Question

Question 93 (c)

Find a rational number exactly halfway between
$\frac{5}{-13}and\frac{-7}{9}$

Answer 1

We know that, a rational number, which is halfways between two rational number i.e. a and b $=\frac{a+b}{2}$
Given rational numbers are $\frac{5}{-13}and\frac{-7}{9}$
Here, $a=-\frac{5}{13}andb=-\frac{7}{9}$
$\therefore \frac{a+b}{2}=\frac{\frac{-5}{13}+(-\frac{7}{9})}{2}=\frac{\frac{-5}{13}-\frac{7}{9}}{2}=\frac{\frac{-5\times 9}{13\times 9}-\frac{7\times 13}{9\times 13}}{2}=\frac{\frac{-45}{117}-\frac{91}{117}}{2}=\frac{\frac{-45-91}{117}}{2}=\frac{-136}{117\times 2}=\frac{-136}{234}$