If '+' means '-' , '-' mean '+' `'xx'` means ` ' div '`, and ` 'div '` means `'xx'` , then the value of
`( 42-12 xx 3 + 8 div 2 + 15)/(8 xx 2-4 + 9 div 3)` is :

Options

A. `-(15)/(19)`
B. `(15)/(19)`
C. `5/3`
D. `-(5)/(3)`

Answer

To solve the expression given in the question, we need to first interpret the operations according to the rules provided:

1. **Interpret the operations**:
- '+' means '-'
- '-' means '+'
- 'xx' (multiply) means 'div' (divide)
- 'div' means 'xx' (multiply)

2. **Rewrite the expression**:
The original expression is:
\[ \frac{(42 - 12 \, xx \, 3 + 8 \, div \, 2 + 15)}{(8 \, xx \, 2 - 4 + 9 \, div \, 3)} \]
Applying the interpretations:
- Replace '-' with '+'
- Replace '+' with '-'
- Replace 'xx' with 'div'
- Replace 'div' with 'xx'

This gives us:
\[ \frac{(42 + 12 \, div \, 3 - 8 \, xx \, 2 - 15)}{(8 \, div \, 2 + 4 - 9 \, xx \, 3)} \]

3. **Evaluate the expression**:
Now we evaluate the rewritten expression step by step.

**Numerator**:
- Calculate \(12 \, div \, 3\):
\[ 12 \, div \, 3 = 12 \div 3 = 4 \]
- Calculate \(8 \, xx \, 2\):
\[ 8 \, xx \, 2 = 8 \times 2 = 16 \]
- Now substitute these values back into the numerator:
\[ 42 + 4 - 16 - 15 \]
- Combine the terms:
\[ 42 + 4 = 46 \]
\[ 46 - 16 = 30 \]
\[ 30 - 15 = 15 \]
So, the numerator evaluates to 15.

**Denominator**:
- Calculate \(8 \, div \, 2\):
\[ 8 \, div \, 2 = 8 \div 2 = 4 \]
- Calculate \(9 \, xx \, 3\):
\[ 9 \, xx \, 3 = 9 \times 3 = 27 \]
- Now substitute these values back into the denominator:
\[ 4 + 4 - 27 \]
- Combine the terms:
\[ 4 + 4 = 8 \]
\[ 8 - 27 = -19 \]
So, the denominator evaluates to -19.

4. **Final calculation**:
Now we can calculate the final value:
\[ \frac{15}{-19} = -\frac{15}{19} \]

Thus, the final value of the expression is:
\[ -\frac{15}{19} \]