To divide the fraction \(-5 \frac{1}{2}\) by \(-\frac{3}{4}\), let's break it down step by step:

### Step 1: Convert the mixed number to an improper fraction
\[
-5 \frac{1}{2} = -\frac{11}{2}
\]
### Step 2: Set up the division
We now have:
\[
\frac{-11}{2} \div \frac{-3}{4}
\]

### Step 3: Convert division to multiplication by the reciprocal
When dividing fractions, you multiply by the reciprocal of the second fraction:
\[
\frac{-11}{2} \times \frac{4}{-3}
\]

### Step 4: Multiply the fractions
Now multiply the numerators and the denominators:
\[
\frac{-11 \times 4}{2 \times -3} = \frac{-44}{-6} = \frac{44}{6}
\]

### Step 5: Simplify the fraction
\[
\frac{44}{6} = \frac{22}{3}
\]

So, the result is \(\frac{22}{3}\), or in mixed number form:

\[
7 \frac{1}{3}
\]

Let me know if you need further clarification on any part!

---

Here are 5 related questions to expand your understanding:

1. How do you convert mixed numbers into improper fractions?
2. How can you simplify fractions after multiplication?
3. What is the process for dividing negative fractions?
4. How does changing the signs of both numerator and denominator affect the fraction?
5. How can you convert improper fractions back into mixed numbers?

**Tip**: When dividing by a fraction, always remember to multiply by its reciprocal (flip the second fraction).

Learn how to divide the mixed number -5 1/2 by the fraction -3/4 through a step-by-step solution. This guide covers converting mixed numbers to improper fractions, reciprocal multiplication, and simplifying results, suitable for students in Grades 6-8.

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