To evaluate the division of two negative fractions, such as -\frac{7}{27} \div \left(-\frac{35}{36} ight), start by rewriting the division as multiplication by the reciprocal of the second fraction: -\frac{7}{27} \cdot \left(-\frac{36}{35} ight). Determine the sign of the product; because both fractions are negative, the result is positive. Multiply the numerators and denominators to get $\frac{7 \cdot 36}{27 \cdot 35}$. Before multiplying completely, rewrite the numbers to reveal their common factors: $\frac{7 \cdot 9 \cdot 4}{9 \cdot 3 \cdot 7 \cdot 5}$. Divide out the common factors of $7$ and $9$ from both the numerator and denominator, which leaves $\frac{4}{3 \cdot 5}$. This simplifies to the final quotient of $\frac{4}{15}$.