question_answer

Find five rational number between.

(a)\[\frac{2}{3}\,\,and\,\,\frac{4}{5}~\]

(b)\[\frac{-3}{2}\,\,and\,\,\frac{5}{3}~\]

(c) \[\frac{1}{4}\,\,and\,\,\frac{1}{2}~\]

Answer:

(a)\[\frac{2}{3}\] and\[\frac{4}{5}\]

LCM of 3 and 5 is 15

\[\therefore \]    \[\frac{2}{3}\times \frac{5}{5}=\frac{10}{15}\]and \[\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}\]

Again,  \[\frac{10}{15}\times \frac{4}{4}=\frac{40}{60}\] and \[\frac{12}{15}\times \frac{4}{4}=\frac{48}{60}\]

\[\therefore \] Five rational numbers between \[\frac{2}{3}\]and \[\frac{4}{5}\]are

\[\frac{41}{60},\frac{42}{60},\frac{43}{60},\frac{44}{60},\frac{45}{60}.\]

(b) \[\frac{-3}{2}\] and \[\frac{5}{3}\]

LCM of 2 and 3 is 6

\[\therefore \]    \[\frac{-3}{2}\times \frac{3}{3}=\frac{-9}{6}\]and \[\frac{5}{3}\times \frac{2}{2}=\frac{10}{6}\]

\[\therefore \] Five rational number between \[\frac{-3}{2}\]and \[\frac{5}{3}\]are

\[\frac{-8}{6},\frac{-7}{6},0,\frac{1}{6},\frac{2}{6}.\]

(c) \[\frac{1}{4}\]and\[\frac{1}{2}\] LCM of 4 and 2 is 4

\[\frac{1}{4}\times \frac{1}{1}=\frac{1}{4}\,\,\]and \[\frac{1}{2}\times \frac{2}{2}=\frac{2}{4}\]

Again, \[\frac{1}{4}\times \frac{8}{8}=\frac{8}{32}\]and \[\frac{2}{4}\times \frac{8}{8}=\frac{16}{32}\]

\[\therefore \] Five rational numbers between \[\frac{1}{4}\]and \[\frac{1}{2}\]are

\[\frac{9}{32},\frac{10}{32},\frac{11}{32},\frac{12}{32},\frac{13}{32}.\]