`9 - 1 (2)/(9) "of 3" (3)/(11) + 5 (1)/(7) "of" (7)/(9)` is equal to :

Options

A. 8
B. 9
C. `8 (32)/(81)`
D. `(3)/(4)`

Answer

To solve the expression \( 9 - 1 \frac{2}{9} \text{ of } 3 \frac{3}{11} + 5 \frac{1}{7} \text{ of } \frac{7}{9} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions.

1. \( 1 \frac{2}{9} = \frac{9 \times 1 + 2}{9} = \frac{11}{9} \)
2. \( 3 \frac{3}{11} = \frac{11 \times 3 + 3}{11} = \frac{36}{11} \)
3. \( 5 \frac{1}{7} = \frac{7 \times 5 + 1}{7} = \frac{36}{7} \)

Now, we rewrite the expression:
\[ 9 - \frac{11}{9} \text{ of } \frac{36}{11} + \frac{36}{7} \text{ of } \frac{7}{9} \]

### Step 2: Calculate the "of" Operations
Next, we calculate the "of" operations, which means multiplication.

1. \( \frac{11}{9} \text{ of } \frac{36}{11} = \frac{11}{9} \times \frac{36}{11} = \frac{36}{9} = 4 \)
2. \( \frac{36}{7} \text{ of } \frac{7}{9} = \frac{36}{7} \times \frac{7}{9} = \frac{36}{9} = 4 \)

Now, we can rewrite the expression:
\[ 9 - 4 + 4 \]

### Step 3: Simplify the Expression
Now, we simplify the expression:
\[ 9 - 4 + 4 = 9 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{9} \]

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