Understanding the Equation Balancing Problem

The question asks us to find the correct sequence of mathematical signs to replace the asterisks (*) in the given expression to make it a balanced equation. The expression is 23 * 2 * 2 * 5 * 18. We are given four options, each providing a sequence of four signs.

To solve this equation balancing problem, we need to substitute the signs from each option into the expression sequentially from left to right and then evaluate the resulting equation using the order of operations (BODMAS/PEMDAS). The option that results in a true equation is the correct answer.

Applying the Order of Operations (BODMAS/PEMDAS)

Remember the order of operations:

• Brackets (or Parentheses)
• Orders (or Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Testing the Options for Equation Balancing

Option 1: -, ÷, ×, =

Let's substitute these signs into the expression:

23 - 2 ÷ 2 × 5 = 18

Now, we evaluate the left side following BODMAS:

• First, Division: $\frac{2}{2} = 1$
• The expression becomes: $23 - 1 \times 5 = 18$
• Next, Multiplication: $1 \times 5 = 5$
• The expression becomes: $23 - 5 = 18$
• Finally, Subtraction: $23 - 5 = 18$

So, the equation becomes: $18 = 18$.

This equation is true, so this option balances the given expression.

Option 2: -, ÷, +, =

Let's substitute these signs into the expression:

23 - 2 ÷ 2 + 5 = 18

Evaluate the left side:

• First, Division: $\frac{2}{2} = 1$
• The expression becomes: $23 - 1 + 5 = 18$
• Next, Addition and Subtraction from left to right:
• $23 - 1 = 22$
• $22 + 5 = 27$

So, the equation becomes: $27 = 18$.

This equation is false.

Option 3: -, ÷, =, +

Let's substitute these signs into the expression:

23 - 2 ÷ 2 = 5 + 18

Evaluate both sides:

Left side:

• Division: $\frac{2}{2} = 1$
• Subtraction: $23 - 1 = 22$

Right side:

• Addition: $5 + 18 = 23$

So, the equation becomes: $22 = 23$.

This equation is false.

Option 4: -, ×, ÷, =

Let's substitute these signs into the expression:

23 - 2 × 2 ÷ 5 = 18

Evaluate the left side:

• First, Multiplication and Division from left to right:
• Multiplication: $2 \times 2 = 4$
• The expression becomes: $23 - 4 \div 5 = 18$
• Division: $\frac{4}{5} = 0.8$
• The expression becomes: $23 - 0.8 = 18$
• Finally, Subtraction: $23 - 0.8 = 22.2$

So, the equation becomes: $22.2 = 18$.

This equation is false.

Conclusion

After testing all the options, only Option 1 provides the correct combination of mathematical signs (-, ÷, ×, =) that balances the given equation 23 * 2 * 2 * 5 * 18, resulting in $18 = 18$.

Revision Table: Checking Equation Balancing

Here's a summary of the evaluation for each option:

Additional Information: Strategies for Mathematical Sign Problems

Problems involving finding the correct mathematical signs to balance an equation are common in competitive exams. Here are some tips:

• Understand BODMAS/PEMDAS: Always follow the correct order of operations. Division and Multiplication have equal priority and are done from left to right. Similarly, Addition and Subtraction have equal priority and are done from left to right.
• Look for Division possibilities: If division is one of the options, check if it's placed where the numbers are divisible. This can quickly eliminate options that would result in fractions or non-integers if the right side is an integer.
• Estimate the result: Before detailed calculation, quickly estimate the magnitude of the result with the given operators. For example, using multiplication might significantly increase the number.
• Systematic Testing: Test each option systematically. Don't guess.
• Double Check: After finding an option that works, quickly double-check the calculations to avoid errors.

Practicing more problems like this helps in improving speed and accuracy in equation balancing and mathematical sign substitution questions.