Question

The smallest of the fractions $\frac{3}{5},\frac{2}{3},\frac{5}{6},\frac{7}{10}$ is
(a) $\frac{2}{3}$
(b) $\frac{7}{10}$
(c) $\frac{3}{5}$
(d) $\frac{5}{6}$

Answer 1

(c) $\frac{3}{5}$

$$\begin{gathered} 2\underline{\overline{)5,3,6,10}} \\ \underline{5\underline{\overline{)5,3,3}},5} \\ 3\overline{)\underline{1,3,3,1}} \\ \overline{)\underline{1,1,1,1}} \end{gathered}$$

L.C.M. of 5, 3, 6 and 10 = (2 $\times$ 3 $\times$ 5) = 30
Thus, we have:
$$\begin{gathered} \frac{3}{5}=\frac{3\times 6}{5\times 6}=\frac{18}{30} \\ \frac{2}{3}=\frac{2\times 10}{3\times 10}=\frac{20}{30} \\ \frac{5}{6}=\frac{5\times 5}{6\times 5}=\frac{25}{30} \\ \frac{7}{10}=\frac{7\times 3}{10\times 3}=\frac{21}{30} \\ \therefore \mathrm{The}\mathrm{smallest}\mathrm{fraction}=\frac{18}{30}=\frac{3}{5} \end{gathered}$$