Question

Arrange the following fraction in ascending order.

$\frac{3}{4},\frac{7}{8},\frac{11}{16}and\frac{23}{32}$

Answer 1

We have, $\frac{3}{4},\frac{7}{8},\frac{11}{16}and\frac{23}{32}$

LCM of denominators $4,8,16$ and $32=$$2\times 2\times 2\times 2\times 2=32$ ( on taking lcm of denominators )

$\Rightarrow converteachofthegivenfractionintoanequivalentfractionwithdenominators32$

$$\begin{gathered} \frac{3}{4}=\frac{3\times 8}{4\times 8}=\frac{24}{32},\frac{7}{8}=\frac{7\times 4}{8\times 4}=\frac{28}{32}, \\ \frac{11}{16}=\frac{11\times 2}{16\times 2}=\frac{22}{32}and\frac{23}{32}=\frac{23\times 1}{32\times 1}=\frac{23}{32} \end{gathered}$$

Clearly, $\frac{22}{32}<\frac{23}{32}<\frac{24}{32}<\frac{28}{32}$

$\Rightarrow \frac{11}{16}<\frac{23}{32}<\frac{3}{4}<\frac{7}{8}$

Hence, ascending order of given fractions are $\frac{11}{16}<\frac{23}{32}<\frac{3}{4}<\frac{7}{8}$.