1. **Problem:** Compare the fractions $\frac{2}{5}$ and $\frac{3}{10}$. **Step 1:** Find a common denominator. The denominators are 5 and 10. The least common denominator (LCD) is 10. **Step 2:** Convert $\frac{2}{5}$ to a fraction with denominator 10: $$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$$ **Step 3:** Now compare $\frac{4}{10}$ and $\frac{3}{10}$. Since 4 > 3, $$\frac{4}{10} > \frac{3}{10}$$ **Answer:** $\frac{2}{5} > \frac{3}{10}$ 2. **Problem:** Compare the fractions $\frac{5}{4}$ and $\frac{11}{12}$. **Step 1:** Find the LCD of 4 and 12, which is 12. **Step 2:** Convert $\frac{5}{4}$ to twelfths: $$\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$$ **Step 3:** Compare $\frac{15}{12}$ and $\frac{11}{12}$. Since 15 > 11, $$\frac{15}{12} > \frac{11}{12}$$ **Answer:** $\frac{5}{4} > \frac{11}{12}$ 3. **Problem:** Compare $\frac{1}{3}$ and $\frac{1}{5}$. **Step 1:** Find the LCD of 3 and 5, which is 15. **Step 2:** Convert both fractions: $$\frac{1}{3} = \frac{5}{15}, \quad \frac{1}{5} = \frac{3}{15}$$ **Step 3:** Since 5 > 3, $$\frac{1}{3} > \frac{1}{5}$$ **Answer:** $\frac{1}{3} > \frac{1}{5}$ 4. **Problem:** Compare $\frac{8}{9}$ and $\frac{8}{12}$. **Step 1:** Find the LCD of 9 and 12, which is 36. **Step 2:** Convert both fractions: $$\frac{8}{9} = \frac{8 \times 4}{9 \times 4} = \frac{32}{36}, \quad \frac{8}{12} = \frac{8 \times 3}{12 \times 3} = \frac{24}{36}$$ **Step 3:** Since 32 > 24, $$\frac{8}{9} > \frac{8}{12}$$ **Answer:** $\frac{8}{9} > \frac{8}{12}$ 5. **Problem:** Compare $\frac{3}{6}$ and $\frac{2}{4}$. **Step 1:** Simplify both fractions: $$\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}, \quad \frac{2}{4} = \frac{2 \div 2}{4 \div 2} = \frac{1}{2}$$ **Step 2:** Both fractions are equal. **Answer:** $\frac{3}{6} = \frac{2}{4}$