The expression you provided is:

\[
\frac{-15}{27} \div \frac{-9}{20}
\]

To solve this, follow these steps:

### Step 1: Rewrite the division as multiplication
When dividing fractions, multiply by the reciprocal of the second fraction:

\[
\frac{-15}{27} \div \frac{-9}{20} = \frac{-15}{27} \times \frac{20}{-9}
\]

### Step 2: Multiply the numerators and the denominators
Now multiply the fractions:

\[
\frac{-15 \times 20}{27 \times -9} = \frac{-300}{-243}
\]

### Step 3: Simplify the result
The negative signs cancel out, so the fraction becomes:

\[
\frac{300}{243}
\]

### Step 4: Simplify the fraction
Find the greatest common divisor (GCD) of 300 and 243, which is 3. Divide both the numerator and the denominator by 3:

\[
\frac{300 \div 3}{243 \div 3} = \frac{100}{81}
\]

Thus, the final answer is:

\[
\frac{100}{81}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do you divide complex fractions?
2. How do you convert a division problem into a multiplication one?
3. What is the reciprocal of a fraction, and why is it useful?
4. How do you find the greatest common divisor (GCD) of two numbers?
5. Can you simplify mixed number fractions after division?

**Tip**: Always remember to cancel out common factors when simplifying fractions to make the process faster!

Learn how to divide fractions with a step-by-step guide using -15/27 ÷ -9/20. This problem explores fraction division, multiplication by reciprocal, and simplifying fractions using GCD. Suitable for students in Grades 6-8.

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