The expression you provided:

\[
-\left( \frac{a}{b} \right) = \frac{-a}{b} \quad \text{where} \quad b \neq 0
\]

is mathematically valid and describes the equivalence between two negative fractions. Here's the explanation:

- The negative sign in front of the fraction \(-\left(\frac{a}{b}\right)\) can be moved to the numerator, resulting in \(\frac{-a}{b}\).
- This works because the negative sign applies to the entire fraction, and whether it's placed in front of the entire fraction or just in the numerator, it gives the same result.

Thus:

\[
-\left( \frac{a}{b} \right) = \frac{-a}{b}
\]

This rule is consistent with how fractions work under multiplication by \(-1\). It can also be expanded further with the following key points:

1. \(-\left(\frac{a}{b}\right) = \frac{a}{-b}\) (you can also place the negative sign in the denominator).
2. \(\frac{-a}{b} = \frac{a}{-b}\) (moving the negative sign between the numerator and denominator).
3. A fraction where both the numerator and denominator are negative becomes positive: \(\frac{-a}{-b} = \frac{a}{b}\).

Would you like more details on this property or have any other questions?

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Here are 5 relative questions for further exploration:
1. How do we handle negative signs in more complex algebraic fractions?
2. How does this property apply to operations like addition and subtraction of fractions?
3. Can you explain the rules for simplifying fractions with negative numerators or denominators?
4. What is the role of absolute value in handling negative fractions?
5. How do these fraction properties apply in solving algebraic equations?

**Tip:** Always remember that moving the negative sign in a fraction between the numerator, denominator, or the whole expression does not change the value of the fraction!

Explore the properties of negative fractions with the equation -(a/b) = (-a)/b, where b ≠ 0. Learn how the negative sign affects fractions and how the concept applies to algebraic expressions. Suitable for Grades 6-8.

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