To solve \(-8 \frac{1}{4} \div 4 \frac{3}{8}\), we first convert the mixed numbers into improper fractions and then divide them.

### Step 1: Convert mixed numbers to improper fractions
- \(-8 \frac{1}{4}\) becomes \(-\frac{33}{4}\), since:
  \[
  8 \times 4 + 1 = 33
  \]
- \(4 \frac{3}{8}\) becomes \(\frac{35}{8}\), since:
  \[
  4 \times 8 + 3 = 35
  \]

### Step 2: Divide the fractions
To divide fractions, multiply the first fraction by the reciprocal of the second:
\[
-\frac{33}{4} \div \frac{35}{8} = -\frac{33}{4} \times \frac{8}{35}
\]

### Step 3: Multiply the fractions
Now, multiply the numerators and denominators:
\[
-\frac{33 \times 8}{4 \times 35} = -\frac{264}{140}
\]

### Step 4: Simplify the fraction
Simplify \(\frac{264}{140}\) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 4:
\[
-\frac{264 \div 4}{140 \div 4} = -\frac{66}{35}
\]

So, \(-8 \frac{1}{4} \div 4 \frac{3}{8} = -\frac{66}{35}\), which is approximately \(-1.8857\) in decimal form.

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### Related Questions:
1. How do you find the reciprocal of a fraction?
2. What is the GCD, and how do you calculate it?
3. How do you simplify improper fractions to mixed numbers?
4. Can you show how to multiply two fractions step-by-step?
5. What are the rules for dividing negative fractions?

### Tip:
When dividing fractions, always remember to multiply by the reciprocal of the divisor.

Learn how to divide mixed fractions with the example -8 1/4 ÷ 4 3/8. This step-by-step guide covers converting mixed numbers to improper fractions, multiplying by reciprocals, and simplifying the result. Suitable for Grades 6-8.

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