Question

Find a rational number between
(i) $\frac{3}{8}\mathrm{and}\frac{2}{5}$
(ii) 1.3 and 1.4
(iii) $-1\mathrm{and}\frac{1}{2}$
(iv) $-\frac{3}{4}\mathrm{and}-\frac{2}{5}$
(v) $\frac{1}{9}\mathrm{and}\frac{2}{9}$

Answer 1

(i) $\frac{3}{8}\mathrm{and}\frac{2}{5}$
Let:
x = $\frac{3}{8}$ and y = $\frac{2}{5}$
Rational number lying between x and y:
$\frac{1}{2}\left(x+y\right)=\frac{1}{2}\left(\frac{3}{8}+\frac{2}{5}\right)$
= $\frac{1}{2}\left(\frac{15+16}{40}\right)=\frac{31}{80}$

(ii) 1.3 and 1.4
Let:
x = 1.3 and y = 1.4
Rational number lying between x and y:
$\frac{1}{2}\left(x+y\right)=\frac{1}{2}\left(1.3+1.4\right)$
= $\frac{1}{2}\left(2.7\right)=1.35$

(iii) $-1\mathrm{and}\frac{1}{2}$
Let:
x = $-$1 and y = $\frac{1}{2}$
Rational number lying between x and y:
$\frac{1}{2}\left(x+y\right)=\frac{1}{2}\left(-1+\frac{1}{2}\right)$
= $-\frac{1}{4}$

(iv) $-\frac{3}{4}\mathrm{and}-\frac{2}{5}$
Let:
x = $-\frac{3}{4}$ and y = $-\frac{2}{5}$
Rational number lying between x and y:
$\frac{1}{2}\left(x+y\right)=\frac{1}{2}\left(-\frac{3}{4}-\frac{2}{5}\right)$
= $\frac{1}{2}\left(\frac{-15-8}{20}\right)=-\frac{23}{40}$

(v) $\frac{1}{9}\mathrm{and}\frac{2}{9}$
A rational number lying between $\frac{1}{9}\mathrm{and}\frac{2}{9}$ will be
$\frac{1}{2}\left(\frac{1}{9}+\frac{2}{9}\right)=\frac{1}{2}\times \frac{1}{3}=\frac{1}{6}$