Fill in the blanks so that the equality holds. Also state the property used in each case.
`765+(321+589)=(765+"_________")+589`

Options

A. `765`, addition is associative for whole numbers.
B. `321`, addition is associative for whole numbers.
C. `589`, addition is associative for whole numbers.
D. `589`, addition is commutative for whole numbers.

Answer

To solve the equation \( 765 + (321 + 589) = (765 + "_________") + 589 \), we need to fill in the blank so that the equality holds true. We will also state the property used in each case.

### Step-by-Step Solution:

1. **Identify the Expression**: We start with the expression on the left side: \( 765 + (321 + 589) \).

2. **Use the Associative Property of Addition**: According to the associative property of addition, we can group the numbers in any way without changing the sum. This property states that \( a + (b + c) = (a + b) + c \).

3. **Rewrite the Left Side**: We can rewrite the left side using the associative property:
\[ 765 + (321 + 589) = (765 + 321) + 589 \]

4. **Fill in the Blank**: From the rewritten expression, we see that the blank should be filled with \( 321 \):
\[ 765 + (321 + 589) = (765 + 321) + 589 \]
Therefore, the blank is \( 321 \).

5. **Final Expression**: Now we can write the complete equation:
\[ 765 + (321 + 589) = (765 + 321) + 589 \]

### Conclusion:
The filled blank is \( 321 \), and the property used is the **Associative Property of Addition**.