To determine which equations demonstrate the associative property, we need to recall that the associative property applies to addition and multiplication but not to subtraction and division.
Let's analyze each equation step-by-step:
1. Equation 1: (12 - 6) - 3 = 12 - (6 - 3)
- This equation involves subtraction. The associative property does not apply to subtraction. Thus, Equation 1 does not demonstrate the associative property.
2. Equation 2: (12 × 6) × 3 = 12 × (6 × 3)
- This equation involves multiplication. The associative property applies to multiplication, meaning the equation should hold true regardless of how the numbers are grouped. Therefore, Equation 2 demonstrates the associative property.
3. Equation 3: (12 ÷ 6) × 3 = 12 ÷ (6 ÷ 3)
- This equation involves both division and multiplication. The associative property does not apply to division. Hence, Equation 3 does not demonstrate the associative property.
4. Equation 4: (12 + 6) + 3 = 12 + (6 + 3)
- This equation involves addition. The associative property applies to addition, meaning the equation should hold true regardless of how the numbers are grouped. Thus, Equation 4 demonstrates the associative property.
Based on the analysis, the equations that demonstrate the associative property are:
b. Equation 2
d. Equation 4
