1. **Problem Statement:** Order the given dissimilar fractions from smallest to largest (ascending) and from largest to smallest (descending) using models. 2. **Fractions to order:** 4/6, 9/8, 7/12, 5/10. 3. **Formula and Rules:** To compare fractions with different denominators, convert them to equivalent fractions with a common denominator or convert to decimals. 4. **Step-by-step comparison:** - Find the least common denominator (LCD) for all fractions: denominators are 6, 8, 12, 10. - LCD of 6, 8, 12, 10 is 120. - Convert each fraction: $$\frac{4}{6} = \frac{4 \times 20}{6 \times 20} = \frac{80}{120}$$ $$\frac{9}{8} = \frac{9 \times 15}{8 \times 15} = \frac{135}{120}$$ $$\frac{7}{12} = \frac{7 \times 10}{12 \times 10} = \frac{70}{120}$$ $$\frac{5}{10} = \frac{5 \times 12}{10 \times 12} = \frac{60}{120}$$ 5. **Order ascending (smallest to largest):** - Compare numerators: 60 (5/10), 70 (7/12), 80 (4/6), 135 (9/8) - So ascending order is: $$\frac{5}{10} < \frac{7}{12} < \frac{4}{6} < \frac{9}{8}$$ 6. **Order descending (largest to smallest):** - Reverse the ascending order: $$\frac{9}{8} > \frac{4}{6} > \frac{7}{12} > \frac{5}{10}$$ 7. **Explanation:** By converting fractions to a common denominator, we can directly compare their numerators to determine their relative sizes. This method is reliable and helps visualize ordering using fraction bars or circles. **Final answers:** - Ascending order: $\frac{5}{10}, \frac{7}{12}, \frac{4}{6}, \frac{9}{8}$ - Descending order: $\frac{9}{8}, \frac{4}{6}, \frac{7}{12}, \frac{5}{10}$