https://file.aiquickdraw.com/mathbot/file/1729830973848e24j15wh.jpg

The equation you've provided is:

\[
\frac{-5}{7} \div \left( -1 \frac{1}{8} \right)
\]

To solve this, follow these steps:

1. Convert the mixed number \(-1 \frac{1}{8}\) into an improper fraction.
   \[
   -1 \frac{1}{8} = \frac{-9}{8}
   \]
   
2. Now the expression becomes:
   \[
   \frac{-5}{7} \div \frac{-9}{8}
   \]
   
3. Dividing by a fraction is equivalent to multiplying by its reciprocal. So:
   \[
   \frac{-5}{7} \times \frac{-8}{9}
   \]
   
4. Multiply the numerators and denominators:
   \[
   \frac{-5 \times -8}{7 \times 9} = \frac{40}{63}
   \]

Thus, the solution is:

\[
\frac{40}{63}
\]

Would you like any further details or explanations?

Here are 5 related questions to deepen your understanding:

1. How do you multiply two fractions with negative numbers?
2. What is the method to convert mixed numbers into improper fractions?
3. Why is dividing by a fraction the same as multiplying by its reciprocal?
4. How can you simplify fraction multiplication results?
5. How do you convert improper fractions back into mixed numbers?

**Tip:** When dealing with division of fractions, always remember to multiply by the reciprocal to simplify the process.

Learn how to solve the fraction division problem -5/7 ÷ (-1 1/8) by converting the mixed number into an improper fraction and multiplying by the reciprocal. Follow a step-by-step guide for students in Grades 7-8.

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