(8) Compare the following pairs of fractions and use the signs \( >,< \) or \( = \) : \( \begin{array}{lll}\text { (1) } \frac{3}{5} \text { and } \frac{4}{5} & \text { (2) } \frac{7}{9} \text { and } \frac{2}{9} & \text { (3) } \frac{2}{8} \text { and } \frac{12}{48} \\ \text { (4) }-\frac{3}{5} \text { and }-\frac{4}{5} & \text { (5) }-\frac{7}{9} \text { and }-\frac{2}{9} & \text { (6) } \frac{2}{7} \text { and } \frac{3}{21} \\ \text { (7) } \frac{3}{4} \text { and } \frac{5}{6} & \text { (8) }-\frac{1}{2} \text { and }-\frac{3}{7} & \text { (9) }-\frac{3}{5} \text { and }-\frac{4}{9} \\ \text { (10) } 1 \frac{5}{7} \text { and } \frac{9}{4} & \text { (11) }-3 \frac{1}{3} \text { and }-3 \frac{2}{5} & \text { (12) }-1 \frac{2}{27} \text { and }-1 \frac{1}{18} \\ \text { (b) Arrange in ascending order (from smallest to biggest): }\end{array} \)

Sure, let's compare each pair of fractions using the symbols \( > \), \( < \), or \( = \). ### Comparisons: 1. **\( \frac{3}{5} \) and \( \frac{4}{5} \)** - **Analysis:** Both fractions have the same denominator. Compare the numerators. - **Comparison:** \( 3 < 4 \) - **Result:** \( \frac{3}{5} < \frac{4}{5} \) 2. **\( \frac{7}{9} \) and \( \frac{2}{9} \)** - **Analysis:** Both fractions have the same denominator. Compare the numerators. - **Comparison:** \( 7 > 2 \) - **Result:** \( \frac{7}{9} > \frac{2}{9} \) 3. **\( \frac{2}{8} \) and \( \frac{12}{48} \)** - **Simplify Fractions:** - \( \frac{2}{8} = \frac{1}{4} \) - \( \frac{12}{48} = \frac{1}{4} \) - **Comparison:** Both simplified fractions are equal. - **Result:** \( \frac{2}{8} = \frac{12}{48} \) 4. **\( -\frac{3}{5} \) and \( -\frac{4}{5} \)** - **Analysis:** Both fractions are negative with the same denominator. A larger numerator in absolute value means a smaller number. - **Comparison:** \( -3 > -4 \) (since \( -3 \) is closer to zero) - **Result:** \( -\frac{3}{5} > -\frac{4}{5} \) 5. **\( -\frac{7}{9} \) and \( -\frac{2}{9} \)** - **Analysis:** Both fractions are negative with the same denominator. A larger numerator in absolute value means a smaller number. - **Comparison:** \( -7 < -2 \) - **Result:** \( -\frac{7}{9} < -\frac{2}{9} \) 6. **\( \frac{2}{7} \) and \( \frac{3}{21} \)** - **Simplify Fractions:** - \( \frac{3}{21} = \frac{1}{7} \) - **Comparison:** \( \frac{2}{7} > \frac{1}{7} \) - **Result:** \( \frac{2}{7} > \frac{3}{21} \) 7. **\( \frac{3}{4} \) and \( \frac{5}{6} \)** - **Find Common Denominator:** 12 - \( \frac{3}{4} = \frac{9}{12} \) - \( \frac{5}{6} = \frac{10}{12} \) - **Comparison:** \( 9 < 10 \) - **Result:** \( \frac{3}{4} < \frac{5}{6} \) 8. **\( -\frac{1}{2} \) and \( -\frac{3}{7} \)** - **Convert to Decimals:** - \( -\frac{1}{2} = -0.5 \) - \( -\frac{3}{7} \approx -0.4286 \) - **Comparison:** \( -0.5 < -0.4286 \) - **Result:** \( -\frac{1}{2} < -\frac{3}{7} \) 9. **\( -\frac{3}{5} \) and \( -\frac{4}{9} \)** - **Convert to Decimals:** - \( -\frac{3}{5} = -0.6 \) - \( -\frac{4}{9} \approx -0.4444 \) - **Comparison:** \( -0.6 < -0.4444 \) - **Result:** \( -\frac{3}{5} < -\frac{4}{9} \) 10. **\( 1 \frac{5}{7} \) and \( \frac{9}{4} \)** - **Convert to Improper Fractions:** - \( 1 \frac{5}{7} = \frac{12}{7} \approx 1.714 \) - \( \frac{9}{4} = 2.25 \) - **Comparison:** \( 1.714 < 2.25 \) - **Result:** \( 1 \frac{5}{7} < \frac{9}{4} \) 11. **\( -3 \frac{1}{3} \) and \( -3 \frac{2}{5} \)** - **Convert to Improper Fractions:** - \( -3 \frac{1}{3} = -\frac{10}{3} \approx -3.333 \) - \( -3 \frac{2}{5} = -\frac{17}{5} = -3.4 \) - **Comparison:** \( -3.333 > -3.4 \) - **Result:** \( -3 \frac{1}{3} > -3 \frac{2}{5} \) 12. **\( -1 \frac{2}{27} \) and \( -1 \frac{1}{18} \)** - **Convert to Improper Fractions:** - \( -1 \frac{2}{27} = -\frac{29}{27} \approx -1.074 \) - \( -1 \frac{1}{18} = -\frac{19}{18} \approx -1.0556 \) - **Comparison:** \( -1.074 < -1.0556 \) - **Result:** \( -1 \frac{2}{27} < -1 \frac{1}{18} \) ### Summary of Results: 1. \( \frac{3}{5} < \frac{4}{5} \) 2. \( \frac{7}{9} > \frac{2}{9} \) 3. \( \frac{2}{8} = \frac{12}{48} \) 4. \( -\frac{3}{5} > -\frac{4}{5} \) 5. \( -\frac{7}{9} < -\frac{2}{9} \) 6. \( \frac{2}{7} > \frac{3}{21} \) 7. \( \frac{3}{4} < \frac{5}{6} \) 8. \( -\frac{1}{2} < -\frac{3}{7} \) 9. \( -\frac{3}{5} < -\frac{4}{9} \) 10. \( 1 \frac{5}{7} < \frac{9}{4} \) 11. \( -3 \frac{1}{3} > -3 \frac{2}{5} \) 12. \( -1 \frac{2}{27} < -1 \frac{1}{18} \) --- If you have specific fractions you'd like to arrange in ascending order (part **b**), please provide them, and I'd be happy to assist!