# 5. Find five rational numbers between.(i)  $\frac{2}{3}$  and  $\frac{4}{5}$              (ii)  $\frac{-3}{2}$ and  $\frac{5}{3}$             (iii)  $\frac{1}{4}$ and  $\frac{1}{2}$

(i)     For finding rational numbers between 2 numbers one method is to find means between the numbers repeatedly.

Another method is:- For    $\frac{2}{3}$  and  $\frac{4}{5}$

$\frac{2}{3}$  can be written as  $\frac{10}{15}$                            $\left ( \frac{2}{3}\times \frac{5}{5} = \frac{10}{15}\right )$

and  $\frac{4}{5}$ can be written as  $\frac{12}{15}$                              $\left ( \frac{4}{5}\times \frac{3}{3} = \frac{12}{15}\right )$

Thus numbers between $\frac{10}{15}$ and $\frac{12}{15}$ are the required numbers.

Now since we require 5 numbers in between, thus we multiply numerator and denomenator both by 4.

It becomes numbers between $\frac{40}{60}$ and $\frac{48}{60}$.

Thus numbers are $\frac{41}{60}, \frac{42}{60}, \frac{43}{60}, \frac{44}{60}, \frac{45}{60}$.

(ii)      Similarly for $\frac{-3}{2}$and $\frac{5}{3}$

Required numbers fall between $\frac{-9}{6}$ and $\frac{10}{6}$                 $\left \{ \left ( \frac{-3}{2}\times \frac{3}{3} \right )= \frac{-9}{6} \right \}$

Thus numbers are $\frac{-8}{6}, \frac{-7}{6}, \frac{-6}{6}, \frac{-5}{6}, \frac{-4}{6}$

(iii)      For   $\frac{1}{4}$  and  $\frac{1}{2}$

Required numbers lie between $\frac{1}{4}$ and $\frac{2}{4}$   or we can say between $\frac{8}{32}$ and $\frac{16}{32}$

Thus numbers are $\frac{9}{32}, \frac{10}{32}, \frac{11}{32}, \frac{12}{32}, \frac{13}{32}$

Exams
Articles
Questions