Finding the Correct Mathematical Signs to Balance the Equation

The question asks us to find the correct combination of mathematical signs from the given options that, when sequentially placed in the position of the asterisks (*), will balance the equation:

\(50 * 25 * 10 * 2 * 175\)

To solve this, we need to test each option by substituting the signs into the equation and evaluating if the left side equals the right side (175).

We must also remember the order of operations, often remembered by acronyms like BODMAS or PEMDAS:

• 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)

Testing the Given Mathematical Sign Combinations

Option 1: \(+, \div, \times, =\)

Substitute the signs into the equation:

\(50 + 25 \div 10 \times 2 = 175\)

Following the order of operations:

1. First, perform division: \(25 \div 10 = 2.5\)
2. Next, perform multiplication: \(2.5 \times 2 = 5\)
3. Finally, perform addition: \(50 + 5 = 55\)

The equation becomes \(55 = 175\), which is false. So, Option 1 is not correct.

Option 2: \( -, \times, \div, =\)

Substitute the signs into the equation:

\(50 - 25 \times 10 \div 2 = 175\)

Following the order of operations (Multiplication and Division from left to right):

1. Perform multiplication: \(25 \times 10 = 250\)
2. Perform division: \(250 \div 2 = 125\)
3. Perform subtraction: \(50 - 125 = -75\)

The equation becomes \(-75 = 175\), which is false. So, Option 2 is not correct.

Option 3: \( -, \times, +, =\)

Substitute the signs into the equation:

\(50 - 25 \times 10 + 2 = 175\)

Following the order of operations (Multiplication first, then Addition and Subtraction from left to right):

1. Perform multiplication: \(25 \times 10 = 250\)
2. Perform subtraction: \(50 - 250 = -200\)
3. Perform addition: \(-200 + 2 = -198\)

The equation becomes \(-198 = 175\), which is false. So, Option 3 is not correct.

Option 4: \(+, \times, \div, =\)

Substitute the signs into the equation:

\(50 + 25 \times 10 \div 2 = 175\)

Following the order of operations (Multiplication and Division from left to right):

1. Perform multiplication: \(25 \times 10 = 250\)
2. Perform division: \(250 \div 2 = 125\)
3. Perform addition: \(50 + 125 = 175\)

The equation becomes \(175 = 175\), which is true. So, Option 4 is correct.

Conclusion on Balancing the Equation

The combination of mathematical signs \(+, \times, \div, =\) when sequentially placed in the equation \(50 * 25 * 10 * 2 * 175\) balances the equation, resulting in \(50 + 25 \times 10 \div 2 = 175\).

Revision Table: Mathematical Signs and Order of Operations

Additional Information on Equation Balancing and Logic Puzzles

Equation balancing problems are common in logic and quantitative aptitude sections of exams. They test your understanding of basic arithmetic operations and the correct order in which they should be performed. Successfully solving these requires careful substitution and step-by-step calculation according to the BODMAS/PEMDAS rule.

These types of questions help improve numerical reasoning skills and attention to detail. While simple, they emphasize the importance of following standard mathematical conventions precisely to arrive at the correct result.