Question

Arrange the following fractions in ascending order:
(i) $\frac{3}{8},\frac{5}{6},\frac{6}{8}\frac{2}{4},\frac{1}{3}$
(ii) $\frac{4}{3},\frac{3}{8},\frac{6}{12},\frac{5}{16}$

Answer 1

(i)
$$\begin{gathered} \mathrm{LCM}\mathrm{of}\mathrm{the}\mathrm{denominators}8,6,4\mathrm{and}3\mathrm{is}24. \\ \mathrm{Now},\mathrm{convert}\mathrm{all}\mathrm{fractions}\mathrm{into}\mathrm{their}\mathrm{equivalent}\mathrm{fractions}\mathrm{with}\mathrm{denominator}24. \\ \frac{3}{8}=\frac{3}{8}\times \frac{3}{3} \\ \Rightarrow \frac{3}{8}=\frac{9}{24} \\ \frac{5}{6}=\frac{5}{6}\times \frac{4}{4} \\ \Rightarrow \frac{5}{6}=\frac{20}{24} \\ \frac{6}{8}=\frac{6}{8}\times \frac{3}{3} \\ \Rightarrow \frac{6}{8}=\frac{18}{24} \\ \frac{2}{4}=\frac{2}{4}\times \frac{6}{6} \\ \Rightarrow \frac{2}{4}=\frac{12}{24} \\ \frac{1}{3}=\frac{1}{3}\times \frac{8}{8} \\ \Rightarrow \frac{1}{3}=\frac{8}{24} \\ \mathrm{We}\mathrm{know}: \\ 8<9<12<18<20 \\ \Rightarrow \frac{8}{24}<\frac{9}{24}<\frac{12}{24}<\frac{18}{24}<\frac{20}{24} \\ \Rightarrow \frac{1}{3}<\frac{3}{8}<\frac{2}{4}<\frac{6}{8}<\frac{5}{6} \end{gathered}$$
(ii)
$$\begin{gathered} \mathrm{LCM}\mathrm{of}\mathrm{the}\mathrm{denominators}8,12,16\mathrm{and}3\mathrm{is}48. \\ \mathrm{Now},\mathrm{convert}\mathrm{all}\mathrm{fractions}\mathrm{into}\mathrm{their}\mathrm{equivalent}\mathrm{fractions}\mathrm{with}\mathrm{denominator}48. \\ \frac{4}{3}=\frac{4}{3}\times \frac{16}{16} \\ \Rightarrow \frac{4}{3}=\frac{64}{48} \\ \frac{3}{8}=\frac{3}{8}\times \frac{6}{6} \\ \Rightarrow \frac{3}{8}=\frac{18}{48} \\ \frac{6}{12}=\frac{6}{12}\times \frac{4}{4} \\ \Rightarrow \frac{6}{12}=\frac{24}{48} \\ \frac{5}{16}=\frac{5}{16}\times \frac{3}{3} \\ \Rightarrow \frac{5}{16}=\frac{15}{48} \\ \mathrm{we}\mathrm{know} \\ 15<18<24<64 \\ \Rightarrow \frac{15}{48}<\frac{18}{48}<\frac{24}{48}<\frac{64}{48} \\ \Rightarrow \frac{5}{16}<\frac{3}{8}<\frac{6}{12}<\frac{4}{3} \end{gathered}$$