The value of `(1/3div1/3xx1/3)/(1/3div1/3"of"1/3)-1/9` is

Options

A. 0
B. 1
C. `1/3`
D. `1/9`

Answer

To solve the expression \((\frac{1}{3} \div \frac{1}{3} \times \frac{1}{3}) / (\frac{1}{3} \div \frac{1}{3} \text{ of } \frac{1}{3}) - \frac{1}{9}\), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate the "of" part**:
\[ \frac{1}{3} \text{ of } \frac{1}{3} = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9} \]
**Hint**: Remember that "of" in math usually means multiplication.

2. **Substitute the value back into the expression**:
\[ \frac{(\frac{1}{3} \div \frac{1}{3} \times \frac{1}{3})}{(\frac{1}{3} \div \frac{1}{3} \text{ of } \frac{1}{3})} - \frac{1}{9} = \frac{(\frac{1}{3} \div \frac{1}{3} \times \frac{1}{3})}{\frac{1}{9}} - \frac{1}{9} \]
**Hint**: Make sure to replace the "of" with the calculated value.

3. **Calculate the division**:
\[ \frac{1}{3} \div \frac{1}{3} = 1 \]
**Hint**: Dividing a number by itself (except zero) always gives 1.

4. **Substitute back into the expression**:
\[ \frac{(1 \times \frac{1}{3})}{\frac{1}{9}} - \frac{1}{9} = \frac{\frac{1}{3}}{\frac{1}{9}} - \frac{1}{9} \]
**Hint**: Multiplying by 1 does not change the value.

5. **Calculate the division**:
\[ \frac{\frac{1}{3}}{\frac{1}{9}} = \frac{1}{3} \times \frac{9}{1} = 3 \]
**Hint**: Dividing fractions involves multiplying by the reciprocal.

6. **Substitute back into the expression**:
\[ 3 - \frac{1}{9} \]
**Hint**: When subtracting, convert whole numbers to fractions if necessary.

7. **Convert 3 to a fraction**:
\[ 3 = \frac{27}{9} \]
**Hint**: To subtract fractions, they must have a common denominator.

8. **Perform the subtraction**:
\[ \frac{27}{9} - \frac{1}{9} = \frac{27 - 1}{9} = \frac{26}{9} \]
**Hint**: Subtract the numerators while keeping the denominator the same.

### Final Answer:
The value of the expression is \(\frac{26}{9}\).