Question

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

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

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

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

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

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 \(d\), the following is true:

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

For the expression \((b + c) + a + d\), we need to find an equivalent expression based on changing the grouping.

Let's analyze the options:

1. **b + (c + a) + d**
- This can be grouped as \(b + (c + a) + d\), which is valid since we can add \(c\) and \(a\) together first.

2. **d + a + (b + c)**
- This groups \(b\) and \(c\) together and adds \(d\) and \(a\) in front, which is valid thanks to the associative property.

3. **(b + c) + d + a**
- This keeps \(b\) and \(c\) together and adds \(d\) and \(a\) afterwards, maintaining the order through addition.

4. **d + (b + c) + a**
- This groups \(b\) and \(c\) together and moves \(d\) in front of that grouping, while \(a\) is outside, which is also valid.

All provided expressions can be rearranged using the associative property without changing the overall sum.

Therefore, the equivalent expressions to \((b + c) + a + d\) are:

- \(b + (c + a) + d\)
- \(d + a + (b + c)\)
- \((b + c) + d + a\)
- \(d + (b + c) + a\)

So, any of the options listed is equivalent! If you need just one, any one would be correct. If you have to pick only one, you could select any of them.

Please clarify if you want to select only one, and if so, provide the criteria for selection!