question_answer 18)

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

Answer:

                \[\frac{3}{5}=\frac{3\times 4}{5\times 4}\,=\frac{12}{20}\]                 \[\frac{3}{4}=\frac{3\times 5}{4\times 5}\,=\frac{15}{20}\]                           | Converting them into rational numbers with the same denominators.                 Now, \[\frac{12}{20}=\frac{12\times 8}{20\times 8}\,=\frac{96}{160}\]   | Multiplying the numerator and denominator both by 8 \[\frac{15}{20}=\frac{15\times 8}{20\times 8}\,=\frac{120}{160}\]                             | Multiplying the numerator and denominator both by 8 Thus, ten rational numbers between  \[\frac{3}{5}\] and \[\frac{3}{4}\] may be taken as: \[\frac{97}{160},\,\frac{98}{160},\,\frac{99}{160},\,\frac{100}{160},\,\frac{101}{160},\] \[\frac{102}{160},\,\frac{103}{160},\,\frac{104}{160},\,\frac{105}{160},\,\frac{106}{160}\].