Question

Write three rational numbers that lie between the two given numbers
$\frac{4}{5},\frac{2}{3}$

Answer 1

Making the same denominator of the rational numbers $\frac{4}{5}$ and $\frac{2}{3}$.

$\frac{4}{5}=\frac{4\times 3}{5\times 3}=\frac{12}{15}$

$\frac{2}{3}=\frac{2\times 5}{3\times 5}=\frac{10}{15}$

The rational numbers between $\frac{12}{15}$ and $\frac{10}{15}$ is,

$\frac{\frac{12}{15}+\frac{10}{15}}{2}=\frac{22}{30}$

So, $\frac{10}{15}<\frac{22}{30}<\frac{12}{15}$

The rational number between $\frac{10}{15}$ and $\frac{22}{30}$ is,

$\frac{\frac{10}{15}+\frac{22}{30}}{2}=\frac{42}{30\times 2}$

$=\frac{21}{30}$

The rational number between $\frac{12}{15}$ and $\frac{22}{30}$ is,

$\frac{\frac{12}{15}+\frac{22}{30}}{2}=\frac{46}{30\times 2}$

$=\frac{23}{30}$

Thus, $\frac{10}{15}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{12}{15}$.

Therefore the three rational numbers are $\frac{21}{30},\frac{22}{30},\frac{23}{30}$.