Question

Find a rational number exactly halfway between

$\frac{1}{6}$ and $\frac{1}{9}$

Answer 1

We know that, a rational number, which is halfway between two rational number $a$ and $b$ is given as $\frac{a+b}{2}$

Given rational numbers are $\frac{1}{6}$ and $\frac{1}{9}$
Here, $a=\frac{1}{6}$ and $b=\frac{1}{9}$

$\therefore \frac{a+b}{2}=\frac{\frac{1}{6}+\frac{1}{9}}{2}=\frac{\frac{1\times 3}{6\times 3}+\frac{1\times 2}{9\times 2}}{2}$

$=\frac{\frac{3}{18}+\frac{2}{18}}{2}$

$=\frac{\frac{3+2}{18}}{2}$

$=\frac{\frac{5}{18}}{2}$

$=\frac{5}{18\times 2}$

$=\frac{5}{36}$

Therefore, a rational number exactly halfway between $\frac{1}{6}$ and $\frac{1}{9}$ is $\frac{5}{36}$.