What is the value of `(11-:4-(2/3)"of"(9/8)+11)`?

Options

A. 13
B. 11
C. 15
D. 7

Answer

To solve the expression \( 11 \div 4 - \left( \frac{2}{3} \text{ of } \frac{9}{8} \right) + 11 \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Identify the components of the expression:**
\[ 11 \div 4 - \left( \frac{2}{3} \text{ of } \frac{9}{8} \right) + 11 \]

2. **Calculate the "of" part:**
- The term "of" indicates multiplication. Thus, we calculate:
\[ \frac{2}{3} \times \frac{9}{8} \]
- Multiply the numerators and the denominators:
\[ = \frac{2 \times 9}{3 \times 8} = \frac{18}{24} \]
- Simplify \( \frac{18}{24} \):
\[ = \frac{3}{4} \]

3. **Substitute back into the expression:**
\[ 11 \div 4 - \frac{3}{4} + 11 \]

4. **Perform the division:**
- Convert \( 11 \div 4 \) into a fraction:
\[ = \frac{11}{4} \]

5. **Now rewrite the expression:**
\[ \frac{11}{4} - \frac{3}{4} + 11 \]

6. **Combine the fractions:**
- Since \( \frac{11}{4} \) and \( \frac{3}{4} \) have the same denominator, we can subtract them:
\[ = \frac{11 - 3}{4} + 11 = \frac{8}{4} + 11 \]
- Simplify \( \frac{8}{4} \):
\[ = 2 + 11 \]

7. **Final calculation:**
\[ = 13 \]

### Final Answer:
The value of the expression is \( 13 \).