The question asks for the location of point $P$ on the number line, and the options are fractions near $-2$.

Step-by-step solution:

1. Observe the number line: $P$ is located between $-2$ and $-3$, slightly closer to $-2$.

2. Analyze the fractional options provided:

   • Option A: $-\frac{1}{3}$ - This is close to $0$, not near $-2$. This is incorrect.
   • Option B: $-\frac{2}{3}$ - Also closer to $0$, not $-2$. This is incorrect.
   • Option C: $-2 \frac{1}{3}$ - This represents $-2 - \frac{1}{3}$, which is slightly beyond $-2$, closer to $-2.3$. This is plausible.
   • Option D: $-2 \frac{2}{3}$ - This represents $-2 - \frac{2}{3}$, which is much closer to $-3$, not near $-2$. This is incorrect.

3. Comparing the location of $P$ (closer to $-2.3$), the correct answer is Option C: $-2 \frac{1}{3}$.

Would you like further clarification or a different explanation?

Related Questions:

1. How can fractions be converted to decimals for better comparison on a number line?
2. Why is $-2 \frac{1}{3}$ closer to $-2$ than $-3$?
3. What are mixed numbers, and how do they relate to improper fractions?
4. How do you plot fractions like $-\frac{2}{3}$ and $-2 \frac{1}{3}$ on a number line?
5. Why does the number line have equal spacing for fractions?

Tip:

When working with fractions on a number line, it helps to estimate their decimal equivalents for easier placement! For example, $\frac{1}{3} \approx 0.33$.