If '+' means `'div', 'xx'`, means '-', `'div'` means `'xx'` and '-' means '+', what will be the value of the following expression ?
`9 + 3 + 4 - 8 xx 2 = ?`

Options

A. `6 (1)/(4)`
B. `6 (3)/(4)`
C. `-1 (3)/(4)`
D. 18

Answer

To solve the expression `9 + 3 + 4 - 8 xx 2`, we first need to interpret the symbols according to the rules given in the question:

1. **Interpret the symbols:**
- `+` means `div` (division)
- `xx` means `-` (subtraction)
- `div` means `xx` (multiplication)
- `-` means `+` (addition)

2. **Rewrite the expression using the new meanings:**
The original expression is:
\[ 9 + 3 + 4 - 8 xx 2 \]
Replacing the symbols according to the rules:
\[ 9 \div 3 \div 4 + 8 - 2 \]

3. **Perform the operations step by step:**
- First, we perform the division from left to right:
\[ 9 \div 3 = 3 \]
- Now, substitute back into the expression:
\[ 3 \div 4 + 8 - 2 \]
- Next, perform the division:
\[ 3 \div 4 = \frac{3}{4} \]
- Substitute back:
\[ \frac{3}{4} + 8 - 2 \]
- Now, perform the addition:
\[ \frac{3}{4} + 8 = \frac{3}{4} + \frac{32}{4} = \frac{35}{4} \]
- Substitute back:
\[ \frac{35}{4} - 2 \]
- Convert 2 into a fraction:
\[ 2 = \frac{8}{4} \]
- Now perform the subtraction:
\[ \frac{35}{4} - \frac{8}{4} = \frac{27}{4} \]

4. **Final answer:**
The value of the expression is:
\[ \frac{27}{4} \]