To determine which of the given equations are correct, we will analyze each equation separately and verify if the left-hand side (LHS) equals the right-hand side (RHS).
Equation 1: [tex]\((12 - 6) - 3 = 12 - (6 - 3)\)[/tex]
- LHS: [tex]\((12 - 6) - 3\)[/tex]
[tex]\(= 6 - 3\)[/tex]
[tex]\(= 3\)[/tex]
- RHS: [tex]\(12 - (6 - 3)\)[/tex]
[tex]\(= 12 - 3\)[/tex]
[tex]\(= 9\)[/tex]
Since the LHS ([tex]\(3\)[/tex]) is not equal to the RHS ([tex]\(9\)[/tex]), Equation 1 is not correct.
Equation 2: [tex]\((12 \times 6) \times 3 = 12 \times (6 \times 3)\)[/tex]
- LHS: [tex]\((12 \times 6) \times 3\)[/tex]
[tex]\(= 72 \times 3\)[/tex]
[tex]\(= 216\)[/tex]
- RHS: [tex]\(12 \times (6 \times 3)\)[/tex]
[tex]\(= 12 \times 18\)[/tex]
[tex]\(= 216\)[/tex]
Since the LHS ([tex]\(216\)[/tex]) is equal to the RHS ([tex]\(216\)[/tex]), Equation 2 is correct.
Equation 3: [tex]\((12 \div 6) \times 3 = 12 \div (6 \div 3)\)[/tex]
- LHS: [tex]\((12 \div 6) \times 3\)[/tex]
[tex]\(= 2 \times 3\)[/tex]
[tex]\(= 6\)[/tex]
- RHS: [tex]\(12 \div (6 \div 3)\)[/tex]
[tex]\(= 12 \div 2\)[/tex]
[tex]\(= 6\)[/tex]
Since the LHS ([tex]\(6\)[/tex]) is equal to the RHS ([tex]\(6\)[/tex]), Equation 3 is correct.
Equation 4: [tex]\((12 + 6) + 3 = 12 + (6 + 3)\)[/tex]
- LHS: [tex]\((12 + 6) + 3\)[/tex]
[tex]\(= 18 + 3\)[/tex]
[tex]\(= 21\)[/tex]
- RHS: [tex]\(12 + (6 + 3)\)[/tex]
[tex]\(= 12 + 9\)[/tex]
[tex]\(= 21\)[/tex]
Since the LHS ([tex]\(21\)[/tex]) is equal to the RHS ([tex]\(21\)[/tex]), Equation 4 is correct.
Summary of Correct Equations:
- Equation 2
- Equation 3
- Equation 4
Therefore, the correct answers from the given options are:
- b. Equation 2
- c. Equation 3
- d. Equation 4
