Question

Arrange the descending order of fractions.

$\frac{7}{19},\frac{7}{11},\frac{7}{13}and\frac{7}{5}$

Answer 1

Explanation:

we have, $\frac{7}{19},\frac{7}{11},\frac{7}{13},\frac{7}{5}$

LCM of denominators $19,11,13$ and $5=$$5\times 11\times 13\times 19=13,585$ ( on taking L.C.M of denominators )

Convert each of the given fraction into an equivalent fraction with denominator $13,585$.

$$\begin{gathered} \frac{7}{19}=\frac{7\times 715}{19\times 715}=\frac{5,005}{13,585},\frac{7}{11}=\frac{7\times 1235}{11\times 1235}=\frac{8,645}{13,585}, \\ \frac{7}{13}=\frac{7\times 1045}{13\times 1045}=\frac{7,315}{13,585}and\frac{7}{5}=\frac{7\times 2717}{5\times 2717}=\frac{19,019}{13,585} \end{gathered}$$

Clearly , $\frac{19,019}{13,585}>\frac{8,645}{13,585}>\frac{7,315}{13,585}>\frac{5,005}{13,585}$ $\Rightarrow \frac{7}{5}>\frac{7}{11}>\frac{7}{13}>\frac{7}{19}$

Hence, descending order of given fractions are $\frac{7}{5}>\frac{7}{11}>\frac{7}{13}>\frac{7}{19}$