If + means -, - means $\times$, $\times$ means $\div$ and $\div$ means +, then what will come in place of the question mark (?) in the following equation?
$29+14\times7\div11-9=?$
Understanding Operator Substitution
This question tests your ability to solve a mathematical equation by substituting operators based on a given set of rules. We need to carefully replace each operator in the original equation and then solve the new equation using the standard order of operations (BODMAS/PEMDAS).
Operator Substitution Rules
The question provides the following substitutions:
- '+' means '-'
- '-' means '$\times$'
- '$\times$' means '$\div$'
- '$\div$' means '+'
Let's represent these rules in a table for clarity:
| Original Operator | New Operator |
|---|---|
| + | - |
| - | $\times$ |
| $\times$ | $\div$ |
| $\div$ | + |
Applying the Substitutions
The original equation is:
$29 + 14 × 7 ÷ 11 - 9 = ?$
Now, let's apply the substitution rules to each operator:
- The '+' sign becomes '-'.
- The '$\times$' sign becomes '$\div$'.
- The '$\div$' sign becomes '+'.
- The '-' sign becomes '$\times$'.
After substitution, the equation becomes:
$29 - 14 ÷ 7 + 11 × 9 = ?$
Solving the New Equation
We will now solve the new equation using the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction).
- Division: First, perform the division: $14 \div 7 = 2$ The equation now is: $29 - 2 + 11 × 9 = ?$
- Multiplication: Next, perform the multiplication: $11 \times 9 = 99$ The equation now is: $29 - 2 + 99 = ?$
- Addition and Subtraction: Finally, perform subtraction and addition from left to right. First, subtraction: $29 - 2 = 27$ The equation becomes: $27 + 99 = ?$ Then, addition: $27 + 99 = 126$
So, the value of the expression after substituting the operators is 126.
Final Answer
The correct value for the equation after operator substitution is 126.
Important Questions from Quick Math
Evaluate $5.29 \bar{8} - 6.29 \bar{8} + 7.29 \bar{8} $
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