The activity requires comparing two rational numbers, writing the correct inequality sign (either < or >), and placing the numbers on the number line. Let's go through each problem step-by-step:

1. 4.5 vs. $\frac{1}{3}$

• Convert to decimals:
  • $4.5 = 4.5$
  • $\frac{1}{3} \approx 0.333$
• Comparison: $4.5 > \frac{1}{3}$
• Placement on Number Line: $4.5$ is much greater than $\frac{1}{3}$, so $4.5$ would be on the right side of the number line closer to 5, and $\frac{1}{3}$ is close to 0.

2. 0.9 vs. 1.9

• Convert to decimals:
  • Both are already in decimal form.
• Comparison: $0.9 < 1.9$
• Placement on Number Line: $0.9$ is between 0 and 1, and $1.9$ is just before 2.

3. 3 vs. $\frac{17}{5}$

• Convert to decimals:
  • $\frac{17}{5} = 3.4$
• Comparison: $3 < \frac{17}{5}$
• Placement on Number Line: $3$ is on the left, and $3.4$ (or $\frac{17}{5}$) is to the right of 3 but before 4.

4. $\frac{5}{6}$ vs. 3

• Convert to decimals:
  • $\frac{5}{6} \approx 0.833$
• Comparison: $\frac{5}{6} < 3$
• Placement on Number Line: $\frac{5}{6}$ is between 0 and 1, while 3 is farther right on the number line.

5. 5.3 vs. $\frac{28}{5}$

• Convert to decimals:
  • $\frac{28}{5} = 5.6$
• Comparison: $5.3 < \frac{28}{5}$
• Placement on Number Line: $5.3$ is just past 5, while $5.6$ is slightly farther right, between 5 and 6.

6. 0.2 vs. $\frac{3}{5}$

• Convert to decimals:
  • $\frac{3}{5} = 0.6$
• Comparison: $0.2 < \frac{3}{5}$
• Placement on Number Line: $0.2$ is closer to 0, while $0.6$ is between 0 and 1, but closer to 1.

7. $6 \frac{1}{7}$ vs. 6.69

• Convert to decimals:
  • $6 \frac{1}{7} \approx 6.14$
• Comparison: $6 \frac{1}{7} < 6.69$
• Placement on Number Line: $6 \frac{1}{7}$ is between 6 and 7, closer to 6, while $6.69$ is closer to 7.

8. 1 vs. 0

• Convert to decimals:
  • Both are already in decimal form.
• Comparison: $1 > 0$
• Placement on Number Line: $1$ is on the right, and $0$ is on the left.

9. 10.78 vs. $\frac{120}{10}$

• Convert to decimals:
  • $\frac{120}{10} = 12$
• Comparison: $10.78 < 12$
• Placement on Number Line: $10.78$ is between 10 and 12, but closer to 11, while $12$ is exactly at 12.

10. $5 \frac{5}{9}$ vs. $5 \frac{13}{15}$

• Convert to decimals:
  • $5 \frac{5}{9} \approx 5.56$
  • $5 \frac{13}{15} \approx 5.87$
• Comparison: $5 \frac{5}{9} < 5 \frac{13}{15}$
• Placement on Number Line: $5 \frac{5}{9}$ is closer to 5, while $5 \frac{13}{15}$ is nearer to 6.

Would you like more details, or have any specific questions about these problems?

Related Questions:

1. How do you convert fractions into decimal form?
2. Why is comparing decimals important when placing them on a number line?
3. What are some strategies for understanding the relative sizes of fractions?
4. How can you use a number line to visualize operations like addition or subtraction?
5. What are some common mistakes to avoid when comparing rational numbers?

Tip:

When comparing fractions, converting them to decimals can make it easier to understand their relative sizes!