What approximate value should comein place of the question mark (?) in the following equation? `(1/9 div 1/9 " of " 1/3) " of " 1/6 =?`

Options

A. `1/6`
B. `1/2`
C. `1/9`
D. `1/3`

Answer

To solve the equation `(1/9 div 1/9 " of " 1/3) " of " 1/6 = ?`, we will follow the order of operations (BODMAS/BIDMAS). Here’s a step-by-step breakdown:

### Step 1: Understand the Operations
The equation involves division and multiplication (referred to as "of" in the context). The term "of" indicates multiplication.

### Step 2: Rewrite the Equation
We can rewrite the equation for clarity:
\[ \left(\frac{1}{9} \div \frac{1}{9} \times \frac{1}{3}\right) \times \frac{1}{6} \]

### Step 3: Solve Inside the Bracket
First, we will solve the expression inside the bracket:
\[ \frac{1}{9} \div \frac{1}{9} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{1}{9} \div \frac{1}{9} = \frac{1}{9} \times \frac{9}{1} = 1 \]

### Step 4: Multiply by 1/3
Now, we multiply the result by \( \frac{1}{3} \):
\[ 1 \times \frac{1}{3} = \frac{1}{3} \]

### Step 5: Multiply by 1/6
Now, we take the result from the previous step and multiply it by \( \frac{1}{6} \):
\[ \frac{1}{3} \times \frac{1}{6} = \frac{1 \times 1}{3 \times 6} = \frac{1}{18} \]

### Final Answer
Thus, the approximate value that should come in place of the question mark (?) is:
\[ \frac{1}{18} \]