1. **State the problem:** Order each set of fractions using the number line. 2. **Convert mixed numbers and fractions to decimals:** This helps to compare them easily. - For the first set: - $\frac{4}{5} = 0.8$ - $\frac{1}{20} = 0.05$ - $1 \frac{3}{4} = 1 + \frac{3}{4} = 1.75$ - $1 \frac{1}{3} = 1 + \frac{1}{3} \approx 1.33$ - $\frac{1}{2} = 0.5$ 3. **Order the first set by decimal values:** - $0.05 < 0.5 < 0.8 < 1.33 < 1.75$ - So, ordered fractions: $\frac{1}{20}, \frac{1}{2}, \frac{4}{5}, 1 \frac{1}{3}, 1 \frac{3}{4}$ 4. **For the second set:** - $\frac{1}{2} = 0.5$ - $\frac{4}{5} = 0.8$ - $\frac{1}{20} = 0.05$ - $1 \frac{1}{3} = 1.33$ - $1 \frac{3}{4} = 1.75$ 5. **Order the second set by decimal values:** - $0.05 < 0.5 < 0.8 < 1.33 < 1.75$ - So, ordered fractions: $\frac{1}{20}, \frac{1}{2}, \frac{4}{5}, 1 \frac{1}{3}, 1 \frac{3}{4}$ 6. **For the third set:** - $1 \frac{1}{10} = 1.1$ - $\frac{2}{3} \approx 0.67$ - $\frac{1}{4} = 0.25$ - $1 \frac{2}{5} = 1.4$ - $1 \frac{2}{3} = 1.67$ 7. **Order the third set by decimal values:** - $0.25 < 0.67 < 1.1 < 1.4 < 1.67$ - So, ordered fractions: $\frac{1}{4}, \frac{2}{3}, 1 \frac{1}{10}, 1 \frac{2}{5}, 1 \frac{2}{3}$ 8. **For the fourth set:** - $1 \frac{1}{6} = 1 + \frac{1}{6} \approx 1.1667$ - $1 \frac{1}{12} = 1 + \frac{1}{12} \approx 1.0833$ - $1 \frac{3}{4} = 1.75$ - $1 \frac{1}{2} = 1.5$ - $\frac{1}{3} \approx 0.3333$ 9. **Order the fourth set by decimal values:** - $0.3333 < 1.0833 < 1.1667 < 1.5 < 1.75$ - So, ordered fractions: $\frac{1}{3}, 1 \frac{1}{12}, 1 \frac{1}{6}, 1 \frac{1}{2}, 1 \frac{3}{4}$ **Final answers:** - Set 1 ordered: $\frac{1}{20}, \frac{1}{2}, \frac{4}{5}, 1 \frac{1}{3}, 1 \frac{3}{4}$ - Set 2 ordered: $\frac{1}{20}, \frac{1}{2}, \frac{4}{5}, 1 \frac{1}{3}, 1 \frac{3}{4}$ - Set 3 ordered: $\frac{1}{4}, \frac{2}{3}, 1 \frac{1}{10}, 1 \frac{2}{5}, 1 \frac{2}{3}$ - Set 4 ordered: $\frac{1}{3}, 1 \frac{1}{12}, 1 \frac{1}{6}, 1 \frac{1}{2}, 1 \frac{3}{4}$