Question

Arrange the following fractions in the ascending order:

(i) $\frac{2}{9},\frac{7}{9},\frac{3}{9},\frac{4}{9},\frac{1}{9},\frac{6}{9},\frac{5}{9}$
(ii) $\frac{7}{8},\frac{7}{25},\frac{7}{11},\frac{7}{18},\frac{7}{10}$
(iii) $\frac{37}{47},\frac{37}{50},\frac{37}{100},\frac{37}{1000},\frac{37}{85},\frac{37}{41}$
(iv) $\frac{3}{5},\frac{1}{5},\frac{4}{5},\frac{2}{5}$
(v) $\frac{2}{5},\frac{3}{4},\frac{1}{2},\frac{3}{5}$
(vi) $\frac{3}{8},\frac{3}{12},\frac{3}{6},\frac{3}{4}$
(vii) $\frac{4}{6},\frac{3}{8},\frac{6}{12},\frac{5}{16}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{2}{9},\frac{7}{9},\frac{3}{9},\frac{4}{9},\frac{1}{9},\frac{6}{9},\frac{5}{9} \\ \mathrm{When}\mathrm{denominators}\mathrm{are}\mathrm{the}\mathrm{same}\&\mathrm{numerators}\mathrm{are}\mathrm{different},\mathrm{then}\mathrm{the}\mathrm{fraction}\mathrm{with}\mathrm{greater}\mathrm{numerator}\mathrm{has}\mathrm{a}\mathrm{larger}\mathrm{value}. \\ \left(\mathrm{ii}\right)\frac{7}{8},\frac{7}{25},\frac{7}{11},\frac{7}{18},\frac{7}{10} \\ \mathrm{When}\mathrm{numerators}\mathrm{are}\mathrm{the}\mathrm{same}\&\mathrm{denominators}\mathrm{are}\mathrm{different},\mathrm{then}\mathrm{the}\mathrm{fraction}\mathrm{with}\mathrm{smaller}\mathrm{denominator}\mathrm{has}\mathrm{a}\mathrm{smaller}\mathrm{value}. \\ \frac{7}{25}<\frac{7}{18}<\frac{7}{11}<\frac{7}{10}<\frac{7}{8} \\ \left(\mathrm{iii}\right)\frac{37}{47},\frac{37}{50},\frac{37}{100},\frac{37}{1000},\frac{37}{85},\frac{37}{41} \\ \mathrm{When}\mathrm{numerators}\mathrm{are}\mathrm{the}\mathrm{same}\&\mathrm{denominators}\mathrm{are}\mathrm{different},\mathrm{then}\mathrm{the}\mathrm{fraction}\mathrm{with}\mathrm{greater}\mathrm{denominator}\mathrm{has}\mathrm{a}\mathrm{smaller}\mathrm{value}. \\ \frac{37}{1000}<\frac{37}{100}<\frac{37}{85}<\frac{37}{50}<\frac{37}{47}<\frac{37}{41} \\ \left(\mathrm{iv}\right)\frac{3}{5},\frac{1}{5},\frac{4}{5},\frac{2}{5} \\ \mathrm{When}\mathrm{denominators}\mathrm{are}\mathrm{the}\mathrm{same}\&\mathrm{numerators}\mathrm{are}\mathrm{different},\mathrm{then}\mathrm{the}\mathrm{fraction}\mathrm{with}\mathrm{greater}\mathrm{numerator}\mathrm{has}\mathrm{a}\mathrm{larger}\mathrm{value}. \\ \frac{1}{5}<\frac{2}{5}<\frac{3}{5}<\frac{4}{5} \end{gathered}$$

(v)
$$\begin{gathered} \mathrm{LCM}\mathrm{of}2,4\mathrm{and}5\mathrm{is}20. \\ \frac{2}{5}=\frac{2}{5}\times \frac{4}{4}=\frac{8}{20} \\ \frac{3}{4}=\frac{3}{4}\times \frac{5}{5}=\frac{15}{20} \\ \frac{1}{2}=\frac{1}{2}\times \frac{10}{10}=\frac{10}{20} \\ \frac{3}{5}=\frac{3}{5}\times \frac{4}{4}=\frac{12}{20} \end{gathered}$$

$\frac{2}{5}<\frac{1}{2}<\frac{3}{5}<\frac{3}{4}$
(vi)$$\begin{gathered} \frac{3}{8},\frac{3}{12},\frac{3}{6},\frac{3}{4} \\ \mathrm{When}\mathrm{numerators}\mathrm{are}\mathrm{the}\mathrm{same}\&\mathrm{denominators}\mathrm{are}\mathrm{different},\mathrm{then}\mathrm{the}\mathrm{fraction}\mathrm{with}\mathrm{smaller}\mathrm{denominator}\mathrm{has}\mathrm{a}\mathrm{greater}\mathrm{value}. \\ \frac{3}{12}<\frac{3}{8}<\frac{3}{6}<\frac{3}{4} \end{gathered}$$
(vii)
$$\begin{gathered} \frac{4÷2}{6÷2}=\frac{2}{3}(\mathrm{Dividing}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}4\&6) \\ \frac{6}{12}=\frac{1}{2}(\mathrm{Dividing}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}6\&12) \\ \mathrm{LCM}\mathrm{of}2,8,3\mathrm{and}16\mathrm{is}48. \\ \frac{4}{6}=\frac{2}{3}\times \frac{16}{16}=\frac{32}{48} \\ \frac{6}{12}=\frac{1}{2}\times \frac{24}{24}=\frac{24}{48} \\ \frac{3}{8}=\frac{3}{8}\times \frac{6}{6}=\frac{18}{48} \\ \frac{5}{16}=\frac{5}{16}\times \frac{3}{3}=\frac{15}{48} \end{gathered}$$

When denominators are the same & numerators are different, then the fraction with greater numerator has a greater value.

$\frac{5}{16}<\frac{3}{8}<\frac{6}{12}<\frac{4}{6}$