To solve the expression \(\frac{-2}{7} \div \frac{-2}{8}\), we follow these steps:

### Step 1: Rewrite the division as multiplication
Division by a fraction is the same as multiplying by its reciprocal. So,

\[
\frac{-2}{7} \div \frac{-2}{8} = \frac{-2}{7} \times \frac{8}{-2}
\]

### Step 2: Simplify the expression
Now, multiply the numerators and the denominators:

\[
\frac{-2 \times 8}{7 \times -2} = \frac{-16}{-14}
\]

### Step 3: Simplify the fraction
Since both the numerator and denominator are negative, the fraction becomes positive:

\[
\frac{-16}{-14} = \frac{16}{14}
\]

### Step 4: Reduce the fraction
Simplify \(\frac{16}{14}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

\[
\frac{16 \div 2}{14 \div 2} = \frac{8}{7}
\]

### Final Answer:
\[
\frac{-2}{7} \div \frac{-2}{8} = \frac{8}{7}
\]

Would you like more details, or do you have any other questions?

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Here are 5 related questions to expand on this topic:
1. How do you multiply and divide fractions with different signs?
2. How can you find the reciprocal of a fraction?
3. What is the general process for simplifying fractions?
4. Can you explain how to add and subtract fractions with different denominators?
5. How do you solve complex fractions with multiple terms?

**Tip:** Always check if the fractions can be simplified early to make calculations easier.

Learn how to solve the fraction division -2/7 ÷ -2/8 with a detailed step-by-step solution. This problem covers division of fractions, finding reciprocals, and simplifying fractions. Ideal for students in Grades 6-8.

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