What is the simplified value of `(9div9" of "9+9)/(9div9xx9+9)`?

Options

A. `1/324`
B. 1
C. `41/81`
D. `81/41`

Answer

To simplify the expression \((9 \div 9 \text{ of } 9 + 9) / (9 \div 9 \times 9 + 9)\), we will follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:

1. **Identify the Expression**:
\[ \frac{(9 \div 9 \text{ of } 9 + 9)}{(9 \div 9 \times 9 + 9)} \]

2. **Convert "of" to Multiplication**:
The term "of" indicates multiplication. Thus, we rewrite the expression as:
\[ \frac{(9 \div 9 \times 9 + 9)}{(9 \div 9 \times 9 + 9)} \]

3. **Calculate the Numerator**:
- First, calculate \(9 \div 9\):
\[ 9 \div 9 = 1 \]
- Now substitute back:
\[ 1 \times 9 + 9 = 9 + 9 = 18 \]

4. **Calculate the Denominator**:
- Again, calculate \(9 \div 9\):
\[ 9 \div 9 = 1 \]
- Substitute back:
\[ 1 \times 9 + 9 = 9 + 9 = 18 \]

5. **Combine the Results**:
Now we have:
\[ \frac{18}{18} = 1 \]

### Final Answer:
The simplified value of the expression is:
\[ \boxed{1} \]