Question

Arrange the following fractions in descending order:
(i) $\frac{4}{5},\frac{7}{10},\frac{11}{15},\frac{17}{20}$
(ii) $\frac{2}{7},\frac{11}{35},\frac{9}{14},\frac{13}{28}$

Answer 1

(i)
$$\begin{gathered} \mathrm{LCM}\mathrm{of}\mathrm{the}\mathrm{denominators}5,10,15\mathrm{and}20\mathrm{is}60. \\ \mathrm{Now},\mathrm{convert}\mathrm{all}\mathrm{fractions}\mathrm{to}\mathrm{their}\mathrm{equivalent}\mathrm{fractions}\mathrm{with}\mathrm{denominator}60. \\ \frac{4}{5}=\frac{4}{5}\times \frac{12}{12}=\frac{48}{60} \\ \frac{7}{10}=\frac{7}{10}\times \frac{6}{6}=\frac{42}{60} \\ \frac{11}{15}=\frac{11}{15}\times \frac{4}{4}=\frac{44}{60} \\ \frac{17}{20}=\frac{17}{20}\times \frac{3}{3}=\frac{51}{60} \\ \mathrm{We}\mathrm{know}: \\ 51>48>44>42 \\ \Rightarrow \frac{51}{60}>\frac{48}{60}>\frac{44}{60}>\frac{42}{60} \\ \Rightarrow \frac{17}{20}>\frac{4}{5}>\frac{11}{15}>\frac{7}{10} \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{LCM}\mathrm{of}\mathrm{the}\mathrm{denominators}7,35,14\mathrm{and}28\mathrm{is}140. \\ \mathrm{Now},\mathrm{convert}\mathrm{all}\mathrm{fractions}\mathrm{to}\mathrm{their}\mathrm{equivalent}\mathrm{fractions}\mathrm{with}\mathrm{denominator}140. \\ \frac{2}{7}=\frac{2}{7}\times \frac{20}{20}=\frac{40}{140} \\ \frac{11}{35}=\frac{11}{35}\times \frac{4}{4}=\frac{44}{140} \\ \frac{9}{14}=\frac{9}{14}\times \frac{10}{10}=\frac{90}{140} \\ \frac{13}{28}=\frac{13}{28}\times \frac{5}{5}=\frac{65}{140} \\ \mathrm{We}\mathrm{know}: \\ 90>65>44>40 \\ \Rightarrow \frac{90}{140}>\frac{65}{140}>\frac{44}{140}>\frac{40}{140} \\ \Rightarrow \frac{9}{14}>\frac{13}{28}>\frac{11}{35}>\frac{2}{7} \end{gathered}$$