To determine which operations satisfy the associative law for whole numbers, we need to understand what the associative law is and then test each operation given in the options.
### Step-by-Step Solution:
1. **Understanding the Associative Law**:
The associative law states that for any three numbers \( a \), \( b \), and \( c \), the way in which the numbers are grouped does not change their sum or product. In mathematical terms:
- For addition: \( (a + b) + c = a + (b + c) \)
- For multiplication: \( (a \times b) \times c = a \times (b \times c) \)
2. **Testing Addition**:
- Let's take three numbers, for example, \( 1, 2, \) and \( 3 \).
- Calculate \( (1 + 2) + 3 \):
\[
(1 + 2) + 3 = 3 + 3 = 6
\]
- Now calculate \( 1 + (2 + 3) \):
\[
1 + (2 + 3) = 1 + 5 = 6
\]
- Since both expressions equal \( 6 \), addition satisfies the associative law.
3. **Testing Subtraction**:
- Using the same numbers \( 1, 2, \) and \( 3 \):
- Calculate \( (1 - 2) - 3 \):
\[
(1 - 2) - 3 = -1 - 3 = -4
\]
- Now calculate \( 1 - (2 - 3) \):
\[
1 - (2 - 3) = 1 - (-1) = 1 + 1 = 2
\]
- Since \( -4 \neq 2 \), subtraction does not satisfy the associative law.
4. **Testing Multiplication**:
- Again, using \( 1, 2, \) and \( 3 \):
- Calculate \( (1 \times 2) \times 3 \):
\[
(1 \times 2) \times 3 = 2 \times 3 = 6
\]
- Now calculate \( 1 \times (2 \times 3) \):
\[
1 \times (2 \times 3) = 1 \times 6 = 6
\]
- Since both expressions equal \( 6 \), multiplication satisfies the associative law.
5. **Testing Division**:
- Using \( 1, 2, \) and \( 3 \):
- Calculate \( (1 \div 2) \div 3 \):
\[
(1 \div 2) \div 3 = \frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}
\]
- Now calculate \( 1 \div (2 \div 3) \):
\[
1 \div (2 \div 3) = 1 \div \frac{2}{3} = 1 \times \frac{3}{2} = \frac{3}{2}
\]
- Since \( \frac{1}{6} \neq \frac{3}{2} \), division does not satisfy the associative law.
### Conclusion:
The operations that satisfy the associative law for whole numbers are **Addition and Multiplication**.
### Final Answer:
(d) Addition and multiplication.
