Question

Find a rational number lying between
(i) $\frac{1}{4}\mathrm{and}\frac{1}{3}$
(ii) $\frac{3}{8}\mathrm{and}\frac{2}{5}$
(iii) 1.3 and 1.4
(iv) 0.75 and 1.2
(v) $-1\mathrm{and}\frac{1}{2}$
(vi) $-\frac{3}{4}\mathrm{and}-\frac{2}{5}$

Answer 1

(i) Let:
x = $\frac{1}{4}$ and y = $\frac{1}{3}$
Rational number lying between x and y:
$\frac{1}{2}\left(x+y\right)=\frac{1}{2}\left(\frac{1}{4}+\frac{1}{3}\right)$
= $\frac{7}{24}$

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

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

(iv) Let:
x = 0.75 and y = 1.2
Rational number lying between x and y:
$\frac{1}{2}\left(x+y\right)=\frac{1}{2}\left(0.75+1.2\right)$
= $\frac{1}{2}\left(1.95\right)=0.975$

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

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