The value of `(1)/(3) div (5)/(6) xx (-5)/(3)` is equal to :

Options

A. `(-2)/(3)`
B. 0
C. 1
D. `(1)/(4)`

Answer

To solve the expression \(\frac{1}{3} \div \frac{5}{6} \times \left(-\frac{5}{3}\right)\), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Rewrite the expression**:
\[ \frac{1}{3} \div \frac{5}{6} \times \left(-\frac{5}{3}\right) \]

2. **Perform the division**:
Dividing by a fraction is the same as multiplying by its reciprocal. Thus, we can rewrite the division:
\[ \frac{1}{3} \div \frac{5}{6} = \frac{1}{3} \times \frac{6}{5} \]

3. **Multiply the fractions**:
Now we multiply \(\frac{1}{3}\) by \(\frac{6}{5}\):
\[ \frac{1 \times 6}{3 \times 5} = \frac{6}{15} \]

4. **Simplify the fraction**:
The fraction \(\frac{6}{15}\) can be simplified:
\[ \frac{6 \div 3}{15 \div 3} = \frac{2}{5} \]

5. **Multiply by \(-\frac{5}{3}\)**:
Now we multiply \(\frac{2}{5}\) by \(-\frac{5}{3}\):
\[ \frac{2}{5} \times \left(-\frac{5}{3}\right) = -\frac{2 \times 5}{5 \times 3} = -\frac{10}{15} \]

6. **Simplify the final fraction**:
The fraction \(-\frac{10}{15}\) can be simplified:
\[ -\frac{10 \div 5}{15 \div 5} = -\frac{2}{3} \]

Thus, the final answer is:
\[ -\frac{2}{3} \]