Balancing Equations with Mathematical Signs

The question asks us to find the correct combination of mathematical signs to replace the asterisks (*) in the equation 52 * 4 * 38 * 5 * 5 * 0 so that the equation is balanced. We need to test the given options by substituting the signs and evaluating the resulting expressions according to the order of operations (BODMAS/PEMDAS).

Testing the Correct Combination of Signs

Let's test the combination of signs provided in Option 2, which is ÷, =, −, ×, +. Substituting these signs into the equation gives:

\( 52 \div 4 = 38 - 5 \times 5 + 0 \)

Now, we evaluate both sides of the equation. According to the order of operations, we perform division and multiplication before addition and subtraction.

Evaluating the Left Side of the Equation

The left side is \( 52 \div 4 \).

\( 52 \div 4 = 13 \)

So, the left side simplifies to 13.

Evaluating the Right Side of the Equation

The right side is \( 38 - 5 \times 5 + 0 \).

First, perform the multiplication:

\( 5 \times 5 = 25 \)

Substitute this back into the right side expression:

\( 38 - 25 + 0 \)

Now, perform the subtraction and addition from left to right:

\( 38 - 25 = 13 \)

\( 13 + 0 = 13 \)

So, the right side also simplifies to 13.

Checking if the Equation Balances

Comparing the evaluated left side and right side:

Left Side = 13

Right Side = 13

Since Left Side = Right Side (13 = 13), the equation is balanced with the signs from Option 2.

Therefore, the correct combination of mathematical signs to balance the given equation is ÷, =, −, ×, +.

Order of Operations (BODMAS/PEMDAS) Explanation

When evaluating mathematical expressions with multiple operations, we follow a specific order:

• B/P: Brackets/Parentheses
• O/E: Orders/Exponents
• D/M: Division and Multiplication (from left to right)
• A/S: Addition and Subtraction (from left to right)

In this problem, we used Division and Multiplication first, and then Addition and Subtraction.

Revision Table: Balancing Equations

Additional Information: Solving Equation Puzzles

Equation balancing puzzles like this one are common in mathematical reasoning and aptitude tests. They require a good understanding of basic arithmetic operations and the order of operations. A systematic approach of testing each option, carefully applying BODMAS/PEMDAS, is key to solving these problems accurately. Sometimes, looking at the numbers and the operators might give hints (e.g., checking for divisibility if division is an option early in the equation). However, rigorous evaluation is always necessary to confirm the correct combination.