Balancing Mathematical Equation Steps

The question asks us to find the correct combination of mathematical signs (+, -, ×, ÷) that will replace the asterisks (*) in the given equation to make it mathematically correct.

The equation is:

\(36 * 12 * 6 * 12 * 3 = 63\)

We need to test the given options, replacing the asterisks sequentially from left to right with the signs provided in each option. The option that results in the left side of the equation equaling the right side (63) is the correct answer.

Testing the Correct Combination of Signs

Let's take the combination of signs from the correct option: ×, ÷, -, +.

Substitute these signs into the equation:

\(36 \times 12 \div 6 - 12 + 3 = 63\)

Applying Order of Operations (BODMAS/PEMDAS)

To solve this equation, we follow the order of operations:

1. Brackets first (none here).
2. Orders (powers and square roots) next (none here).
3. Division and Multiplication from left to right.
4. Addition and Subtraction from left to right.

Step-by-Step Calculation:

• First, perform the multiplication: \(36 \times 12\)
• \(36 \times 12 = 432\)
• The equation becomes: \(432 \div 6 - 12 + 3 = 63\)

• Next, perform the division: \(432 \div 6\)
• \(432 \div 6 = 72\)
• The equation becomes: \(72 - 12 + 3 = 63\)

• Now, perform the subtraction from left to right: \(72 - 12\)
• \(72 - 12 = 60\)
• The equation becomes: \(60 + 3 = 63\)

• Finally, perform the addition: \(60 + 3\)
• \(60 + 3 = 63\)

The left side of the equation is \(63\), which is equal to the right side of the equation \(63\).

\(63 = 63\)

Since the equation is balanced with the signs ×, ÷, -, and +, this combination is the correct one.

Summary of Balancing the Equation

Replacing the asterisks with the signs ×, ÷, -, and + in order makes the equation true:

\(36 \times 12 \div 6 - 12 + 3 = 63\)

\(432 \div 6 - 12 + 3 = 63\)

\(72 - 12 + 3 = 63\)

\(60 + 3 = 63\)

\(63 = 63\)

Revision Table: Key Concepts

Additional Information: Order of Operations (BODMAS/PEMDAS) Explained

The order of operations is crucial for solving mathematical expressions consistently. It tells us which operation to perform first when there are multiple operations in an expression.

• Brackets (or Parentheses): Solve anything inside brackets first.
• Orders (or Exponents): Solve powers, roots, etc., next.
• Division and Multiplication: Perform these from left to right.
• Addition and Subtraction: Perform these from left to right.

Following this order ensures that everyone gets the same answer for a given mathematical expression, which is essential for balancing equations correctly.