To express \(-8.6666\) as a fraction:

1. Let \( x = -8.6666 \).
2. Rewrite \( x \) as a decimal with repeating digits: \( x = -8.\overline{6666} \) (since 6666 repeats).
3. Multiply both sides of the equation by 10,000 to eliminate the repeating decimal:
   \[
   10,000x = -86,666.6666
   \]
4. Subtract the original equation \( x = -8.6666 \) from the new equation:
   \[
   10,000x - x = -86,666.6666 - (-8.6666)
   \]
   Simplifying this:
   \[
   9,999x = -86,658
   \]
5. Divide both sides by 9,999:
   \[
   x = \frac{-86,658}{9,999}
   \]
6. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3:
   \[
   x = \frac{-28,886}{3,333}
   \]

So, \(-8.6666\) as a fraction is \( \frac{-28,886}{3,333} \).

Would you like more details or have any questions?

Here are five related questions:
1. How do you simplify fractions?
2. What is a repeating decimal?
3. How do you find the GCD of two numbers?
4. How do you convert non-repeating decimals to fractions?
5. Can all repeating decimals be expressed as fractions?

**Tip:** Always check if the numerator and denominator can be simplified by their GCD to express a fraction in its simplest form.

Learn how to convert -8.6666 (a repeating decimal) into a simplified fraction with a detailed step-by-step solution. This example uses the concept of repeating decimals, the multiplication method to eliminate repeating digits, and simplification using the GCD. Suitable for students in Grades 7-10.

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