Which two signs should be interchanged to make the given equation correct?
$36+8 \times 184-23\div10 = 90$
Analyzing the Equation and Operator Interchange
The problem asks us to find which pair of signs (operators) can be interchanged in the equation '$36+8 \times 184-23\div10 = 90$' to make it mathematically correct. We need to test each option by swapping the specified signs and evaluating the equation using the standard order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Evaluating Operator Swaps
Let's test the original equation and then each option:
Original Equation:
$$36 + 8 \times 184 - 23 \div 10$$
Applying BODMAS:
- Multiplication: $8 \times 184 = 1472$. The equation becomes: $36 + 1472 - 23 \div 10$.
- Division: $23 \div 10 = 2.3$. The equation becomes: $36 + 1472 - 2.3$.
- Addition: $36 + 1472 = 1508$. The equation becomes: $1508 - 2.3$.
- Subtraction: $1508 - 2.3 = 1505.7$.
Since $1505.7 \neq 90$, the original equation is incorrect.
Now, let's test the options:
| Option | Signs Interchanged | Resulting Equation | Evaluation Steps (BODMAS) | Final Result | Correct? |
|---|---|---|---|---|---|
| 1 | $\div$ and - | $$36 + 8 \times 184 \div 23 - 10$$ |
|
$90$ | Yes |
| 2 | $\div$ and x | $$36 + 8 \div 184 \times 23 - 10$$ |
|
$27$ | No |
| 3 | + and x | $$36 \times 8 + 184 - 23 \div 10$$ |
|
$469.7$ | No |
| 4 | - and + | $$36 - 8 + 184 \times 23 \div 10$$ |
|
$451.2$ | No |
Conclusion on Sign Interchange
By evaluating each option, we found that interchanging the division ($\div$) and subtraction (- ) signs results in the equation $36 + 8 \times 184 \div 23 - 10$, which correctly evaluates to $90$. Therefore, this is the pair of signs that needs to be interchanged.
Similar Questions
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:
