What will come in the place of the question mark (?) in the following equation, if '+' and '-' are interchanged and 'x' and '÷' are
interchanged?
$98 \times 14 + 24 - 12 \div 8 = ?$
Understanding the Operator Interchange Problem
The question asks us to find the value of the given mathematical expression after applying specific rules for interchanging operators. We need to swap '+' with '-' and 'x' with '÷'. The original equation is:
$$98 \times 14 + 24 - 12 \div 8 = ?$$
The rules for interchanging operators are:
- '+' becomes '-'
- '-' becomes '+'
- 'x' becomes '÷'
- '÷' becomes 'x'
Transforming the Equation Based on Operator Interchange
Let's apply these interchange rules to the original equation:
- The multiplication symbol '
×' will be replaced by the division symbol '÷'. - The addition symbol '
+' will be replaced by the subtraction symbol '-'. - The subtraction symbol '
-' will be replaced by the addition symbol '+'. - The division symbol '
÷' will be replaced by the multiplication symbol '×'.
Applying these changes, the equation becomes:
$$98 \div 14 - 24 + 12 \times 8 = ?$$
Step-by-Step Solution Using BODMAS Rule
Now, we need to solve the transformed equation using the standard order of operations (BODMAS/PEMDAS), which stands for Brackets, Orders (powers/roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
- Division: First, perform the division operation. $$98 \div 14 = 7$$
- Multiplication: Next, perform the multiplication operation. $$12 \times 8 = 96$$
- Rewrite Equation: Substitute the results back into the equation. $$7 - 24 + 96 = ?$$
- Subtraction: Perform the subtraction from left to right. $$7 - 24 = -17$$
- Addition: Finally, perform the addition. $$-17 + 96 = 79$$
Therefore, the value that comes in the place of the question mark is 79.
Final Answer
The value of the equation after interchanging the operators is 79.
Similar Questions
Which two signs should be interchanged to make the given equation correct?
$36+8 \times 184-23\div10 = 90$Which two signs should be interchanged to make the given equation correct?
$152 + 8 \times 16 \div 9 - 4 = 309$
Important Questions from Bodmas Rule
The value of 30 ÷ 6 × 5 of (2 + 3) - 12(3 × 2) is equal to:
solve the following:
523 + 523 × 523 ÷ 523
The value of 96 - 4 of (18 - 13) + 4 × 7 is:
Find the value of 45 - 3 × (4 of 6 + 12 ÷ 3 × 6 - 4 × 5) + 6.
The value of \(\frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} - \frac{1}{5} \times \left( {\frac{7}{8} - \frac{5}{4}} \right)} \right] - \frac{4}{5}\) is:
