Let's solve the expression step by step:

\[
\left( \frac{8}{125} \right) - \frac{1}{2} + 27 - \frac{1}{3} - 49 \frac{1}{2}
\]

1. Convert mixed numbers to improper fractions:
   - \( 49 \frac{1}{2} = 49 + \frac{1}{2} = \frac{99}{2} \)

2. Rewrite the expression:
   \[
   \frac{8}{125} - \frac{1}{2} + 27 - \frac{1}{3} - \frac{99}{2}
   \]

3. Combine like terms:
   - \( \frac{8}{125} \) stays as it is.
   - Combine the constants \( 27 - 49 = -22 \).

   Now the expression is:
   \[
   \frac{8}{125} - \frac{1}{2} - \frac{99}{2} - \frac{1}{3} - 22
   \]

4. Combine the fractions with a common denominator:
   - For \( \frac{1}{2} \) and \( \frac{99}{2} \): \( \frac{1}{2} + \frac{99}{2} = \frac{100}{2} = 50 \).

   Now the expression is:
   \[
   \frac{8}{125} - 50 - \frac{1}{3} - 22
   \]

5. Combine constants:
   - \( -50 - 22 = -72 \).

   So the expression is:
   \[
   \frac{8}{125} - \frac{1}{3} - 72
   \]

6. Combine \( \frac{8}{125} \) and \( \frac{1}{3} \) using a common denominator of 375:
   \[
   \frac{8}{125} = \frac{24}{375}, \quad \frac{1}{3} = \frac{125}{375}
   \]
   Now subtract:
   \[
   \frac{24}{375} - \frac{125}{375} = \frac{-101}{375}
   \]

7. The final expression is:
   \[
   \frac{-101}{375} - 72
   \]

8. Convert \( \frac{-101}{375} \) to a decimal:
   \[
   \frac{-101}{375} \approx -0.2693
   \]

9. Add to \( -72 \):
   \[
   -72 - 0.2693 = -72.2693
   \]

Thus, the final result is approximately \( \boxed{-72.2693} \).

Do you want further details or have any questions?

Here are 5 related questions:
1. How do you simplify mixed numbers to improper fractions?
2. What is the process of finding a common denominator for fractions?
3. How do you convert a fraction to a decimal?
4. How do constants affect the final result in arithmetic expressions?
5. What role does the order of operations play in solving this type of expression?

**Tip:** When working with fractions and decimals together, converting all terms to decimals can often simplify calculations.

This detailed solution explains how to solve the expression (8/125) - 1/2 + 27 - 1/3 - 49 1/2 by converting mixed numbers to improper fractions, finding common denominators, and simplifying the result to a decimal. Suitable for students in Grades 6-8.

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