To show that \(-\frac{18}{24}\) and \(-\frac{3}{4}\) are equivalent rational numbers, we will simplify \(-\frac{18}{24}\) and see if it equals \(-\frac{3}{4}\).
### Step-by-Step Solution:
1. **Identify the Rational Numbers**:
We have two rational numbers:
\[
-\frac{18}{24} \quad \text{and} \quad -\frac{3}{4}
\]
2. **Simplify \(-\frac{18}{24}\)**:
To simplify \(-\frac{18}{24}\), we need to find the greatest common divisor (GCD) of the numerator (18) and the denominator (24).
3. **Find the GCD of 18 and 24**:
- The factors of 18 are: \(1, 2, 3, 6, 9, 18\)
- The factors of 24 are: \(1, 2, 3, 4, 6, 8, 12, 24\)
- The common factors are: \(1, 2, 3, 6\)
- The greatest common factor is \(6\).
4. **Divide the Numerator and Denominator by the GCD**:
Now, we divide both the numerator and the denominator of \(-\frac{18}{24}\) by \(6\):
\[
-\frac{18 \div 6}{24 \div 6} = -\frac{3}{4}
\]
5. **Conclusion**:
We have simplified \(-\frac{18}{24}\) to \(-\frac{3}{4}\). Therefore, we can conclude that:
\[
-\frac{18}{24} = -\frac{3}{4}
\]
This shows that \(-\frac{18}{24}\) and \(-\frac{3}{4}\) are equivalent rational numbers.
