question_answer

Find ten rational numbers between \[\frac{3}{5}\] and \[\frac{3}{4}\].

Answer:

LCM of 5 and 4 is 20

\[\therefore \] \[\frac{3}{5}\times \frac{4}{4}=\frac{12}{20}\,\,and\,\,\frac{3}{4}\times \frac{5}{5}=\frac{15}{20}\]

Again,       \[\frac{12}{20}\times \frac{8}{8}=\frac{96}{160}\,\,and\,\frac{15}{20}\times \frac{8}{8}=\frac{120}{160}\]

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

\[\frac{97}{160},\frac{98}{160},\frac{99}{160},\frac{100}{160},\frac{101}{160},\frac{102}{160},\frac{103}{160},\frac{104}{160},\frac{105}{160},\frac{106}{160}.\]