The expression you provided is:

\[
\frac{-10}{1/2} \times \frac{2}{5/6}
\]

Let’s break it down:

### Step 1: Simplify each fraction.
1. **Simplify \(\frac{-10}{1/2}\)**:
   Dividing by a fraction is the same as multiplying by its reciprocal, so:
   \[
   \frac{-10}{1/2} = -10 \times 2 = -20
   \]

2. **Simplify \(\frac{2}{5/6}\)**:
   Similarly, divide by \(\frac{5}{6}\) by multiplying by its reciprocal:
   \[
   \frac{2}{5/6} = 2 \times \frac{6}{5} = \frac{12}{5}
   \]

### Step 2: Multiply the results.
Now multiply the simplified values:
\[
-20 \times \frac{12}{5} = \frac{-20 \times 12}{5} = \frac{-240}{5} = -48
\]

### Final Answer:
\[
-48
\]

Would you like further details or explanations? Here are 5 related questions you could explore:

1. What is the general rule for dividing fractions?
2. How do you convert improper fractions to mixed numbers?
3. What is the result of multiplying negative numbers with fractions?
4. How can you simplify complex fractions in algebra?
5. How does reciprocal multiplication work with decimals?

**Tip**: When dividing by a fraction, always remember to multiply by its reciprocal for quicker results.

Understand how to simplify the expression -10/1/2 × 2/5/6 by applying the concept of reciprocal multiplication. This step-by-step guide breaks down the problem using key fraction concepts and rules for dividing fractions. Suitable for students in Grades 6-8.

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