Solutions: Section 7.7

Page 174: Figure It Out

Q1. Compare and Justify:

• a. $\frac{8}{3}, \frac{5}{2}$:
  • LCM of 3 and 2 is 6.
  • $\frac{16}{6}$ vs $\frac{15}{6}$.
  • $\frac{8}{3} > \frac{5}{2}$.
• b. $\frac{4}{9}, \frac{3}{7}$:
  • $\frac{28}{63}$ vs $\frac{27}{63}$.
  • $\frac{4}{9} > \frac{3}{7}$.
• c. $\frac{7}{10}, \frac{9}{14}$:
  • LCM is 70.
  • $\frac{49}{70}$ vs $\frac{45}{70}$.
  • $\frac{7}{10} > \frac{9}{14}$.

Q2. Ascending Order:

• a. $\frac{7}{10}, \frac{11}{15}, \frac{2}{5}$:
  • LCM of 10, 15, 5 is 30.
  • $\frac{21}{30}, \frac{22}{30}, \frac{12}{30}$.
  • Order: $\frac{2}{5} < \frac{7}{10} < \frac{11}{15}$.

Q3. Descending Order:

• a. $\frac{25}{16}, \frac{7}{8}, \frac{13}{4}, \frac{17}{32}$:
  • LCM is 32.
  • $\frac{50}{32}, \frac{28}{32}, \frac{104}{32}, \frac{17}{32}$.
  • Order: $\frac{13}{4} > \frac{25}{16} > \frac{7}{8} > \frac{17}{32}$.