To determine which equations demonstrate the associative property, we need to understand that the associative property applies to addition and multiplication. This property states that the way in which numbers are grouped does not change their sum or product.
Let's examine each equation step-by-step:
1. Equation 1: \((12 - 6) - 3 = 12 - (6 - 3)\)
- Subtraction is not associative.
- Evaluating each side:
- Left side: \((12 - 6) - 3 = 6 - 3 = 3\)
- Right side: \(12 - (6 - 3) = 12 - 3 = 9\)
- The left side and right side are not equal.
2. Equation 2: \((12 \times 6) \times 3 = 12 \times (6 \times 3)\)
- Multiplication is associative.
- Evaluating each side:
- Left side: \((12 \times 6) \times 3 = 72 \times 3 = 216\)
- Right side: \(12 \times (6 \times 3) = 12 \times 18 = 216\)
- The left side and right side are equal.
3. Equation 3: \((12 \div 6) \times 3 = 12 \div (6 \div 3)\)
- Division is not typically associative, but this equation simplifies correctly.
- Evaluating each side:
- Left side: \((12 \div 6) \times 3 = 2 \times 3 = 6\)
- Right side: \(12 \div (6 \div 3) = 12 \div 2 = 6\)
- The left side and right side are equal in this special case.
4. Equation 4: \((12 + 6) + 3 = 12 + (6 + 3)\)
- Addition is associative.
- Evaluating each side:
- Left side: \((12 + 6) + 3 = 18 + 3 = 21\)
- Right side: \(12 + (6 + 3) = 12 + 9 = 21\)
- The left side and right side are equal.
Based on these evaluations, the equations that demonstrate the associative property are:
- Equation 2
- Equation 3
- Equation 4
So, the correct answers are:
b. Equation 2
c. Equation 3
d. Equation 4
