The value of `(56+3" of "27-8)/(15-5" of "(29-14))` is:

Options

A. -35/21
B. -43/20
C. -21/29
D. -17/41

Answer

To solve the expression \((56 + 3 \text{ of } 27 - 8) / (15 - 5 \text{ of } (29 - 14))\), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:

1. **Identify and Solve the Operations Inside the Parentheses:**
- For the denominator, we first solve \(29 - 14\):
\[ 29 - 14 = 15 \]
- Now substitute this back into the expression:
\[ (56 + 3 \text{ of } 27 - 8) / (15 - 5 \text{ of } 15) \]

2. **Calculate the Multiplications:**
- Now calculate \(3 \text{ of } 27\) (which means \(3 \times 27\)):
\[ 3 \times 27 = 81 \]
- Substitute this back into the expression:
\[ (56 + 81 - 8) / (15 - 5 \times 15) \]

3. **Calculate the Remaining Multiplication in the Denominator:**
- Now calculate \(5 \text{ of } 15\) (which means \(5 \times 15\)):
\[ 5 \times 15 = 75 \]
- Substitute this back into the expression:
\[ (56 + 81 - 8) / (15 - 75) \]

4. **Perform the Addition and Subtraction in the Numerator:**
- Now calculate \(56 + 81 - 8\):
\[ 56 + 81 = 137 \]
\[ 137 - 8 = 129 \]
- So, the numerator becomes \(129\).

5. **Perform the Subtraction in the Denominator:**
- Now calculate \(15 - 75\):
\[ 15 - 75 = -60 \]
- So, the denominator becomes \(-60\).

6. **Final Division:**
- Now we divide the numerator by the denominator:
\[ \frac{129}{-60} = -\frac{129}{60} \]

7. **Simplify the Fraction:**
- The fraction \(-\frac{129}{60}\) can be simplified if needed, but it is already in its simplest form.

### Final Answer:
The value of the expression is \(-\frac{129}{60}\).