7. Arrange the following rational numbers in ascending order: $$ \begin{array}{lll} ext { (i) } \frac{3}{4}, \frac{-4}{5}, \frac{14}{10} & ext { (ii) } \frac{5}{18}, \frac{4}{9}, \frac{-5}{3} & ext { (iii) } \frac{3}{7}, \frac{4}{14}, \frac{5}{21}\end{array} $$

Question

7. Arrange the following rational numbers in ascending order: $$ \begin{array}{lll}	ext { (i) } \frac{3}{4}, \frac{-4}{5}, \frac{14}{10} & 	ext { (ii) } \frac{5}{18}, \frac{4}{9}, \frac{-5}{3} & 	ext { (iii) } \frac{3}{7}, \frac{4}{14}, \frac{5}{21}\end{array} $$

UpStudy AI · Accepted Answer

1. **Part (i): $$\frac{3}{4}, \frac{-4}{5}, \frac{14}{10}$$**

- Convert each fraction to a decimal:
     - $$\frac{3}{4} = 0.75$$
     - $$\frac{-4}{5} = -0.8$$
     - $$\frac{14}{10} = 1.4$$
   
   - Arranging in ascending order:
     $$
     \frac{-4}{5} \, (-0.8) < \frac{3}{4} \, (0.75) < \frac{14}{10} \, (1.4)
     $$

2. **Part (ii): $$\frac{5}{18}, \frac{4}{9}, \frac{-5}{3}$$**

- Convert each fraction to a decimal:
     - $$\frac{5}{18} \approx 0.2778$$
     - $$\frac{4}{9} \approx 0.4444$$
     - $$\frac{-5}{3} \approx -1.6667$$
   
   - Arranging in ascending order:
     $$
     \frac{-5}{3} \, (-1.6667) < \frac{5}{18} \, (0.2778) < \frac{4}{9} \, (0.4444)
     $$

3. **Part (iii): $$\frac{3}{7}, \frac{4}{14}, \frac{5}{21}$$**

- Simplify where possible:
     - $$\frac{4}{14} = \frac{2}{7}$$
   
   - Convert each fraction to a decimal:
     - $$\frac{3}{7} \approx 0.4286$$
     - $$\frac{2}{7} \approx 0.2857$$
     - $$\frac{5}{21} \approx 0.2381$$
   
   - Arranging in ascending order:
     $$
     \frac{5}{21} \, (0.2381) < \frac{2}{7} \, (0.2857) < \frac{3}{7} \, (0.4286)
     $$

**Final Answers:**

- Part (i): $$\frac{-4}{5} < \frac{3}{4} < \frac{14}{10}$$
- Part (ii): $$\frac{-5}{3} < \frac{5}{18} < \frac{4}{9}$$
- Part (iii): $$\frac{5}{21} < \frac{4}{14} < \frac{3}{7}$$
- Part (i): $$\frac{-4}{5} < \frac{3}{4} < \frac{14}{10}$$ - Part (ii): $$\frac{-5}{3} < \frac{5}{18} < \frac{4}{9}$$ - Part (iii): $$\frac{5}{21} < \frac{4}{14} < \frac{3}{7}$$

Arrange the following rational numbers in ascending order:

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