1. **State the problem:** We need to write the given fractions in descending order for two sets: a. $\frac{25}{16}, \frac{7}{8}, \frac{13}{4}, \frac{17}{32}$ b. $\frac{3}{4}, \frac{12}{5}, \frac{7}{12}, \frac{5}{4}$ 2. **Formula and rules:** To compare fractions, convert them to a common denominator or decimal form. Descending order means from largest to smallest. 3. **Part a:** Find a common denominator for $16, 8, 4, 32$. The least common denominator (LCD) is $32$. Convert each fraction: - $\frac{25}{16} = \frac{25 \times 2}{16 \times 2} = \frac{50}{32}$ - $\frac{7}{8} = \frac{7 \times 4}{8 \times 4} = \frac{28}{32}$ - $\frac{13}{4} = \frac{13 \times 8}{4 \times 8} = \frac{104}{32}$ - $\frac{17}{32}$ stays $\frac{17}{32}$ 4. **Order by numerators:** $104, 50, 28, 17$ So descending order is: $$\frac{13}{4} > \frac{25}{16} > \frac{7}{8} > \frac{17}{32}$$ 5. **Part b:** Find a common denominator for $4, 5, 12, 4$. The LCD is $60$. Convert each fraction: - $\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}$ - $\frac{12}{5} = \frac{12 \times 12}{5 \times 12} = \frac{144}{60}$ - $\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}$ - $\frac{5}{4} = \frac{5 \times 15}{4 \times 15} = \frac{75}{60}$ 6. **Order by numerators:** $144, 75, 45, 35$ So descending order is: $$\frac{12}{5} > \frac{5}{4} > \frac{3}{4} > \frac{7}{12}$$