Question

Show that $\frac{3}{7}$ lies between $\frac{2}{5}$ and $\frac{5}{7}$

Answer 1

$\frac{3}{7}$ will lie between $\frac{2}{5}$ and $\frac{5}{7}$ if

$\frac{2}{5}>\frac{3}{7}>\frac{5}{7}$ or $\frac{2}{5}<\frac{3}{7}<\frac{5}{7}$

Now, comparing $\frac{2}{5},\frac{3}{7},\frac{5}{7}$

L.C.M of $5$ and $7-35$

$\therefore \frac{2}{5}=\frac{2\times 7}{5\times 7}=\frac{14}{35}$

$\frac{3}{7}=\frac{3\times 5}{7\times 5}=\frac{15}{35}$

and $\frac{5}{7}=\frac{5\times 5}{7\times 5}=\frac{25}{35}$

$\therefore \frac{14}{35}<\frac{15}{35}<\frac{25}{35}$

$\frac{2}{5}<\frac{3}{7}<\frac{5}{7}$

$\therefore \frac{3}{7}$ lies between $\frac{2}{5}$ and $\frac{5}{7}$