correct answer is that all the provided expressions are equivalent to the expression \((b+c)+a+d\) under the Associative Property of Addition. Each one correctly respects the property by rearranging and regrouping the terms.