The task in this problem is to plot the fractions and mixed numbers on the number line. Let's solve each problem step by step.

1. $1 \frac{1}{2}$

• Convert $1 \frac{1}{2}$ into an improper fraction:
  $1 \frac{1}{2} = \frac{3}{2}$
• Locate $\frac{3}{2}$ on the number line:
  • Since $6/6 = 1$, and $12/6 = 2$, divide this into sixths.
  • $\frac{3}{2} = \frac{9}{6}$. Plot this on the number line at $\frac{9}{6}$.

2. $\frac{1}{3}$

• Convert $\frac{1}{3}$ to match the denominator in sixths: $\frac{1}{3} = \frac{2}{6}$
• Locate $\frac{2}{6}$ on the number line:
  • It is between 0 and $6/6 = 1$. Plot it at $\frac{2}{6}$.

3. $\frac{14}{6}$

• Simplify $\frac{14}{6}$: $\frac{14}{6} = 2 \frac{2}{6} = 2 \frac{1}{3}$
• Locate $2 \frac{2}{6}$ on the number line:
  • It is just past $2 = 12/6$, at $\frac{14}{6}$.

Final Notes:

1. $1 \frac{1}{2} = 9/6$, plot at $1.5$ on the number line.
2. $1/3 = 2/6$, plot at approximately $0.33$.
3. $14/6 = 2.33$, plot between 2 and 3.

Would you like a more detailed explanation or visualization?

Here are 5 related questions to deepen understanding:

1. How do you convert a mixed number into an improper fraction?
2. Why is it helpful to express fractions with a common denominator?
3. What is the process for simplifying a fraction?
4. How would you plot $5/6$ on this number line?
5. Can you explain why $6/6$ is equal to 1?

Tip: Always ensure the denominators are the same when comparing or plotting fractions!