Question

Two rational numbers between $\frac{2}{3}$ and $\frac{5}{3}$ are

(a)$\frac{1}{6}$ and $\frac{2}{6}$
(b)$\frac{1}{2}$ and $\frac{2}{1}$
(c)$\frac{5}{6}$ and $\frac{7}{6}$
(d)$\frac{2}{3}$ and $\frac{4}{3}$

Answer 1

Given $\frac{2}{3}\text{and}\frac{5}{3}$
Since, as denominators are equals , So the numbers lies between their denominators are $2<3<4<5$
Dividing $3$, we get
$\frac{2}{3}<\frac{3}{3}<\frac{4}{3}<\frac{5}{3}$
As $\frac{3}{3}=1$ and $\frac{4}{3}$ are not available in the any given options.
Let's increase the range of numerator values of given rational number by multiplying $\frac{2}{2}$, we get, $\frac{2}{3}\times \frac{2}{2}\text{and}\frac{5}{3}\times \frac{2}{2}$
$\Rightarrow \frac{4}{6}\text{and}\frac{10}{6}$
So, the numbers lies between $4$ and $10$ are
$4<5<6<7<8<9<10$
Dividing $6$, we get
$\frac{4}{6}<\frac{5}{6}<\frac{6}{6}<\frac{7}{6}<\frac{8}{6}<\frac{9}{6}<\frac{10}{6}$
Clearly, the option (c) values $\frac{5}{6},\frac{7}{6}$ lies between $\frac{4}{6}$ and $\frac{10}{6}$
Hence, the correct option is C. ($\frac{5}{6},\frac{7}{6}$)