To solve \(\frac{-9}{10} \div \frac{-6}{15}\), follow these steps:

1. **Rewrite the division as multiplication by the reciprocal**:
   \[
   \frac{-9}{10} \div \frac{-6}{15} = \frac{-9}{10} \times \frac{15}{-6}
   \]
2. **Multiply the numerators and the denominators**:
   \[
   \frac{-9 \times 15}{10 \times -6} = \frac{-135}{-60}
   \]
3. **Simplify the fraction**: 
   Since both the numerator and denominator are negative, the fraction becomes positive:
   \[
   \frac{135}{60}
   \]
4. **Reduce the fraction**: 
   Find the greatest common divisor (GCD) of 135 and 60, which is 15. Then divide both the numerator and denominator by 15:
   \[
   \frac{135 \div 15}{60 \div 15} = \frac{9}{4}
   \]

Thus, \(\frac{-9}{10} \div \frac{-6}{15} = \frac{9}{4}\).

Would you like a further breakdown or have any questions?

Here are 5 related questions to explore:
1. How do you multiply and divide negative fractions?
2. How do you find the reciprocal of a fraction?
3. How do you simplify complex fractions?
4. What happens when you divide negative numbers?
5. How do you convert improper fractions to mixed numbers?

**Tip**: Always remember that dividing by a fraction is the same as multiplying by its reciprocal!

Learn how to divide fractions with the example -9/10 ÷ -6/15. This problem demonstrates dividing fractions by multiplying by the reciprocal and simplifying the result. Perfect for students in Grades 6-8. Includes step-by-step explanation.

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