Question

Insert three fractions between:
$\left(i\right)$ $\frac{2}{5}$ and $\frac{4}{9}$

Answer 1

Inserting three fraction between $\frac{2}{5}$ and $\frac{4}{9}$

If $\frac{a}{b}$ and $\frac{c}{d}$ are two fractions, then $\frac{a+c}{b+d}$ is a fraction that lies between them.

By using above property, fraction between $\frac{2}{5}$and $\frac{4}{9}$ is,

$\frac{2+4}{5+9}=\frac{6}{14}$ $=\frac{3}{7}$

fraction between $\frac{2}{5}$ and $\frac{3}{7}$ is,

$\frac{2+3}{5+7}=\frac{5}{12}$

fraction between $\frac{3}{7}$ and $\frac{4}{9}$ is,

$\frac{3+4}{7+9}=\frac{7}{16}$

Hence, $\frac{3}{7},\frac{5}{12}$ and $\frac{7}{16}$ are the three fractions between $\frac{2}{5}$ and $\frac{4}{9}$