Which of the following operations satisfies the associative law for whole numbers?

Options

A. Subtraction and division
B. Subtraction and multiplication
C. Division and multiplication
D. Addition and multiplication

Answer

To determine which operations satisfy the associative law for whole numbers, we need to understand what the associative law means. The associative law states that the way in which numbers are grouped in an operation does not change the result of that operation.

### Step-by-Step Solution:

1. **Understand the Associative Law**:
The associative law applies to operations where changing the grouping of the numbers does not change the result. For example, in addition, (A + B) + C = A + (B + C).

2. **Test Addition**:
Let's take three whole numbers, A, B, and C.
- Calculate (A + B) + C.
- Calculate A + (B + C).
- Both calculations will yield the same result, demonstrating that addition satisfies the associative law.

3. **Test Multiplication**:
Now, let's test multiplication with the same numbers A, B, and C.
- Calculate (A × B) × C.
- Calculate A × (B × C).
- Again, both calculations will yield the same result, showing that multiplication also satisfies the associative law.

4. **Test Subtraction**:
Next, we will test subtraction.
- Calculate (A - B) - C.
- Calculate A - (B - C).
- These two calculations will generally yield different results, indicating that subtraction does not satisfy the associative law.

5. **Test Division**:
Finally, we will test division.
- Calculate (A ÷ B) ÷ C.
- Calculate A ÷ (B ÷ C).
- Similar to subtraction, these two calculations will generally yield different results, showing that division does not satisfy the associative law.

6. **Conclusion**:
Based on the tests, we conclude that addition and multiplication satisfy the associative law for whole numbers, while subtraction and division do not.

### Final Answer:
The operations that satisfy the associative law for whole numbers are **addition and multiplication**.