Question

Insert three fractions between:
$\left(ii\right)$ $\frac{1}{2}$ and $\frac{5}{7}$

Answer 1

Inserting three fraction between $\frac{1}{2}$ and $\frac{5}{7}$

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 $\frac{1}{2}$and $\frac{5}{7}$ is,

$\frac{1+5}{2+7}=\frac{6}{9}$ $=\frac{2}{3}$

fraction between $\frac{1}{2}$ and $\frac{2}{3}$ is,

$\frac{1+2}{2+3}=\frac{3}{5}$

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

$\frac{2+5}{3+7}=\frac{7}{10}$

Hence, $\frac{2}{3},\frac{3}{5}$ and $\frac{7}{10}$ are the three fractions between $\frac{1}{2}$ and $\frac{5}{7}$