Question

Find ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$

Answer 1

-2/5 & 1/2

Finding LCM of 5 & 2
LCM = 10
MULTIPLYING BOTH BY 4

$\frac{-8}{20}and\frac{10}{20}$
that is $\frac{-2}{5}=\frac{-8}{20}$
and $\frac{1}{2}=\frac{10}{20}$
instead of finding rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$
we are finding the rational numbers between $\frac{-8}{20}$ and $\frac{10}{20}$
here both the denominators are same
so any rational number with same denominator and a numerator having a value between -8 and 10 gives rational numbers between the given numbers
So rational number between $\frac{-8}{20}$ & $\frac{10}{20}$ WILL BE

$\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},\frac{0}{20},\frac{1}{20},\frac{2}{20}$

ANSWER = $\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},\frac{0}{20},\frac{1}{20},\frac{2}{20}$