Question

The smallest of the fractions $\frac{3}{4},\frac{5}{6},\frac{7}{12},\frac{2}{3}$ is
(a) $\frac{2}{3}$
(b) $\frac{3}{4}$
(c) $\frac{5}{6}$
(d) $\frac{7}{12}$

Answer 1

(d) $\frac{7}{12}$

Explanation:
$$\begin{gathered} 2\underline{\overline{)4,6,12,3}} \\ \underline{2\underline{\overline{)2,3,6,3}}} \\ 3\overline{)\underline{1,3,3,3}} \\ \overline{)\underline{1,1,1,1}} \end{gathered}$$

​​L.C.M. of 4, 6, 12 and 3 = (2 $\times$ 2 $\times$ 3) = 12
Thus, we have:
$$\begin{gathered} \frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12} \\ \frac{5}{6}=\frac{5\times 2}{6\times 2}=\frac{10}{12} \\ \frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12} \\ \frac{7}{12} \\ \mathrm{Clearly},\frac{7}{12}\mathrm{is}\mathrm{the}\mathrm{smallest}\mathrm{fraction}. \end{gathered}$$