To simplify the fraction \( \frac{33}{-9} \) to its lowest terms:

1. **Find the Greatest Common Divisor (GCD):** The GCD of 33 and 9 is 3.

2. **Divide both the numerator and the denominator by the GCD:**

   \[
   \frac{33 \div 3}{-9 \div 3} = \frac{11}{-3}
   \]

3. **Simplify the sign:** A fraction with a negative denominator can be rewritten with the negative sign in the numerator:

   \[
   \frac{11}{-3} = -\frac{11}{3}
   \]

So, the simplified form of \( \frac{33}{-9} \) is \( -\frac{11}{3} \).

Would you like more details on the steps? Here are some related questions:

1. How do you find the GCD of two numbers?
2. Why does a negative sign move from the denominator to the numerator?
3. Can a fraction be further simplified after reaching lowest terms?
4. What happens if both the numerator and denominator are negative?
5. How do improper fractions differ from mixed numbers?

**Tip:** Always simplify fractions by finding the GCD of the numerator and denominator first.

Learn how to simplify the fraction 33/-9 to its lowest terms using the greatest common divisor (GCD) method. This step-by-step guide covers the basic concepts of fractions, negative numbers, and how to simplify a fraction correctly. Suitable for students in Grades 6-8.

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