Question

The smallest of the fractions $\frac{3}{5},\frac{2}{3},\frac{5}{6},\frac{7}{10}$ is

(a) $\frac{2}{3}$
(b) $\frac{3}{5}$
(c) $\frac{5}{6}$
(d) $\frac{7}{10}$

Answer 1

Fractions can be compared by converting them into like fractions and then arranging them in ascending or descending order.

$\frac{3}{5}=\frac{3\times 6}{5\times 6}=\frac{18}{30}$,
$\frac{2}{3}=\frac{2\times 10}{3\times 10}=\frac{20}{30}$,
$\frac{5}{6}=\frac{5\times 5}{6\times 5}=\frac{25}{30}$,
$\frac{7}{10}=\frac{7\times 3}{10\times 3}=\frac{21}{30}$.

We know,
18 < 20 < 21 < 25
$$\begin{gathered} \Rightarrow \frac{18}{30}<\frac{20}{30}<\frac{21}{30}<\frac{25}{30} \\ \Rightarrow \frac{3}{5}<\frac{2}{3}<\frac{7}{10}<\frac{5}{6} \end{gathered}$$

∴ the smallest fraction is $\frac{3}{5}$.

Hence, the correct option is (b).