1. **Stating the problem:** We are given two fractions, $\frac{1}{2}$ and $\frac{9}{14}$, and we want to compare their values and understand their positions on the number line. 2. **Formula and rules:** To compare fractions, we can either convert them to decimals or find a common denominator and compare numerators. 3. **Convert to decimals:** - $\frac{1}{2} = 0.5$ - $\frac{9}{14} \approx 0.6429$ 4. **Find common denominator:** - The denominators are 2 and 14. The least common denominator (LCD) is 14. - Convert $\frac{1}{2}$ to fourteenths: $\frac{1}{2} = \frac{7}{14}$. 5. **Compare numerators:** - $\frac{7}{14}$ vs $\frac{9}{14}$ - Since $7 < 9$, $\frac{1}{2} < \frac{9}{14}$. 6. **Interpretation on the number line:** - $\frac{1}{2}$ is at 0.5. - $\frac{9}{14}$ is approximately 0.6429, which is to the right of $\frac{1}{2}$. **Final answer:** $\frac{1}{2} < \frac{9}{14}$, so on the number line, $\frac{1}{2}$ is to the left of $\frac{9}{14}$.