Question

Arrange the following fraction in ascending order.

$\frac{5}{7},\frac{3}{8},\frac{9}{14}and\frac{20}{21}$

Answer 1

We have, $\frac{5}{7},\frac{3}{8},\frac{9}{14}and\frac{20}{21}$

LCM of denominators $7,8,14$ and $21=$$2\times 2\times 2\times 3\times 7=168$ ( on taking lcm of denominators )

$\Rightarrow converteachofthegivenfractionintoanequivalentfractionwithdenominators168$

$$\begin{gathered} \frac{5}{7}=\frac{5\times 24}{7\times 24}=\frac{120}{168},\frac{3}{8}=\frac{3\times 21}{8\times 21}=\frac{63}{168}, \\ \frac{9}{14}=\frac{9\times 12}{14\times 12}=\frac{108}{168}and\frac{20}{21}=\frac{20\times 8}{21\times 8}=\frac{160}{168} \end{gathered}$$

Clearly, $\frac{63}{168}<\frac{108}{168}<\frac{120}{168}<\frac{160}{168}$

$\Rightarrow \frac{3}{8}<\frac{9}{14}<\frac{5}{7}<\frac{20}{21}$

Hence, ascending order of given fractions are $\frac{3}{8}<\frac{9}{14}<\frac{5}{7}<\frac{20}{21}$