Question

Which two signs should be interchanged to make the given equation correct?
16 – 18 $\times$ 216 $\div$ 432 + 40 = 20

• A. + and –
• B. $\times$ and $\div$
• C. $\times$ and +
• D. $\div$ and –

Hint:

Look for the division sign first. In the original equation, $216 \div 432$ results in $0.5$. Since the final answer is a whole number (20), we likely need to move the division sign to a place where it divides perfectly.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem is based on the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) rule. To solve it, we must replace the signs as suggested in the options and calculate the result for each until the equation holds true (RHS = 20).
Step 2: Key Formula or Approach:
Rule of BODMAS:
1. Perform Division (\( \div \)) and Multiplication (\( \times \)) from left to right.
2. Perform Addition (\( + \)) and Subtraction (\( - \)) from left to right.
Step 3: Detailed Explanation:
Let's test Option (B) by interchanging \( \times \) and \( \div \).
The original equation: \( 16 - 18 \times 216 \div 432 + 40 = 20 \).
New equation after interchanging: \( 16 - 18 \div 216 \times 432 + 40 = 20 \).
Execution:
1. Division First: Calculate \( 18 \div 216 \).
\( 18 / 216 \) can be simplified by dividing both by 18.
\( 18 \div 18 = 1 \).
\( 216 \div 18 = 12 \).
So, the term becomes \( 1/12 \).
2. Multiplication: Now multiply the result by 432.
\( (1/12) \times 432 \).
\( 432 \div 12 = 36 \).
3. Update the Equation:
The equation is now: \( 16 - 36 + 40 \).
4. Addition and Subtraction:
Perform subtraction: \( 16 - 36 = -20 \).
Perform addition: \( -20 + 40 = 20 \).
Since 20 = 20, the LHS equals the RHS. Option (B) is the correct choice.
Step 4: Final Answer:
The signs \( \times \) and \( \div \) must be interchanged to satisfy the equation.