`144-:[40-{37-(25-112-: bar(7xx4))}]=?`

Options

A. 4
B. 2
C. 8
D. 6

Answer

To solve the expression \( 144 - : [40 - \{37 - (25 - 112 - : \text{bar}(7 \times 4))\}] = ? \), we will follow the order of operations known as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the innermost operation**:
We start with the expression inside the parentheses: \( 7 \times 4 \).
\[ 7 \times 4 = 28 \]

**Hint**: Always start with the innermost brackets or parentheses.

2. **Substitute back into the expression**:
Replace \( 7 \times 4 \) with \( 28 \):
\[ 144 - : [40 - \{37 - (25 - 112 - 28)\}] \]

**Hint**: Keep the expression organized as you substitute values.

3. **Calculate the expression inside the parentheses**:
Now, calculate \( 25 - 112 - 28 \):
\[ 25 - 112 = -87 \]
\[ -87 - 28 = -115 \]

**Hint**: Perform operations step by step to avoid confusion.

4. **Substitute back into the expression**:
Now replace \( (25 - 112 - 28) \) with \( -115 \):
\[ 144 - : [40 - \{37 - (-115)\}] \]

**Hint**: Ensure you maintain the signs correctly when substituting.

5. **Calculate the expression inside the curly brackets**:
Now calculate \( 37 - (-115) \):
\[ 37 + 115 = 152 \]

**Hint**: Remember that subtracting a negative is the same as adding.

6. **Substitute back into the expression**:
Replace \( \{37 - (-115)\} \) with \( 152 \):
\[ 144 - : [40 - 152] \]

**Hint**: Keep track of the operations as you substitute.

7. **Calculate the expression inside the square brackets**:
Now calculate \( 40 - 152 \):
\[ 40 - 152 = -112 \]

**Hint**: Double-check your arithmetic to avoid mistakes.

8. **Substitute back into the expression**:
Replace \( [40 - 152] \) with \( -112 \):
\[ 144 - : (-112) \]

**Hint**: Ensure the expression is clear before performing the final operations.

9. **Perform the division**:
Now divide \( 144 \) by \( -112 \):
\[ 144 \div -112 = -\frac{144}{112} = -\frac{9}{7} \]

**Hint**: Simplify fractions where possible.

10. **Final Result**:
The final result of the expression is:
\[ -\frac{9}{7} \]

### Summary of Steps:
- Start with the innermost operation.
- Substitute values back into the expression after each calculation.
- Perform operations in the correct order.
- Simplify fractions where possible.