To solve \( 18.15 \div \left(-5 \frac{1}{2}\right) \), we first need to convert the mixed number \( -5 \frac{1}{2} \) into an improper fraction.

### Step 1: Convert \( -5 \frac{1}{2} \) to an improper fraction
\[ -5 \frac{1}{2} = -\left(\frac{5 \times 2 + 1}{2}\right) = -\frac{11}{2} \]

### Step 2: Divide 18.15 by \( -\frac{11}{2} \)
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ 18.15 \div -\frac{11}{2} = 18.15 \times -\frac{2}{11} \]

### Step 3: Perform the multiplication
\[ 18.15 \times -\frac{2}{11} = 18.15 \times -\frac{2}{11} = -\frac{36.3}{11} \]

### Step 4: Simplify the fraction
\[ -\frac{36.3}{11} \approx -3.3 \]

So, \( 18.15 \div -5 \frac{1}{2} \approx -3.3 \).

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What is the result of \( 25.8 \div -6 \frac{2}{3} \)?
2. How do you multiply and divide mixed numbers?
3. How does dividing by a negative number affect the sign of the result?
4. What is the decimal representation of \( -\frac{11}{2} \)?
5. How can improper fractions be converted back to mixed numbers?

**Tip:** When dividing by a fraction, remember to multiply by the reciprocal of that fraction to simplify your calculations.

Learn how to divide 18.15 by -5 1/2 using fractions and mixed numbers. Follow a step-by-step solution to understand the process and its mathematical implications. Suitable for Grades 6-8.

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