Question

Arrange the following fraction in ascending order.

$\frac{2}{3},\frac{3}{4},\frac{5}{12}and\frac{9}{16}$

Answer 1

We have, $\frac{2}{3},\frac{3}{4},\frac{5}{12}and\frac{9}{16}$

LCM of denominators $3,4,12$ and $16=$$2\times 2\times 2\times 2\times 3=48$ ( on taking lcm of denominators )

$\Rightarrow converteachofthegivenfractionintoanequivalentfractionwithdenominators48$

$$\begin{gathered} \frac{2}{3}=\frac{2\times 16}{3\times 16}=\frac{32}{48},\frac{3}{4}=\frac{3\times 12}{4\times 12}=\frac{36}{48}, \\ \frac{5}{12}=\frac{5\times 4}{12\times 4}=\frac{20}{48}and\frac{9}{16}=\frac{9\times 3}{16\times 3}=\frac{27}{48} \end{gathered}$$

Clearly, $\frac{20}{48}<\frac{27}{48}<\frac{32}{48}<\frac{36}{48}$

$\Rightarrow \frac{5}{12}<\frac{9}{16}<\frac{2}{3}<\frac{3}{4}$

Hence, ascending order of given fractions are $\frac{5}{12}<\frac{9}{16}<\frac{2}{3}<\frac{3}{4}$.