Question

Arrange the following fraction in ascending order.

$\frac{5}{6},\frac{7}{8},\frac{11}{12}and\frac{3}{10}$

Answer 1

We have, $\frac{5}{6},\frac{7}{8},\frac{11}{12}and\frac{3}{10}$

LCM of denominators $6,8,12$ and $10=$$2\times 2\times 2\times 3\times 5=120$ ( on taking lcm of denominators )

$\Rightarrow converteachofthegivenfractionintoanequivalentfractionwithdenominators120$

$$\begin{gathered} \frac{5}{6}=\frac{5\times 20}{6\times 20}=\frac{100}{120},\frac{7}{8}=\frac{7\times 15}{8\times 15}=\frac{105}{120}, \\ \frac{11}{12}=\frac{11\times 10}{12\times 10}=\frac{110}{120}and\frac{3}{10}=\frac{3\times 12}{10\times 12}=\frac{36}{120} \end{gathered}$$

Clearly, $\frac{36}{120}<\frac{100}{120}<\frac{105}{120}<\frac{110}{120}$

$\Rightarrow \frac{3}{10}<\frac{5}{6}<\frac{7}{8}<\frac{11}{12}$

Hence, ascending order of given fractions are $\frac{3}{10}<\frac{5}{6}<\frac{7}{8}<\frac{11}{12}$.